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Swiss Post E-Voting Go PoC
Proof-of-concept reimplementation of the Swiss Post e-voting cryptographic protocol in Go. Single binary, 52 source files, 2 dependencies. Covers ElGamal encryption, Bayer-Groth verifiable shuffles, zero-knowledge proofs, return codes, and a full election ceremony demo.
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9
.gitignore
vendored
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9
.gitignore
vendored
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# Compiled binary (root only, not cmd/evote/)
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/evote
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*.exe
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# Test artifacts
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testdata/*.json
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# macOS
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.DS_Store
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24
cmd/evote/demo.go
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24
cmd/evote/demo.go
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package main
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import (
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"github.com/spf13/cobra"
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"github.com/user/evote/pkg/protocol"
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)
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var demoVoters int
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var demoOptions int
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var demoCmd = &cobra.Command{
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Use: "demo",
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Short: "Run a full election ceremony end-to-end",
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Long: "Runs setup → vote → tally → verify in one command.",
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Run: func(cmd *cobra.Command, args []string) {
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protocol.RunDemoElection(demoVoters, demoOptions)
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},
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}
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func init() {
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demoCmd.Flags().IntVar(&demoVoters, "voters", 10, "Number of voters")
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demoCmd.Flags().IntVar(&demoOptions, "options", 2, "Number of voting options")
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rootCmd.AddCommand(demoCmd)
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}
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21
cmd/evote/main.go
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21
cmd/evote/main.go
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package main
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import (
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"fmt"
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"os"
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"github.com/spf13/cobra"
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)
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var rootCmd = &cobra.Command{
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Use: "evote",
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Short: "Swiss Post E-Voting Protocol PoC",
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Long: "A proof-of-concept reimplementation of the Swiss Post e-voting cryptographic protocol in Go.",
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}
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func main() {
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if err := rootCmd.Execute(); err != nil {
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fmt.Fprintln(os.Stderr, err)
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os.Exit(1)
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}
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}
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772
cmd/evote/presentation.go
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772
cmd/evote/presentation.go
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package main
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import (
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"fmt"
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"math/big"
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"strings"
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"time"
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"github.com/spf13/cobra"
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"github.com/user/evote/pkg/elgamal"
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"github.com/user/evote/pkg/hash"
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"github.com/user/evote/pkg/mixnet"
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"github.com/user/evote/pkg/returncodes"
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"github.com/user/evote/pkg/zkp"
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emath "github.com/user/evote/pkg/math"
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"github.com/user/evote/pkg/protocol"
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)
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var presentCmd = &cobra.Command{
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Use: "present",
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Short: "Theatrical step-by-step election presentation",
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Run: runPresentation,
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}
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func init() {
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rootCmd.AddCommand(presentCmd)
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}
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func banner(text string) {
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width := 72
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line := strings.Repeat("=", width)
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pad := (width - len(text) - 2) / 2
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if pad < 0 {
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pad = 0
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}
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fmt.Println()
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fmt.Println(line)
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fmt.Printf("%s %s %s\n", strings.Repeat(" ", pad), text, strings.Repeat(" ", pad))
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fmt.Println(line)
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}
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func section(text string) {
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fmt.Printf("\n --- %s ---\n\n", text)
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}
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func truncBig(b *big.Int, chars int) string {
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s := b.String()
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if len(s) <= chars {
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return s
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}
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half := (chars - 3) / 2
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return s[:half] + "..." + s[len(s)-half:]
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}
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func truncHex(b *big.Int, chars int) string {
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s := fmt.Sprintf("%X", b)
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if len(s) <= chars {
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return s
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}
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half := (chars - 3) / 2
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return s[:half] + "..." + s[len(s)-half:]
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}
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func narrator(text string) {
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fmt.Printf(" %s\n", text)
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}
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func showValue(label string, val string) {
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fmt.Printf(" %-26s %s\n", label+":", val)
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}
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func showSecret(label string, val string) {
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fmt.Printf(" %-26s %s [SECRET]\n", label+":", val)
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}
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func showPublic(label string, val string) {
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fmt.Printf(" %-26s %s [PUBLIC]\n", label+":", val)
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}
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func runPresentation(cmd *cobra.Command, args []string) {
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numVoters := 6
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numOptions := 3
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// =====================================================================
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// TITLE
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// =====================================================================
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fmt.Println()
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fmt.Println(" +================================================================+")
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fmt.Println(" | |")
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fmt.Println(" | SWISS POST E-VOTING: A CRYPTOGRAPHIC ELECTION |")
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fmt.Println(" | |")
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fmt.Println(" | Live demonstration of a verifiable electronic vote |")
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fmt.Println(" | |")
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fmt.Println(" +================================================================+")
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fmt.Println()
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narrator("Today we are holding an election.")
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narrator(fmt.Sprintf("%d citizens will choose between %d candidates.", numVoters, numOptions))
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narrator("Their votes will be encrypted, shuffled, and counted.")
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narrator("Nobody will know who voted for whom.")
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narrator("But EVERYONE can verify the result is correct.")
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fmt.Println()
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narrator("You will experience this election from three perspectives:")
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fmt.Println()
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narrator(" [1] As a CONTROL COMPONENT operator -- you hold part of the master key")
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narrator(" [2] As a VOTER -- you cast your secret ballot")
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narrator(" [3] As a PUBLIC AUDITOR -- you verify nothing was rigged")
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fmt.Println()
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// =====================================================================
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// ACT 1: SETUP (do it silently, then show internals)
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// =====================================================================
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banner("ACT 1: THE SETUP")
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fmt.Println()
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narrator("Before any vote is cast, we need to build the infrastructure.")
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narrator("Think of it like constructing a ballot box that requires 5 different")
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narrator("keys to open. No single person holds all the keys.")
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// Run setup
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cfg := protocol.DefaultConfig(numVoters, numOptions)
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group := cfg.Group
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zqGroup := emath.ZqGroupFromGqGroup(group)
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section("Step 1.1: The Mathematical Universe")
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narrator("All the cryptography runs inside a mathematical structure called")
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narrator("a \"safe prime group.\" These are the agreed-upon rules of the game:")
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fmt.Println()
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showPublic("Prime p (257 bits)", truncBig(group.P(), 60))
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showPublic("Safe prime q (256 bits)", truncBig(group.Q(), 60))
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showPublic("Generator g", group.Generator().Value().String())
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fmt.Println()
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narrator("These numbers are PUBLIC. Everyone agrees on them before the election starts.")
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fmt.Println()
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// Run full setup
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event := protocol.Setup(cfg)
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section("Step 1.2: The Control Components Generate Their Keys")
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fmt.Println()
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fmt.Println(" +----------------------------------------------------------------+")
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fmt.Println(" | YOU ARE NOW: Control Component Operator (CC0) |")
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fmt.Println(" | Location: Secure data center, Bern, Switzerland |")
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fmt.Println(" +----------------------------------------------------------------+")
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fmt.Println()
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narrator("You are one of 4 independent operators. You don't know each other.")
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narrator("You're in a locked room with an air-gapped computer.")
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narrator("Your job: generate a secret key and share ONLY the public part.")
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fmt.Println()
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ccNames := []string{"CC0 (Bern)", "CC1 (Zurich)", "CC2 (Geneva)", "CC3 (Lugano)"}
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cc0 := event.CCs[0]
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narrator("Your computer generates a random secret key:")
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fmt.Println()
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for i := 0; i < cfg.NumOptions; i++ {
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showSecret(fmt.Sprintf("Secret key [%d]", i), truncBig(cc0.ElectionKeyPair.SK.Get(i).Value(), 50))
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}
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fmt.Println()
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narrator("From the secret, your computer derives the public key: PK = g ^ SK mod p")
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fmt.Println()
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for i := 0; i < cfg.NumOptions; i++ {
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showPublic(fmt.Sprintf("Public key [%d]", i), truncBig(cc0.ElectionKeyPair.PK.Get(i).Value(), 50))
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}
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fmt.Println()
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narrator("You also generate a SCHNORR PROOF for each key component.")
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narrator("This proves you know the secret behind the public key, WITHOUT revealing it.")
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narrator("That's a zero-knowledge proof -- the verifier learns NOTHING except \"they know it.\"")
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fmt.Println()
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for i := 0; i < cfg.NumOptions; i++ {
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showPublic(fmt.Sprintf("Schnorr proof [%d].e", i), truncBig(cc0.SchnorrProofs[i].E.Value(), 40))
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showPublic(fmt.Sprintf("Schnorr proof [%d].z", i), truncBig(cc0.SchnorrProofs[i].Z.Value(), 40))
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}
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fmt.Println()
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narrator("Meanwhile, the other 3 operators do the same thing independently:")
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fmt.Println()
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for j := 1; j < cfg.NumCCs; j++ {
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showPublic(fmt.Sprintf("%s PK[0]", ccNames[j]), truncBig(event.CCs[j].ElectionKeyPair.PK.Get(0).Value(), 44))
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}
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fmt.Println()
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section("Step 1.3: Combining Keys Into the Election Key")
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narrator("Now the magic: all 5 public keys (4 CCs + Electoral Board) are")
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narrator("MULTIPLIED together into a single Election Public Key.")
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fmt.Println()
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narrator("Encrypting with this key means you need ALL 5 secrets to decrypt.")
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narrator("If even ONE operator is honest, the others cannot cheat.")
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fmt.Println()
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fmt.Println(" CC0 PK x CC1 PK x CC2 PK x CC3 PK x EB PK")
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fmt.Println(" |")
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fmt.Println(" V")
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showPublic("Election Public Key [0]", truncBig(event.ElectionPK.Get(0).Value(), 50))
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fmt.Println()
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section("Step 1.4: Encoding Candidates as Prime Numbers")
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narrator("Each candidate gets a unique small prime number.")
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narrator("A vote is encoded as g^(prime) -- a group element.")
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fmt.Println()
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candidateNames := []string{"Alice", "Bob", "Carol"}
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for i := 0; i < numOptions; i++ {
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raw := emath.SmallPrimes(numOptions)[i]
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showPublic(fmt.Sprintf("Candidate %d (%s)", i, candidateNames[i]), fmt.Sprintf("prime %d -> squared prime %s", raw, truncBig(event.Primes[i], 20)))
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}
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fmt.Println()
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narrator("Why squared primes? The raw primes must be in the mathematical group.")
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narrator("Squaring guarantees they are quadratic residues (valid group elements).")
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fmt.Println()
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section("Step 1.5: Mailing the Voting Cards")
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narrator("Each voter receives a physical card in the mail:")
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fmt.Println()
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vc0 := event.VotingCards[0]
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fmt.Println(" +------------------------------------------------------+")
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fmt.Println(" | SWISS CONFEDERATION |")
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fmt.Println(" | Electronic Voting Card |")
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fmt.Println(" | |")
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fmt.Printf(" | Voter ID: %-32s |\n", vc0.VoterID)
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fmt.Printf(" | Start Voting Key: %-32s |\n", vc0.StartVotingKey)
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fmt.Printf(" | Ballot Casting Key: %-32s |\n", vc0.BallotCastingKey)
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fmt.Println(" | |")
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fmt.Println(" | Choice Return Codes (to verify your vote): |")
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for i, code := range vc0.ChoiceReturnCodes {
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fmt.Printf(" | Candidate %d (%s): %-32s |\n", i, candidateNames[i], code)
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}
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fmt.Println(" | |")
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fmt.Printf(" | Vote Cast Code: %-32s |\n", vc0.VoteConfirmCode)
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fmt.Println(" | |")
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fmt.Println(" | KEEP THIS CARD SAFE. DO NOT SHARE IT. |")
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fmt.Println(" +------------------------------------------------------+")
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fmt.Println()
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narrator("The Start Voting Key (SVK) = your username.")
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narrator("The Ballot Casting Key (BCK) = your confirmation PIN.")
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narrator("The Choice Return Codes = prove the server recorded YOUR choice, not something else.")
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narrator("The Vote Cast Code = proves your vote was finalized.")
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fmt.Println()
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// =====================================================================
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// ACT 2: VOTING
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// =====================================================================
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banner("ACT 2: THE VOTE")
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fmt.Println()
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fmt.Println(" +----------------------------------------------------------------+")
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fmt.Println(" | YOU ARE NOW: A Citizen (Voter 2) |")
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fmt.Println(" | Location: Your kitchen table, laptop open, voting card in hand |")
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fmt.Println(" +----------------------------------------------------------------+")
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fmt.Println()
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narrator("You open the voting website. You enter your Start Voting Key and")
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narrator("date of birth. The system authenticates you.")
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fmt.Println()
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narrator("On screen you see three candidates:")
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fmt.Println()
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narrator(" [ ] Alice [ ] Bob [ ] Carol")
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fmt.Println()
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narrator("You choose: BOB.")
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fmt.Println()
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narrator(" [ ] Alice [X] Bob [ ] Carol")
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fmt.Println()
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section("Step 2.1: Your Browser Encrypts Your Vote (JavaScript)")
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narrator("This happens INSIDE your web browser. The voting server")
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narrator("never sees your plaintext vote. Let's look under the hood:")
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fmt.Println()
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selectedOption := 1 // Bob
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voteProduct := event.Primes[selectedOption]
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g := group.Generator()
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voteElem, _ := emath.NewZqElement(voteProduct, zqGroup)
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narrator(fmt.Sprintf("Your choice: %s (prime = %s)", candidateNames[selectedOption], truncBig(voteProduct, 20)))
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fmt.Println()
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narrator("Step 1 -- Encode the vote as a group element:")
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msgGq := g.Exponentiate(voteElem)
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showValue("Plaintext", fmt.Sprintf("g^%s = %s", truncBig(voteProduct, 10), truncBig(msgGq.Value(), 40)))
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fmt.Println()
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narrator("Step 2 -- Generate a random number (used once, then discarded):")
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r := emath.RandomZqElement(zqGroup)
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showSecret("Ephemeral r", truncBig(r.Value(), 50))
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fmt.Println()
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narrator("Step 3 -- ElGamal encryption:")
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narrator(" gamma = g^r (random mask)")
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narrator(" phi = PK^r * msg (encrypted payload)")
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fmt.Println()
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l := cfg.NumOptions
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msgElems := make([]emath.GqElement, l)
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for i := 0; i < l; i++ {
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if i == 0 {
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msgElems[i] = msgGq
|
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} else {
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one, _ := emath.NewZqElement(big.NewInt(1), zqGroup)
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msgElems[i] = g.Exponentiate(one)
|
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}
|
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}
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msg := elgamal.NewMessage(emath.GqVectorOf(msgElems...))
|
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ct := elgamal.Encrypt(msg, r, event.ElectionPK)
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|
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showPublic("Encrypted gamma", truncBig(ct.Gamma.Value(), 50))
|
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for i := 0; i < ct.Size(); i++ {
|
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showPublic(fmt.Sprintf("Encrypted phi[%d]", i), truncBig(ct.GetPhi(i).Value(), 50))
|
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}
|
||||
fmt.Println()
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narrator("Look at those numbers. Pure noise. Even if a hacker breaks into")
|
||||
narrator("the voting server, they see only random-looking numbers.")
|
||||
narrator("You need ALL 5 secret keys to decrypt. Your vote is safe.")
|
||||
fmt.Println()
|
||||
|
||||
section("Step 2.2: Zero-Knowledge Proofs (\"I voted correctly\")")
|
||||
|
||||
narrator("Your browser also generates mathematical proofs that:")
|
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narrator(" (a) The ciphertext actually contains a valid vote (not garbage)")
|
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narrator(" (b) It's an encryption of one of the allowed candidates")
|
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fmt.Println()
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||||
narrator("These proofs reveal NOTHING about which candidate you chose.")
|
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narrator("They only prove the vote is well-formed. Think of it as:")
|
||||
narrator(" \"I put a valid ballot in the envelope, but you can't see which one.\"")
|
||||
fmt.Println()
|
||||
|
||||
expProof := zkp.GenExponentiationProof(
|
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emath.GqVectorOf(g),
|
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voteElem,
|
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emath.GqVectorOf(msgGq),
|
||||
group,
|
||||
)
|
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showPublic("Exponentiation proof .e", truncBig(expProof.E.Value(), 40))
|
||||
showPublic("Exponentiation proof .z", truncBig(expProof.Z.Value(), 40))
|
||||
fmt.Println()
|
||||
|
||||
section("Step 2.3: Return Codes (\"My vote was recorded correctly\")")
|
||||
|
||||
narrator("After your encrypted vote arrives, each Control Component computes")
|
||||
narrator("a partial return code -- WITHOUT decrypting your vote!")
|
||||
narrator("They use the mathematical properties of ElGamal (homomorphic encryption).")
|
||||
fmt.Println()
|
||||
narrator("The server combines all partial codes and sends back:")
|
||||
fmt.Println()
|
||||
vc2 := event.VotingCards[2]
|
||||
fmt.Println(" +------------------------------------------+")
|
||||
fmt.Println(" | Your choice was recorded. |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Printf(" | Choice Return Code: %-20s |\n", vc2.ChoiceReturnCodes[selectedOption])
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | Compare with your voting card. |")
|
||||
fmt.Println(" +------------------------------------------+")
|
||||
fmt.Println()
|
||||
narrator("You check your physical card. The code for Bob matches!")
|
||||
narrator("This confirms: the server recorded YOUR actual choice, not something else.")
|
||||
narrator("Even if your computer had malware, the return code would be WRONG")
|
||||
narrator("if the vote was changed -- because the code depends on YOUR specific choice.")
|
||||
fmt.Println()
|
||||
|
||||
section("Step 2.4: All 6 Citizens Vote")
|
||||
|
||||
narrator("Now all 6 citizens cast their ballots. Here's what really happened:")
|
||||
fmt.Println()
|
||||
|
||||
votes := []int{0, 2, 1, 0, 1, 2} // Alice, Carol, Bob, Alice, Bob, Carol
|
||||
for i, opt := range votes {
|
||||
protocol.CastVote(event, i, []int{opt})
|
||||
}
|
||||
|
||||
fmt.Println(" +----------+------------------+------------------------------------+")
|
||||
fmt.Println(" | Voter | Actual Vote | What the server sees |")
|
||||
fmt.Println(" +----------+------------------+------------------------------------+")
|
||||
for i, opt := range votes {
|
||||
gamma := event.BallotBox.Votes[i].Ciphertext.Gamma.Value()
|
||||
fmt.Printf(" | Voter %d | %-14s | %s |\n", i, candidateNames[opt], truncHex(gamma, 34))
|
||||
}
|
||||
fmt.Println(" +----------+------------------+------------------------------------+")
|
||||
fmt.Println()
|
||||
narrator("The left column is the TRUTH (known only to each voter).")
|
||||
narrator("The right column is ALL the server has: meaningless hex noise.")
|
||||
fmt.Println()
|
||||
|
||||
// =====================================================================
|
||||
// ACT 3: TALLY
|
||||
// =====================================================================
|
||||
banner("ACT 3: THE TALLY -- The Verifiable Shuffle")
|
||||
fmt.Println()
|
||||
fmt.Println(" +----------------------------------------------------------------+")
|
||||
fmt.Println(" | YOU ARE NOW: Control Component Operator (CC0) again |")
|
||||
fmt.Println(" | Location: Back in the secure data center, Bern |")
|
||||
fmt.Println(" | Mission: Shuffle the votes so nobody can trace them |")
|
||||
fmt.Println(" +----------------------------------------------------------------+")
|
||||
fmt.Println()
|
||||
narrator("The voting period is over. Time to count.")
|
||||
fmt.Println()
|
||||
narrator("But we CAN'T just decrypt in order -- that reveals who voted for whom.")
|
||||
narrator("Instead, each of the 5 key holders takes a turn:")
|
||||
fmt.Println()
|
||||
narrator(" 1. SHUFFLE -- randomly reorder all encrypted ballots")
|
||||
narrator(" 2. RE-ENCRYPT -- add fresh randomness (so shuffled ballots look different)")
|
||||
narrator(" 3. PARTIALLY DECRYPT -- peel off their key layer")
|
||||
narrator(" 4. PROVE -- generate a Bayer-Groth zero-knowledge proof")
|
||||
narrator(" that the shuffle was honest")
|
||||
fmt.Println()
|
||||
narrator("After 5 rounds, votes are decrypted but disconnected from voters.")
|
||||
fmt.Println()
|
||||
|
||||
// Get initial ciphertexts
|
||||
ballotCts := event.BallotBox.GetCiphertexts()
|
||||
N := ballotCts.Size()
|
||||
if N < 2 {
|
||||
for N < 2 {
|
||||
rr := emath.RandomZqElement(zqGroup)
|
||||
trivial := elgamal.EncryptOnes(rr, event.ElectionPK)
|
||||
ballotCts = ballotCts.Append(trivial)
|
||||
N++
|
||||
}
|
||||
}
|
||||
currentCts := ballotCts
|
||||
event.ShuffleResults = make([]mixnet.VerifiableShuffle, 0)
|
||||
event.PartiallyDecrypted = make([]*elgamal.CiphertextVector, 0)
|
||||
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
cc := event.CCs[j]
|
||||
|
||||
if j == 0 {
|
||||
section(fmt.Sprintf("Step 3.%d: YOUR Turn -- %s Shuffles", j+1, ccNames[j]))
|
||||
narrator("This is YOUR turn. Let's watch every step.")
|
||||
} else {
|
||||
section(fmt.Sprintf("Step 3.%d: %s Shuffles", j+1, ccNames[j]))
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
narrator("Input ciphertexts (what you receive):")
|
||||
fmt.Println()
|
||||
for i := 0; i < currentCts.Size(); i++ {
|
||||
fmt.Printf(" [%d] %s\n", i, truncHex(currentCts.Get(i).Gamma.Value(), 40))
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
// Build remaining PK
|
||||
remainingPKs := make([]elgamal.PublicKey, 0)
|
||||
for k := j; k < cfg.NumCCs; k++ {
|
||||
remainingPKs = append(remainingPKs, event.CCs[k].ElectionKeyPair.PK)
|
||||
}
|
||||
remainingPKs = append(remainingPKs, event.EB.PK)
|
||||
remainingPK := elgamal.CombinePublicKeys(remainingPKs...)
|
||||
|
||||
// Shuffle
|
||||
start := time.Now()
|
||||
vs := mixnet.GenVerifiableShuffle(currentCts, remainingPK, group)
|
||||
shuffleTime := time.Since(start)
|
||||
event.ShuffleResults = append(event.ShuffleResults, vs)
|
||||
|
||||
if j == 0 {
|
||||
narrator("Your computer generates a SECRET permutation and re-encrypts.")
|
||||
narrator("The permutation is DESTROYED after use. Even you can't recover it.")
|
||||
fmt.Println()
|
||||
}
|
||||
|
||||
narrator("Output ciphertexts (after shuffle + re-encryption):")
|
||||
fmt.Println()
|
||||
for i := 0; i < vs.ShuffledCiphertexts.Size(); i++ {
|
||||
fmt.Printf(" [%d] %s\n", i, truncHex(vs.ShuffledCiphertexts.Get(i).Gamma.Value(), 40))
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
if j == 0 {
|
||||
narrator("NOTICE: The values are COMPLETELY DIFFERENT. Not just reordered --")
|
||||
narrator("re-encrypted with fresh randomness. You cannot tell which input")
|
||||
narrator("became which output by looking at the numbers.")
|
||||
fmt.Println()
|
||||
m, n := mixnet.GetMatrixDimensions(N)
|
||||
narrator(fmt.Sprintf("Along with the shuffle, a PROOF was generated (%v):", shuffleTime.Round(time.Millisecond)))
|
||||
narrator(fmt.Sprintf(" Bayer-Groth ShuffleArgument for %d ciphertexts (%dx%d matrix):", N, m, n))
|
||||
fmt.Println()
|
||||
fmt.Println(" ShuffleArgument")
|
||||
fmt.Println(" +-- ProductArgument")
|
||||
if m > 1 {
|
||||
fmt.Println(" | +-- HadamardArgument")
|
||||
fmt.Println(" | | +-- ZeroArgument (proves star-map relation = 0)")
|
||||
fmt.Println(" | +-- SingleValueProductArgument (proves product constraint)")
|
||||
} else {
|
||||
fmt.Println(" | +-- SingleValueProductArgument (proves product constraint)")
|
||||
}
|
||||
fmt.Println(" +-- MultiExponentiationArgument (proves ciphertext relation)")
|
||||
fmt.Println()
|
||||
narrator("This proof is ~800 bytes of math. It guarantees the shuffle is honest.")
|
||||
narrator("Anyone can verify it. No secrets needed.")
|
||||
fmt.Println()
|
||||
} else {
|
||||
narrator(fmt.Sprintf(" Shuffle + proof generated in %v", shuffleTime.Round(time.Millisecond)))
|
||||
fmt.Println()
|
||||
}
|
||||
|
||||
// Partial decrypt
|
||||
decrypted := make([]elgamal.Ciphertext, vs.ShuffledCiphertexts.Size())
|
||||
for i := 0; i < vs.ShuffledCiphertexts.Size(); i++ {
|
||||
decrypted[i] = elgamal.PartialDecrypt(vs.ShuffledCiphertexts.Get(i), cc.ElectionKeyPair.SK)
|
||||
}
|
||||
currentCts = elgamal.NewCiphertextVector(decrypted)
|
||||
event.PartiallyDecrypted = append(event.PartiallyDecrypted, currentCts)
|
||||
|
||||
remaining := cfg.NumCCs - j - 1 + 1
|
||||
narrator(fmt.Sprintf(" Partial decryption done. %d encryption layer(s) remaining.", remaining))
|
||||
fmt.Println()
|
||||
}
|
||||
|
||||
// EB final
|
||||
section("Step 3.5: Electoral Board -- Final Shuffle + Full Decryption")
|
||||
narrator("The Electoral Board performs the final shuffle on an AIR-GAPPED")
|
||||
narrator("computer (no network). Then they remove the last encryption layer.")
|
||||
fmt.Println()
|
||||
|
||||
start := time.Now()
|
||||
vs := mixnet.GenVerifiableShuffle(currentCts, event.EB.PK, group)
|
||||
ebTime := time.Since(start)
|
||||
event.ShuffleResults = append(event.ShuffleResults, vs)
|
||||
narrator(fmt.Sprintf(" Final shuffle + proof generated in %v", ebTime.Round(time.Millisecond)))
|
||||
fmt.Println()
|
||||
|
||||
event.DecryptedVotes = make([]*emath.GqVector, vs.ShuffledCiphertexts.Size())
|
||||
for i := 0; i < vs.ShuffledCiphertexts.Size(); i++ {
|
||||
ct := vs.ShuffledCiphertexts.Get(i)
|
||||
dmsg := elgamal.Decrypt(ct, event.EB.SK)
|
||||
event.DecryptedVotes[i] = dmsg.Elements
|
||||
}
|
||||
|
||||
narrator("The envelope is open. The plaintext votes emerge:")
|
||||
fmt.Println()
|
||||
fmt.Println(" +--------+-------------------------------+-----------------+")
|
||||
fmt.Println(" | Slot | Decrypted Group Element | Decoded Vote |")
|
||||
fmt.Println(" +--------+-------------------------------+-----------------+")
|
||||
for i := 0; i < len(event.DecryptedVotes); i++ {
|
||||
val := event.DecryptedVotes[i].Get(0).Value()
|
||||
decoded := returncodes.DecodeVote(val, event.Primes)
|
||||
voteStr := "(padding)"
|
||||
if len(decoded) > 0 {
|
||||
voteStr = candidateNames[decoded[0]]
|
||||
}
|
||||
fmt.Printf(" | %d | %s | %-13s |\n", i, truncBig(val, 27), voteStr)
|
||||
}
|
||||
fmt.Println(" +--------+-------------------------------+-----------------+")
|
||||
fmt.Println()
|
||||
narrator("The votes are readable -- but in a RANDOM, IRREVERSIBLE order.")
|
||||
narrator("We can count them. We cannot trace them back to any voter.")
|
||||
fmt.Println()
|
||||
|
||||
// Count
|
||||
for i := 0; i < len(event.DecryptedVotes); i++ {
|
||||
val := event.DecryptedVotes[i].Get(0).Value()
|
||||
if event.DecryptedVotes[i].Get(0).IsIdentity() {
|
||||
continue
|
||||
}
|
||||
decoded := returncodes.DecodeVote(val, event.Primes)
|
||||
for _, opt := range decoded {
|
||||
event.FinalResult[opt]++
|
||||
}
|
||||
}
|
||||
|
||||
fmt.Println(" +==========================================+")
|
||||
fmt.Println(" | ELECTION RESULT |")
|
||||
fmt.Println(" +==========================================+")
|
||||
for opt := 0; opt < numOptions; opt++ {
|
||||
count := event.FinalResult[opt]
|
||||
bar := strings.Repeat("#", count*5)
|
||||
fmt.Printf(" | %-8s %d votes %-20s |\n", candidateNames[opt], count, bar)
|
||||
}
|
||||
fmt.Println(" +==========================================+")
|
||||
fmt.Println()
|
||||
|
||||
// Quick sanity: show the real votes matched
|
||||
realCounts := make(map[int]int)
|
||||
for _, v := range votes {
|
||||
realCounts[v]++
|
||||
}
|
||||
narrator("Sanity check (we know the real votes because this is a demo):")
|
||||
for opt := 0; opt < numOptions; opt++ {
|
||||
match := "MATCH"
|
||||
if event.FinalResult[opt] != realCounts[opt] {
|
||||
match = "MISMATCH!"
|
||||
}
|
||||
narrator(fmt.Sprintf(" %s: counted=%d, actual=%d -> %s", candidateNames[opt], event.FinalResult[opt], realCounts[opt], match))
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
// =====================================================================
|
||||
// ACT 4: VERIFICATION
|
||||
// =====================================================================
|
||||
banner("ACT 4: THE AUDIT -- Anyone Can Verify")
|
||||
fmt.Println()
|
||||
fmt.Println(" +----------------------------------------------------------------+")
|
||||
fmt.Println(" | YOU ARE NOW: A Public Auditor |")
|
||||
fmt.Println(" | Location: Anywhere. Your laptop. A coffee shop. |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | You have: The public election data (encrypted ballots, |")
|
||||
fmt.Println(" | shuffled ballots, proofs, commitments) |")
|
||||
fmt.Println(" | You DON'T have: Any secret keys |")
|
||||
fmt.Println(" +----------------------------------------------------------------+")
|
||||
fmt.Println()
|
||||
narrator("This is the moment of truth.")
|
||||
fmt.Println()
|
||||
narrator("You don't trust the government. You don't trust the operators.")
|
||||
narrator("You don't trust the software vendor. You don't trust ANYONE.")
|
||||
narrator("And you don't have to.")
|
||||
fmt.Println()
|
||||
narrator("The mathematics lets you verify the entire election yourself.")
|
||||
fmt.Println()
|
||||
|
||||
section("Step 4.1: Verify Each Operator's Key Proof")
|
||||
|
||||
narrator("First: did each CC actually generate a real key?")
|
||||
narrator("The Schnorr proofs let you check without seeing the secrets.")
|
||||
fmt.Println()
|
||||
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
cc := event.CCs[j]
|
||||
allOk := true
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
auxInfo := []hash.Hashable{
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(i))},
|
||||
hash.HashableString{Value: cfg.ElectionID},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(j))},
|
||||
}
|
||||
ok := zkp.VerifySchnorrProof(cc.SchnorrProofs[i], cc.ElectionKeyPair.PK.Get(i), group, auxInfo...)
|
||||
if !ok {
|
||||
allOk = false
|
||||
}
|
||||
}
|
||||
status := "PASS -- they proved they know their secret"
|
||||
if !allOk {
|
||||
status = "FAIL!"
|
||||
}
|
||||
fmt.Printf(" [%s] %s\n", status[:4], ccNames[j])
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
section("Step 4.2: Verify the 5 Shuffle Proofs")
|
||||
|
||||
narrator("This is the HEART of the verification. The hardest math in the system.")
|
||||
fmt.Println()
|
||||
narrator("For each of the 5 shuffles, you verify that the output contains")
|
||||
narrator("the SAME votes as the input, just in a different order.")
|
||||
fmt.Println()
|
||||
narrator("You don't know the permutation. You can't see which vote went where.")
|
||||
narrator("But the Bayer-Groth proof MATHEMATICALLY GUARANTEES correctness.")
|
||||
fmt.Println()
|
||||
narrator("Each proof contains nested sub-proofs:")
|
||||
narrator(" - ProductArgument: proves the permutation matrix is valid")
|
||||
narrator(" - HadamardArgument: proves element-wise product relationship")
|
||||
narrator(" - ZeroArgument: proves a bilinear identity equals zero")
|
||||
narrator(" - SingleValueProductArgument: proves a scalar product constraint")
|
||||
narrator(" - MultiExponentiationArgument: proves the ciphertext transformation")
|
||||
fmt.Println()
|
||||
narrator("Verifying now...")
|
||||
fmt.Println()
|
||||
|
||||
verifyBallotCts := event.BallotBox.GetCiphertexts()
|
||||
vN := verifyBallotCts.Size()
|
||||
if vN < 2 {
|
||||
for vN < 2 {
|
||||
rr := emath.RandomZqElement(zqGroup)
|
||||
trivial := elgamal.EncryptOnes(rr, event.ElectionPK)
|
||||
verifyBallotCts = verifyBallotCts.Append(trivial)
|
||||
vN++
|
||||
}
|
||||
}
|
||||
|
||||
allValid := true
|
||||
for j, vsShuffle := range event.ShuffleResults {
|
||||
var pk elgamal.PublicKey
|
||||
var name string
|
||||
if j < cfg.NumCCs {
|
||||
remainingPKs := make([]elgamal.PublicKey, 0)
|
||||
for k := j; k < cfg.NumCCs; k++ {
|
||||
remainingPKs = append(remainingPKs, event.CCs[k].ElectionKeyPair.PK)
|
||||
}
|
||||
remainingPKs = append(remainingPKs, event.EB.PK)
|
||||
pk = elgamal.CombinePublicKeys(remainingPKs...)
|
||||
name = ccNames[j]
|
||||
} else {
|
||||
pk = event.EB.PK
|
||||
name = "Electoral Board"
|
||||
}
|
||||
|
||||
m, n := mixnet.GetMatrixDimensions(verifyBallotCts.Size())
|
||||
fmt.Printf(" Shuffle %d (%s) -- %d ciphertexts, %dx%d matrix\n", j, name, verifyBallotCts.Size(), m, n)
|
||||
|
||||
vStart := time.Now()
|
||||
valid := mixnet.VerifyShuffle(verifyBallotCts, vsShuffle, pk, group)
|
||||
elapsed := time.Since(vStart)
|
||||
|
||||
if valid {
|
||||
fmt.Printf(" ProductArgument .............. PASS\n")
|
||||
if m > 1 {
|
||||
fmt.Printf(" HadamardArgument ........... PASS\n")
|
||||
fmt.Printf(" ZeroArgument ............. PASS\n")
|
||||
}
|
||||
fmt.Printf(" SingleValueProductArgument . PASS\n")
|
||||
fmt.Printf(" MultiExponentiationArgument .. PASS\n")
|
||||
fmt.Printf(" ==> VERIFIED in %v\n\n", elapsed.Round(time.Millisecond))
|
||||
} else {
|
||||
fmt.Printf(" ==> FAILED!\n\n")
|
||||
allValid = false
|
||||
}
|
||||
|
||||
if j < cfg.NumCCs && j < len(event.PartiallyDecrypted) {
|
||||
verifyBallotCts = event.PartiallyDecrypted[j]
|
||||
} else {
|
||||
verifyBallotCts = vsShuffle.ShuffledCiphertexts
|
||||
}
|
||||
}
|
||||
|
||||
section("Step 4.3: Verify the Count")
|
||||
|
||||
totalVotes := 0
|
||||
for _, count := range event.FinalResult {
|
||||
totalVotes += count
|
||||
}
|
||||
fmt.Printf(" Decrypted ballots: %d\n", totalVotes)
|
||||
fmt.Printf(" Ballots submitted: %d\n", event.BallotBox.Size())
|
||||
if totalVotes == event.BallotBox.Size() {
|
||||
fmt.Println(" ==> PASS: Every ballot is accounted for.")
|
||||
} else {
|
||||
fmt.Println(" ==> FAIL: Count mismatch!")
|
||||
allValid = false
|
||||
}
|
||||
fmt.Println()
|
||||
|
||||
// =====================================================================
|
||||
// FINALE
|
||||
// =====================================================================
|
||||
banner("THE VERDICT")
|
||||
|
||||
if allValid {
|
||||
fmt.Println()
|
||||
fmt.Println(" +================================================================+")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | ALL VERIFICATIONS PASSED. |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | As a public auditor, you have independently verified: |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | [x] All 4 key holders proved they know their secrets |")
|
||||
fmt.Println(" | [x] All 5 shuffles are mathematically honest |")
|
||||
fmt.Println(" | [x] No votes were added, removed, or changed |")
|
||||
fmt.Println(" | [x] The final count matches the number of ballots |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | You did this WITHOUT any secret keys. |")
|
||||
fmt.Println(" | You did this WITHOUT trusting anyone. |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" | Pure mathematics. |")
|
||||
fmt.Println(" | |")
|
||||
fmt.Println(" +================================================================+")
|
||||
}
|
||||
|
||||
fmt.Println()
|
||||
narrator("RECAP -- What you experienced:")
|
||||
fmt.Println()
|
||||
fmt.Println(" AS THE CC OPERATOR: You generated keys, shuffled votes, created proofs.")
|
||||
fmt.Println(" You never saw anyone's vote. Even you can't undo")
|
||||
fmt.Println(" your own shuffle -- the permutation was destroyed.")
|
||||
fmt.Println()
|
||||
fmt.Println(" AS THE VOTER: Your vote was encrypted in your browser. The server")
|
||||
fmt.Println(" stored only noise. Return codes on your physical")
|
||||
fmt.Println(" card confirmed it was recorded correctly.")
|
||||
fmt.Println()
|
||||
fmt.Println(" AS THE AUDITOR: You verified every step with public data and math.")
|
||||
fmt.Println(" No trust required. No access to secrets. The proofs")
|
||||
fmt.Println(" are either valid or they aren't. No gray area.")
|
||||
fmt.Println()
|
||||
narrator("This is the same protocol used in real Swiss federal elections.")
|
||||
narrator("The production system: 14 repositories, 500,000+ lines, Windows + Kubernetes + 50GB RAM.")
|
||||
narrator("This demo: one 15MB Go binary on a Mac.")
|
||||
narrator("The math is identical.")
|
||||
fmt.Println()
|
||||
}
|
||||
63
cmd/evote/serve.go
Normal file
63
cmd/evote/serve.go
Normal file
|
|
@ -0,0 +1,63 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"embed"
|
||||
"fmt"
|
||||
"io/fs"
|
||||
"net"
|
||||
"net/http"
|
||||
"os"
|
||||
|
||||
"github.com/spf13/cobra"
|
||||
)
|
||||
|
||||
//go:embed web
|
||||
var webContent embed.FS
|
||||
|
||||
var servePort int
|
||||
|
||||
var serveCmd = &cobra.Command{
|
||||
Use: "serve",
|
||||
Short: "Serve the presentation web app on the local network",
|
||||
Run: runServe,
|
||||
}
|
||||
|
||||
func init() {
|
||||
serveCmd.Flags().IntVar(&servePort, "port", 8080, "Port to serve on")
|
||||
rootCmd.AddCommand(serveCmd)
|
||||
}
|
||||
|
||||
func runServe(cmd *cobra.Command, args []string) {
|
||||
webFS, err := fs.Sub(webContent, "web")
|
||||
if err != nil {
|
||||
fmt.Fprintf(os.Stderr, "Error: %v\n", err)
|
||||
os.Exit(1)
|
||||
}
|
||||
|
||||
http.Handle("/", http.FileServer(http.FS(webFS)))
|
||||
|
||||
fmt.Println()
|
||||
fmt.Println(" Swiss Post E-Voting Presentations")
|
||||
fmt.Println(" ==================================")
|
||||
fmt.Println()
|
||||
fmt.Println(" Available at:")
|
||||
fmt.Printf(" http://localhost:%d\n", servePort)
|
||||
|
||||
addrs, _ := net.InterfaceAddrs()
|
||||
for _, addr := range addrs {
|
||||
if ipnet, ok := addr.(*net.IPNet); ok && !ipnet.IP.IsLoopback() && ipnet.IP.To4() != nil {
|
||||
fmt.Printf(" http://%s:%d\n", ipnet.IP.String(), servePort)
|
||||
}
|
||||
}
|
||||
|
||||
fmt.Println()
|
||||
fmt.Println(" Open this URL on your iPad Pro to view the presentations.")
|
||||
fmt.Println(" Press Ctrl+C to stop the server.")
|
||||
fmt.Println()
|
||||
|
||||
listenAddr := fmt.Sprintf("0.0.0.0:%d", servePort)
|
||||
if err := http.ListenAndServe(listenAddr, nil); err != nil {
|
||||
fmt.Fprintf(os.Stderr, "Server error: %v\n", err)
|
||||
os.Exit(1)
|
||||
}
|
||||
}
|
||||
20
cmd/evote/tally.go
Normal file
20
cmd/evote/tally.go
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/spf13/cobra"
|
||||
)
|
||||
|
||||
var tallyCmd = &cobra.Command{
|
||||
Use: "tally",
|
||||
Short: "Run the tally phase (requires voted artifacts)",
|
||||
Run: func(cmd *cobra.Command, args []string) {
|
||||
fmt.Println("Tally subcommand: use 'evote demo' for the full ceremony.")
|
||||
fmt.Println("Standalone tally requires loading voted artifacts from JSON.")
|
||||
},
|
||||
}
|
||||
|
||||
func init() {
|
||||
rootCmd.AddCommand(tallyCmd)
|
||||
}
|
||||
20
cmd/evote/verify.go
Normal file
20
cmd/evote/verify.go
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/spf13/cobra"
|
||||
)
|
||||
|
||||
var verifyCmd = &cobra.Command{
|
||||
Use: "verify",
|
||||
Short: "Verify all proofs (requires tallied artifacts)",
|
||||
Run: func(cmd *cobra.Command, args []string) {
|
||||
fmt.Println("Verify subcommand: use 'evote demo' for the full ceremony.")
|
||||
fmt.Println("Standalone verify requires loading tallied artifacts from JSON.")
|
||||
},
|
||||
}
|
||||
|
||||
func init() {
|
||||
rootCmd.AddCommand(verifyCmd)
|
||||
}
|
||||
20
cmd/evote/vote.go
Normal file
20
cmd/evote/vote.go
Normal file
|
|
@ -0,0 +1,20 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/spf13/cobra"
|
||||
)
|
||||
|
||||
var voteCmd = &cobra.Command{
|
||||
Use: "vote",
|
||||
Short: "Cast a vote (requires setup artifacts)",
|
||||
Run: func(cmd *cobra.Command, args []string) {
|
||||
fmt.Println("Vote subcommand: use 'evote demo' for the full ceremony.")
|
||||
fmt.Println("Standalone vote requires loading setup artifacts from JSON.")
|
||||
},
|
||||
}
|
||||
|
||||
func init() {
|
||||
rootCmd.AddCommand(voteCmd)
|
||||
}
|
||||
1420
cmd/evote/web/crypto.html
Normal file
1420
cmd/evote/web/crypto.html
Normal file
File diff suppressed because it is too large
Load diff
1109
cmd/evote/web/demo.html
Normal file
1109
cmd/evote/web/demo.html
Normal file
File diff suppressed because it is too large
Load diff
691
cmd/evote/web/index.html
Normal file
691
cmd/evote/web/index.html
Normal file
|
|
@ -0,0 +1,691 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0, viewport-fit=cover, user-scalable=no">
|
||||
<meta name="apple-mobile-web-app-capable" content="yes">
|
||||
<meta name="apple-mobile-web-app-status-bar-style" content="default">
|
||||
<title>Swiss Post E-Voting</title>
|
||||
<style>
|
||||
* { margin: 0; padding: 0; box-sizing: border-box; }
|
||||
body {
|
||||
background: #ffffff;
|
||||
color: #24292f;
|
||||
font-family: -apple-system, BlinkMacSystemFont, 'SF Pro Text', 'Segoe UI', Roboto, 'Helvetica Neue', Arial, sans-serif;
|
||||
font-size: 16px;
|
||||
line-height: 1.7;
|
||||
height: 100vh;
|
||||
overflow: hidden;
|
||||
padding-top: env(safe-area-inset-top);
|
||||
padding-bottom: env(safe-area-inset-bottom);
|
||||
padding-left: env(safe-area-inset-left);
|
||||
padding-right: env(safe-area-inset-right);
|
||||
}
|
||||
|
||||
/* === HOME VIEW === */
|
||||
#home-view {
|
||||
height: 100vh;
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
align-items: center;
|
||||
justify-content: center;
|
||||
padding: 40px 20px;
|
||||
}
|
||||
.home-title { text-align: center; margin-bottom: 48px; }
|
||||
.home-title .flag { font-size: 60px; margin-bottom: 20px; }
|
||||
.home-title h1 { font-size: 28px; color: #1f2328; font-weight: 800; }
|
||||
.home-title .sub { font-size: 16px; color: #57606a; margin-top: 8px; }
|
||||
|
||||
.cards {
|
||||
display: flex; gap: 24px; flex-wrap: wrap;
|
||||
justify-content: center; max-width: 1000px;
|
||||
}
|
||||
.card {
|
||||
background: #ffffff; border: 1px solid #d0d7de; border-radius: 16px;
|
||||
padding: 32px 28px; width: 280px; cursor: pointer;
|
||||
transition: all 0.2s ease; text-align: center;
|
||||
-webkit-tap-highlight-color: transparent;
|
||||
box-shadow: 0 1px 3px rgba(0,0,0,0.06);
|
||||
}
|
||||
.card:hover, .card:active {
|
||||
border-color: #0969da; box-shadow: 0 4px 16px rgba(0,0,0,0.1); transform: translateY(-2px);
|
||||
}
|
||||
.card .icon { font-size: 40px; margin-bottom: 16px; }
|
||||
.card .card-title { font-size: 17px; font-weight: 700; color: #1f2328; margin-bottom: 8px; }
|
||||
.card .card-desc { font-size: 14px; color: #57606a; line-height: 1.7; }
|
||||
.card .card-meta { font-size: 12px; color: #8b949e; margin-top: 12px; }
|
||||
|
||||
.manual-link {
|
||||
margin-top: 36px; text-align: center;
|
||||
}
|
||||
.manual-link a {
|
||||
color: #57606a; font-size: 14px; text-decoration: none;
|
||||
border-bottom: 1px solid #d0d7de; padding-bottom: 2px;
|
||||
cursor: pointer;
|
||||
}
|
||||
.manual-link a:hover { color: #0969da; border-color: #0969da; }
|
||||
|
||||
/* === DECK VIEW (iframe) === */
|
||||
#deck-view {
|
||||
position: fixed; top: 0; left: 0; right: 0; bottom: 0; z-index: 10;
|
||||
}
|
||||
#deck-view iframe { width: 100%; height: 100%; border: none; }
|
||||
|
||||
/* === MANUAL VIEW === */
|
||||
#manual-view {
|
||||
height: 100vh; overflow-y: auto;
|
||||
padding: 0 30px 80px;
|
||||
-webkit-overflow-scrolling: touch;
|
||||
}
|
||||
|
||||
.nav-bar {
|
||||
position: sticky; top: 0; z-index: 50;
|
||||
background: rgba(255,255,255,0.92); backdrop-filter: blur(10px);
|
||||
-webkit-backdrop-filter: blur(10px);
|
||||
border-bottom: 1px solid #d8dee4;
|
||||
display: flex; align-items: center;
|
||||
padding: 12px 0; margin-bottom: 20px;
|
||||
}
|
||||
.nav-btn {
|
||||
background: none; border: 1px solid #d0d7de; color: #57606a;
|
||||
padding: 8px 16px; border-radius: 8px; font-family: inherit;
|
||||
font-size: 14px; cursor: pointer; -webkit-tap-highlight-color: transparent;
|
||||
min-height: 44px; display: flex; align-items: center;
|
||||
}
|
||||
.nav-btn:hover, .nav-btn:active { border-color: #0969da; color: #0969da; }
|
||||
.nav-title { flex: 1; text-align: center; font-size: 14px; color: #57606a; font-weight: 600; }
|
||||
|
||||
.mc { max-width: 880px; margin: 0 auto; }
|
||||
.mc h2 {
|
||||
font-size: 22px; color: #1f2328;
|
||||
border-bottom: 2px solid #d8dee4; padding-bottom: 8px;
|
||||
margin-bottom: 20px; margin-top: 40px;
|
||||
}
|
||||
.mc h3 {
|
||||
font-size: 17px; color: #1f2328; margin-top: 24px; margin-bottom: 10px;
|
||||
border-bottom: 1px solid #e8ebef; padding-bottom: 4px;
|
||||
}
|
||||
.mc h4 { font-size: 15px; color: #24292f; margin-top: 16px; margin-bottom: 8px; font-style: italic; }
|
||||
.mc p { margin-bottom: 10px; }
|
||||
.mc ul, .mc ol { margin: 8px 0 12px 24px; }
|
||||
.mc li { margin-bottom: 4px; }
|
||||
.mc strong { color: #1f2328; }
|
||||
.mc em { color: #24292f; }
|
||||
.mc code {
|
||||
color: #0550ae; font-size: 14px;
|
||||
font-family: 'SF Mono', 'Fira Code', Menlo, Consolas, monospace;
|
||||
background: #f6f8fa; padding: 1px 5px; border-radius: 4px;
|
||||
}
|
||||
|
||||
.mc .role-header {
|
||||
background: #f6f8fa; border: 1px solid #d8dee4; border-left: 4px solid #0969da;
|
||||
padding: 14px 18px; margin: 16px 0; border-radius: 0 8px 8px 0;
|
||||
}
|
||||
.mc .role-header .role-name { font-weight: 700; font-size: 16px; color: #1f2328; }
|
||||
.mc .role-header .role-desc { font-size: 14px; color: #57606a; margin-top: 4px; }
|
||||
|
||||
.mc .code-block {
|
||||
background: #f6f8fa; border: 1px solid #d8dee4; border-radius: 8px;
|
||||
padding: 12px 16px; margin: 10px 0; font-size: 14px; line-height: 1.5;
|
||||
overflow-x: auto; white-space: pre; color: #24292f;
|
||||
font-family: 'SF Mono', 'Fira Code', Menlo, Consolas, monospace;
|
||||
}
|
||||
.mc .step {
|
||||
border: 1px solid #d8dee4; border-radius: 10px;
|
||||
padding: 14px 18px; margin: 12px 0; background: #f6f8fa;
|
||||
}
|
||||
.mc .step-num {
|
||||
display: inline-block; background: #0969da; color: #ffffff;
|
||||
width: 26px; height: 26px; border-radius: 50%; text-align: center;
|
||||
line-height: 26px; font-size: 13px; font-weight: 700; margin-right: 10px;
|
||||
}
|
||||
.mc .step-title { font-weight: 700; display: inline; color: #1f2328; }
|
||||
|
||||
.mc .warning {
|
||||
background: #fff8c5; border-left: 4px solid #d4a72c;
|
||||
padding: 12px 16px; margin: 12px 0; font-size: 14px; color: #6f4e00;
|
||||
border-radius: 0 8px 8px 0;
|
||||
}
|
||||
.mc .warning::before { content: 'Warning: '; font-weight: 700; color: #9a6700; }
|
||||
.mc .note-box {
|
||||
background: #ddf4ff; border-left: 4px solid #218bff;
|
||||
padding: 12px 16px; margin: 12px 0; font-size: 14px; color: #0a3069;
|
||||
border-radius: 0 8px 8px 0;
|
||||
}
|
||||
.mc .note-box::before { content: 'Note: '; font-weight: 700; color: #0969da; }
|
||||
.mc .legal-box {
|
||||
background: #fbefff; border-left: 4px solid #a475f9;
|
||||
padding: 12px 16px; margin: 12px 0; font-size: 14px; color: #512a97; font-style: italic;
|
||||
border-radius: 0 8px 8px 0;
|
||||
}
|
||||
.mc .legal-box::before { content: 'Legal basis: '; font-weight: 700; font-style: normal; color: #8250df; }
|
||||
|
||||
.mc table { width: 100%; border-collapse: collapse; margin: 12px 0; font-size: 14px; }
|
||||
.mc th, .mc td { padding: 8px 12px; border: 1px solid #d8dee4; text-align: left; }
|
||||
.mc th { background: #f6f8fa; font-weight: 700; color: #1f2328; }
|
||||
.mc td { color: #24292f; }
|
||||
|
||||
.mc .checklist { list-style: none; margin-left: 0; }
|
||||
.mc .checklist li::before { content: '\2610\00a0'; font-size: 16px; }
|
||||
.mc .separator { border-top: 1px solid #d8dee4; margin: 20px 0; }
|
||||
|
||||
.hide { display: none !important; }
|
||||
|
||||
@media (max-width: 700px) {
|
||||
.cards { gap: 16px; }
|
||||
.card { width: 100%; max-width: 340px; padding: 24px 20px; }
|
||||
.home-title h1 { font-size: 22px; }
|
||||
.home-title .flag { font-size: 48px; }
|
||||
}
|
||||
</style>
|
||||
</head>
|
||||
<body>
|
||||
|
||||
<!-- ========== HOME VIEW ========== -->
|
||||
<div id="home-view">
|
||||
<div class="home-title">
|
||||
<div class="flag">🇨🇭</div>
|
||||
<h1>Swiss Post E-Voting</h1>
|
||||
<div class="sub">Choose a presentation</div>
|
||||
</div>
|
||||
<div class="cards">
|
||||
<div class="card" onclick="openDeck('demo')">
|
||||
<div class="icon">🗳️</div>
|
||||
<div class="card-title">Interactive Demo</div>
|
||||
<div class="card-desc">Run a full election step by step. Play every role: Chancellor, CC Operator, Voter, Auditor.</div>
|
||||
<div class="card-meta">27 slides</div>
|
||||
</div>
|
||||
<div class="card" onclick="openDeck('crypto')">
|
||||
<div class="icon">🔐</div>
|
||||
<div class="card-title">Cryptography Lecture</div>
|
||||
<div class="card-desc">Undergraduate-level lecture. Groups, ElGamal, ZK proofs, Bayer-Groth, then a live election.</div>
|
||||
<div class="card-meta">40 slides · 5 parts</div>
|
||||
</div>
|
||||
<div class="card" onclick="openDeck('swe')">
|
||||
<div class="icon">🏗️</div>
|
||||
<div class="card-title">Software Engineering</div>
|
||||
<div class="card-desc">How to structure a 6,500-line Go codebase. Types, patterns, architecture, error handling.</div>
|
||||
<div class="card-meta">34 slides · 8 parts</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="manual-link">
|
||||
<a onclick="showManual()">Operations Manual</a>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<!-- ========== DECK VIEW (iframe) ========== -->
|
||||
<div id="deck-view" class="hide">
|
||||
<iframe id="deck-iframe" src="about:blank"></iframe>
|
||||
</div>
|
||||
|
||||
<!-- ========== MANUAL VIEW ========== -->
|
||||
<div id="manual-view" class="hide">
|
||||
<div class="mc">
|
||||
<div class="nav-bar">
|
||||
<button class="nav-btn" onclick="goHome()">← Home</button>
|
||||
<div class="nav-title">Operations Manual</div>
|
||||
<div style="width:60px"></div>
|
||||
</div>
|
||||
|
||||
<h2>1. Introduction</h2>
|
||||
|
||||
<h3>1.1 Purpose of This Manual</h3>
|
||||
<p>This manual provides step-by-step operational procedures for all participants in the Swiss Post e-voting election ceremony, as implemented in the Go proof-of-concept (PoC) system <code>evote</code>.</p>
|
||||
<p>The Go PoC reimplements the cryptographic core of the production Swiss Post e-voting system in approximately 6,500 lines of Go. It uses the same algorithms (ElGamal encryption, Schnorr proofs, Bayer-Groth verifiable shuffle) but operates as a single-machine, command-line tool rather than a distributed multi-server deployment.</p>
|
||||
<p>Despite the simplified infrastructure, the Go PoC preserves the <strong>same role structure</strong> as the production system. Each role's responsibilities, trust boundaries, and ceremony steps are faithfully reproduced.</p>
|
||||
|
||||
<h3>1.2 System Overview</h3>
|
||||
<p>The e-voting system operates in three phases across three days:</p>
|
||||
<table>
|
||||
<tr><th>Phase</th><th>Day</th><th>Key Operations</th><th>Primary Roles</th></tr>
|
||||
<tr><td>Configuration</td><td>Day 1</td><td>Key generation, voting card creation, system setup</td><td>Cantonal Admin, CC Operators</td></tr>
|
||||
<tr><td>Release & Voting</td><td>Day 2 + Voting Period</td><td>Electoral Board constitution, setup verification, ballot casting</td><td>Electoral Board, Verifier, Voters</td></tr>
|
||||
<tr><td>Tally</td><td>Day 3</td><td>Mixing, decryption, tally verification, result publication</td><td>CC Operators, Electoral Board, Verifier</td></tr>
|
||||
</table>
|
||||
|
||||
<h3>1.3 Role Structure & Legal Basis</h3>
|
||||
<div class="legal-box">The role structure follows the Ordinance on Electronic Voting (OEV/VEleS) issued by the Federal Chancellery (Bundeskanzlei). All operational roles, trust boundaries, and separation-of-duties requirements are mandated by law.</div>
|
||||
<p>The following organizational hierarchy applies:</p>
|
||||
<div class="code-block">Federal Chancellery (Bundeskanzlei)
|
||||
|-- Issues OEV Ordinance, commissions independent examiners
|
||||
|
|
||||
+-- Cantons (each independent)
|
||||
|-- Electoral Board (>= 2 members)
|
||||
| +-- Verifier Operator
|
||||
|
|
||||
|-- Cantonal Administrator
|
||||
| +-- Operates SDM (Setup, Online, Tally)
|
||||
| +-- Manages 1 Control Component
|
||||
| +-- Manages Printing Office
|
||||
|
|
||||
+-- Contracts with Swiss Post (System Provider)
|
||||
|-- Operates Voting Server, Access Layer
|
||||
+-- Operates 3 of 4 Control Components (separate teams)</div>
|
||||
<div class="note-box">In the Go PoC, all roles are exercised by the same person on the same machine via different <code>evote</code> subcommands. In production, these roles are performed by <strong>different people on different machines</strong> with strict access controls.</div>
|
||||
|
||||
<h3>1.4 Prerequisites</h3>
|
||||
<ul>
|
||||
<li>The <code>evote</code> binary (build with <code>go build ./cmd/evote</code>)</li>
|
||||
<li>Go 1.21 or later (only for building; the binary is self-contained)</li>
|
||||
<li>A terminal (macOS Terminal, Linux shell, or Windows command prompt)</li>
|
||||
<li>No network access, database, or external services required</li>
|
||||
</ul>
|
||||
<div class="code-block"># Build the binary
|
||||
cd evote/
|
||||
go build -o evote ./cmd/evote
|
||||
./evote --help</div>
|
||||
|
||||
<h2>2. Cantonal Administrator</h2>
|
||||
|
||||
<h3>2.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Cantonal Administrator (Kantonale/r Administrator/in)</div>
|
||||
<div class="role-desc">Operates the Secure Data Manager (SDM) and coordinates the election ceremony. Responsible for processing electoral data, managing the key generation ceremony, generating voting cards, and coordinating between all other roles.</div>
|
||||
</div>
|
||||
<div class="legal-box">The Cantonal Administrator operates the SDM under cantonal authority, <strong>not</strong> under Swiss Post. All personal data (electoral registers) remains exclusively at the canton. The four-eyes principle applies to all SDM operations.</div>
|
||||
|
||||
<h3>2.2 Day 1 -- Configuration Phase</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Initialize the election and generate cryptographic parameters</div>
|
||||
<p style="margin-top:8px;">Decide on the number of voters and ballot options.</p>
|
||||
<div class="code-block"># Full automated ceremony:
|
||||
./evote demo --voters=6 --options=2</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Coordinate Control Component key generation</div>
|
||||
<p style="margin-top:8px;">The system generates key pairs for all 4 CCs and the Electoral Board. Each CC generates a Schnorr proof of knowledge.</p>
|
||||
<div class="code-block"> CC0 (Bern): Key generated, Schnorr proof VALID
|
||||
CC1 (Zurich): Key generated, Schnorr proof VALID
|
||||
CC2 (Geneva): Key generated, Schnorr proof VALID
|
||||
CC3 (Lugano): Key generated, Schnorr proof VALID</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Combine public keys into Election Public Key</div>
|
||||
<p style="margin-top:8px;">The 5 public keys are multiplied together to form the joint Election Public Key.</p>
|
||||
<div class="code-block"> ElectionPK = PK0 * PK1 * PK2 * PK3 * PK_EB mod p</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Generate voting cards</div>
|
||||
<p style="margin-top:8px;">Each voter receives a unique voting card with SVK, BCK, Choice Return Codes, and Vote Cast Code.</p>
|
||||
</div>
|
||||
<div class="warning">In the Go PoC, voting cards are displayed on screen. In production, these are printed on physical paper and mailed to voters.</div>
|
||||
|
||||
<h3>2.3 Day 2 -- Release Phase</h3>
|
||||
<p>The Cantonal Administrator coordinates the Electoral Board constitution and triggers setup verification. Once verification passes, the voter portal is activated.</p>
|
||||
|
||||
<h3>2.4 Day 3 -- Tally Phase</h3>
|
||||
<p>The Cantonal Administrator initiates mixing, coordinates Electoral Board password entry for decryption, and triggers tally verification.</p>
|
||||
|
||||
<h2>3. Electoral Board</h2>
|
||||
|
||||
<h3>3.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Electoral Board (Wahlbehörde / Commission électorale)</div>
|
||||
<div class="role-desc">A group of at least 2 board members who collectively hold the 5th encryption key. Each member sets a password during setup; all members must enter their passwords to authorize decryption.</div>
|
||||
</div>
|
||||
<div class="legal-box">The Ordinance requires a minimum of 2 Electoral Board members. Each member's password must meet complexity requirements (minimum 24 characters in production). The board operates on air-gapped machines.</div>
|
||||
|
||||
<h3>3.2 Constituting the Board (Day 2)</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Each board member sets a password</div>
|
||||
<p style="margin-top:8px;">The combined passwords derive the Electoral Board's secret key via Argon2id.</p>
|
||||
<div class="code-block"> EB member 1: enters password --> |
|
||||
EB member 2: enters password --> |-- Argon2id --> sk_EB
|
||||
EB member 3: enters password --> |
|
||||
|
||||
pk_EB = g^sk_EB mod p</div>
|
||||
</div>
|
||||
<div class="warning">If any board member forgets their password, the ballot box <strong>cannot be decrypted</strong>. There is no recovery mechanism.</div>
|
||||
|
||||
<h3>3.3 Authorizing Decryption (Day 3)</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Enter passwords on the Tally SDM</div>
|
||||
<p style="margin-top:8px;">After 4 CC shuffles, each board member enters their password to reconstruct the EB secret key.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Authorize the final shuffle and decryption</div>
|
||||
<p style="margin-top:8px;">The system performs the 5th Bayer-Groth shuffle and removes the last encryption layer.</p>
|
||||
</div>
|
||||
<div class="note-box">The Electoral Board never sees which voter cast which vote. The 5 independent shuffles have permanently destroyed the link between voter identities and ballot contents.</div>
|
||||
|
||||
<h2>4. Swiss Post -- System Provider</h2>
|
||||
|
||||
<h3>4.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Swiss Post (Schweizerische Post / System Provider)</div>
|
||||
<div class="role-desc">Develops and maintains the e-voting software. Operates the central infrastructure and 3 of 4 Control Components. Does <strong>not</strong> operate the SDM, Verifier, or the cantonal CC.</div>
|
||||
</div>
|
||||
|
||||
<h3>4.2 Infrastructure & Central Services</h3>
|
||||
<table>
|
||||
<tr><th>Component</th><th>Technology</th><th>Purpose</th></tr>
|
||||
<tr><td>Access Layer</td><td>WAF, TLS termination</td><td>Protects the Voting Server</td></tr>
|
||||
<tr><td>Voting Server</td><td>Spring Boot, Kubernetes</td><td>Processes vote submissions</td></tr>
|
||||
<tr><td>3 Control Components</td><td>Bare metal, diverse OS</td><td>Distributed key gen, return codes, shuffle</td></tr>
|
||||
<tr><td>Message Broker</td><td>Apache ActiveMQ Artemis</td><td>Async communication</td></tr>
|
||||
<tr><td>Databases</td><td>PostgreSQL</td><td>Encrypted ballots, config, audit logs</td></tr>
|
||||
</table>
|
||||
<div class="note-box">In the Go PoC, all of Swiss Post's infrastructure is simulated within the <code>evote</code> binary.</div>
|
||||
|
||||
<h3>4.3 Red Phase (Voting Period)</h3>
|
||||
<ul>
|
||||
<li>No system modifications permitted</li>
|
||||
<li>Infrastructure access strictly controlled</li>
|
||||
<li>SIEM monitoring active</li>
|
||||
<li>Only pre-authorized personnel may access systems</li>
|
||||
</ul>
|
||||
|
||||
<h2>5. Control Component Operators</h2>
|
||||
|
||||
<h3>5.1 Role Description & Split Trust</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Control Component Operator (CC-Betreiber/in)</div>
|
||||
<div class="role-desc">Each of the 4 Control Components is operated by a separate team. No person with access to one CC may have access to any other CC. Security guarantees hold as long as at least one CC is honest.</div>
|
||||
</div>
|
||||
<div class="legal-box">OEV Art. 3.15: "If a person has physical or logical access to a control component, that person may not have access to any other control component."</div>
|
||||
<table>
|
||||
<tr><th>CC</th><th>Location</th><th>OS</th><th>Operated By</th></tr>
|
||||
<tr><td>CC0</td><td>Canton premises</td><td>RHEL 9.6</td><td>Canton</td></tr>
|
||||
<tr><td>CC1</td><td>Swiss Post DC</td><td>Debian 12.12</td><td>Swiss Post Team A</td></tr>
|
||||
<tr><td>CC2</td><td>Swiss Post DC</td><td>Ubuntu 24.04</td><td>Swiss Post Team B</td></tr>
|
||||
<tr><td>CC3</td><td>Swiss Post DC</td><td>Windows Server 2022</td><td>Swiss Post Team C</td></tr>
|
||||
</table>
|
||||
|
||||
<h3>5.2 Key Generation (Setup Phase)</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Generate the key pair</div>
|
||||
<p style="margin-top:8px;">Each CC generates sk = (sk[0], sk[1]) randomly from Z_q. Publishes pk = (g^sk[0], g^sk[1]).</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Generate the Schnorr proof of knowledge</div>
|
||||
<p style="margin-top:8px;">Non-interactive Schnorr proof (Fiat-Shamir) demonstrating knowledge of the secret key.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Publish public key and proof</div>
|
||||
<p style="margin-top:8px;">Transmitted to the central system for combination with other CCs' keys.</p>
|
||||
</div>
|
||||
|
||||
<h3>5.3 Shuffle & Partial Decryption (Tally Phase)</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Receive the current ciphertext batch</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Generate a random permutation</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Re-encrypt and shuffle</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Generate the Bayer-Groth shuffle proof</div>
|
||||
<p style="margin-top:8px;">Zero-knowledge proof with sub-linear O(√N) size: ProductArgument, HadamardArgument, ZeroArgument, SingleValueProductArgument, MultiExponentiationArgument.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">5</span>
|
||||
<div class="step-title">Destroy the permutation</div>
|
||||
<p style="margin-top:8px;">Securely erase the permutation and all re-encryption randomness.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">6</span>
|
||||
<div class="step-title">Perform partial decryption</div>
|
||||
<p style="margin-top:8px;">Remove this CC's encryption layer.</p>
|
||||
</div>
|
||||
<div class="warning">The permutation must be destroyed <strong>immediately</strong> after the proof is generated.</div>
|
||||
|
||||
<h2>6. Printing Office</h2>
|
||||
|
||||
<h3>6.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Printing Office (Druckerei)</div>
|
||||
<div class="role-desc">Prints and mails the physical voting cards. The voting card is the root of individual verifiability.</div>
|
||||
</div>
|
||||
|
||||
<h3>6.2 Voting Card Generation & Distribution</h3>
|
||||
<table>
|
||||
<tr><th>Field</th><th>Purpose</th><th>Example</th></tr>
|
||||
<tr><td>Start Voting Key (SVK)</td><td>Authentication credential</td><td>SVK-0000</td></tr>
|
||||
<tr><td>Ballot Casting Key (BCK)</td><td>Vote confirmation credential</td><td>BCK-0000</td></tr>
|
||||
<tr><td>Choice Return Codes</td><td>Verify correct recording</td><td>CC00, CC01</td></tr>
|
||||
<tr><td>Vote Cast Code (VCC)</td><td>Confirm vote is sealed</td><td>VCC00</td></tr>
|
||||
</table>
|
||||
<div class="warning">Voting cards must be printed on physical paper and delivered via postal mail. The codes must <strong>never</strong> be transmitted electronically.</div>
|
||||
|
||||
<h2>7. Voter</h2>
|
||||
|
||||
<h3>7.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Voter (Stimmberechtigte/r)</div>
|
||||
<div class="role-desc">An eligible citizen who casts a vote using the e-voting system. Interacts through a web browser and verifies using the physical voting card.</div>
|
||||
</div>
|
||||
|
||||
<h3>7.2 Voting Procedure</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Open the voting portal</div>
|
||||
<p style="margin-top:8px;">Navigate to the official URL. Verify the TLS certificate.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Authenticate</div>
|
||||
<p style="margin-top:8px;">Enter your <strong>Start Voting Key (SVK)</strong> and <strong>date of birth</strong>.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Cast your vote</div>
|
||||
<p style="margin-top:8px;">Your browser encrypts the vote locally using ElGamal. <strong>The plaintext vote never leaves your device.</strong></p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Verify the Choice Return Code</div>
|
||||
<p style="margin-top:8px;">Compare the code on screen to your physical voting card. If they match, proceed. If not, <strong>STOP</strong>.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">5</span>
|
||||
<div class="step-title">Confirm with the Ballot Casting Key</div>
|
||||
<p style="margin-top:8px;">Enter your <strong>BCK</strong> to finalize.</p>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">6</span>
|
||||
<div class="step-title">Verify the Vote Cast Code</div>
|
||||
<p style="margin-top:8px;">Compare the VCC on screen to your card. If it matches, your vote is sealed.</p>
|
||||
</div>
|
||||
|
||||
<h3>7.3 Individual Verifiability</h3>
|
||||
<p>The return code mechanism provides <strong>individual verifiability</strong>: each voter can personally verify their vote was cast as intended and recorded as cast.</p>
|
||||
<div class="note-box">Even if your computer is compromised, the return codes on the physical card were generated independently by the 4 CCs during setup. A malware-modified vote would produce the wrong return code.</div>
|
||||
|
||||
<h2>8. Independent Verifier</h2>
|
||||
|
||||
<h3>8.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Verifier Operator (Prüfer/in)</div>
|
||||
<div class="role-desc">Operates verification software that independently checks all protocol steps. Runs on an offline machine under cantonal authority. Requires no secret keys.</div>
|
||||
</div>
|
||||
<div class="legal-box">The Verifier provides <strong>universal verifiability</strong>: any party can audit the election using only public data and mathematics.</div>
|
||||
|
||||
<h3>8.2 Setup Verification (Day 2)</h3>
|
||||
<ul>
|
||||
<li><strong>Key proofs:</strong> Verify Schnorr proof for each CC</li>
|
||||
<li><strong>Key combination:</strong> Verify Election Public Key is correct product of all 5 keys</li>
|
||||
<li><strong>Voting card integrity:</strong> Verify return code mappings</li>
|
||||
</ul>
|
||||
|
||||
<h3>8.3 Tally Verification (Day 3)</h3>
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Verify all Schnorr proofs (4 key proofs)</div>
|
||||
<div class="code-block"> CC0 (Bern): [PASS]
|
||||
CC1 (Zurich): [PASS]
|
||||
CC2 (Geneva): [PASS]
|
||||
CC3 (Lugano): [PASS]</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Verify all Bayer-Groth shuffle proofs (5 shuffle proofs)</div>
|
||||
<div class="code-block"> Shuffle 0 (CC0, Bern): ==> VERIFIED
|
||||
Shuffle 1 (CC1, Zurich): ==> VERIFIED
|
||||
Shuffle 2 (CC2, Geneva): ==> VERIFIED
|
||||
Shuffle 3 (CC3, Lugano): ==> VERIFIED
|
||||
Shuffle 4 (Electoral Board): ==> VERIFIED</div>
|
||||
</div>
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Verify ballot count consistency</div>
|
||||
<div class="code-block"> Ballots submitted: 6
|
||||
Ballots decrypted: 6
|
||||
==> PASS</div>
|
||||
</div>
|
||||
|
||||
<h3>8.4 Interpreting Results</h3>
|
||||
<p>If all checks pass, the Verifier provides mathematical certainty that the election result is correct.</p>
|
||||
<div class="warning">If <strong>any</strong> check fails, the election result <strong>must not be published</strong>. Contact the Federal Chancellery immediately.</div>
|
||||
|
||||
<h2>9. Federal Chancellery & External Examiners</h2>
|
||||
|
||||
<h3>9.1 Oversight Role</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Federal Chancellery (Bundeskanzlei)</div>
|
||||
<div class="role-desc">Issues the OEV Ordinance, commissions independent examinations, approves cantons for e-voting.</div>
|
||||
</div>
|
||||
|
||||
<h3>9.2 Four Audit Scopes</h3>
|
||||
<table>
|
||||
<tr><th>Scope</th><th>Subject</th><th>Examiner</th></tr>
|
||||
<tr><td>Scope 1</td><td>Cryptographic protocol</td><td>Academic cryptographers</td></tr>
|
||||
<tr><td>Scope 2</td><td>System software</td><td>Software security auditors</td></tr>
|
||||
<tr><td>Scope 3</td><td>Infrastructure & operations</td><td>Infrastructure security auditors</td></tr>
|
||||
<tr><td>Scope 4</td><td>Penetration testing</td><td>Pen testers + bug bounty</td></tr>
|
||||
</table>
|
||||
|
||||
<h2>Appendix A: Command Reference</h2>
|
||||
<table>
|
||||
<tr><th>Command</th><th>Description</th><th>Key Flags</th></tr>
|
||||
<tr><td><code>evote demo</code></td><td>Run a full election ceremony</td><td><code>--voters=N</code>, <code>--options=N</code></td></tr>
|
||||
<tr><td><code>evote present</code></td><td>Interactive step-by-step presentation</td><td>(same as demo)</td></tr>
|
||||
<tr><td><code>evote serve</code></td><td>Serve the web presentations</td><td><code>--port=N</code></td></tr>
|
||||
</table>
|
||||
<div class="code-block"># Minimal election
|
||||
./evote demo --voters=3 --options=2
|
||||
|
||||
# Larger election
|
||||
./evote demo --voters=100 --options=5
|
||||
|
||||
# Step-by-step presentation
|
||||
./evote present
|
||||
|
||||
# Serve web presentations on local network
|
||||
./evote serve --port=8080</div>
|
||||
|
||||
<h2>Appendix B: Ceremony Checklist</h2>
|
||||
|
||||
<h3>Day 1 -- Configuration</h3>
|
||||
<ul class="checklist">
|
||||
<li>Election parameters defined (voters, options)</li>
|
||||
<li>Cryptographic group generated (safe prime p = 2q + 1)</li>
|
||||
<li>CC0: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC1: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC2: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC3: key pair generated, Schnorr proof valid</li>
|
||||
<li>Election Public Key computed</li>
|
||||
<li>Candidate encoding computed</li>
|
||||
<li>Voting cards generated for all voters</li>
|
||||
</ul>
|
||||
|
||||
<h3>Day 2 -- Release</h3>
|
||||
<ul class="checklist">
|
||||
<li>Electoral Board constituted, passwords set</li>
|
||||
<li>EB key pair generated</li>
|
||||
<li>Verifier: setup verification -- all PASS</li>
|
||||
<li>Voter portal activated</li>
|
||||
<li>Voting cards printed and mailed</li>
|
||||
</ul>
|
||||
|
||||
<h3>Voting Period</h3>
|
||||
<ul class="checklist">
|
||||
<li>All voters: authenticated, voted, verified, confirmed</li>
|
||||
<li>System monitoring active (red phase)</li>
|
||||
</ul>
|
||||
|
||||
<h3>Day 3 -- Tally</h3>
|
||||
<ul class="checklist">
|
||||
<li>CC0: shuffle + proof + partial decrypt</li>
|
||||
<li>CC1: shuffle + proof + partial decrypt</li>
|
||||
<li>CC2: shuffle + proof + partial decrypt</li>
|
||||
<li>CC3: shuffle + proof + partial decrypt</li>
|
||||
<li>Electoral Board: final shuffle + full decryption</li>
|
||||
<li>Votes decoded, result tallied</li>
|
||||
<li>Verifier: 4 key proofs -- all PASS</li>
|
||||
<li>Verifier: 5 shuffle proofs -- all PASS</li>
|
||||
<li>Verifier: ballot count -- PASS</li>
|
||||
<li>Result published</li>
|
||||
</ul>
|
||||
|
||||
<h2>Appendix C: Production vs. Go PoC</h2>
|
||||
<table>
|
||||
<tr><th>Aspect</th><th>Production</th><th>Go PoC</th></tr>
|
||||
<tr><td>Language</td><td>Java 21 + TS + C#</td><td>Go</td></tr>
|
||||
<tr><td>Prime size</td><td>3072 bits</td><td>256 bits (demo)</td></tr>
|
||||
<tr><td>Infrastructure</td><td>Kubernetes + 4 bare-metal CCs + SDM</td><td>Single binary</td></tr>
|
||||
<tr><td>Networking</td><td>HTTPS, RSocket/CBOR, ActiveMQ</td><td>In-memory</td></tr>
|
||||
<tr><td>Persistence</td><td>PostgreSQL</td><td>In-memory</td></tr>
|
||||
<tr><td>Voter Portal</td><td>Angular SPA, 4 languages</td><td>Simulated in CLI</td></tr>
|
||||
<tr><td>ElGamal</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Schnorr proofs</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Bayer-Groth</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Source code</td><td>~500K lines, 14 repos</td><td>~6,500 lines, 1 module</td></tr>
|
||||
<tr><td>Dependencies</td><td>BouncyCastle, Spring, Angular, ...</td><td>Cobra + x/crypto</td></tr>
|
||||
</table>
|
||||
|
||||
<div class="separator"></div>
|
||||
<p style="text-align:center; color:#8b949e; font-size:13px; margin-top:30px;">
|
||||
Swiss Post E-Voting Go PoC -- Operator Manual v1.0 -- February 2026
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<script>
|
||||
function openDeck(name) {
|
||||
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|
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|
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|
||||
</body>
|
||||
</html>
|
||||
1070
cmd/evote/web/swe.html
Normal file
1070
cmd/evote/web/swe.html
Normal file
File diff suppressed because it is too large
Load diff
14
go.mod
Normal file
14
go.mod
Normal file
|
|
@ -0,0 +1,14 @@
|
|||
module github.com/user/evote
|
||||
|
||||
go 1.25.7
|
||||
|
||||
require (
|
||||
github.com/spf13/cobra v1.10.2
|
||||
golang.org/x/crypto v0.47.0
|
||||
)
|
||||
|
||||
require (
|
||||
github.com/inconshreveable/mousetrap v1.1.0 // indirect
|
||||
github.com/spf13/pflag v1.0.9 // indirect
|
||||
golang.org/x/sys v0.40.0 // indirect
|
||||
)
|
||||
14
go.sum
Normal file
14
go.sum
Normal file
|
|
@ -0,0 +1,14 @@
|
|||
github.com/cpuguy83/go-md2man/v2 v2.0.6/go.mod h1:oOW0eioCTA6cOiMLiUPZOpcVxMig6NIQQ7OS05n1F4g=
|
||||
github.com/inconshreveable/mousetrap v1.1.0 h1:wN+x4NVGpMsO7ErUn/mUI3vEoE6Jt13X2s0bqwp9tc8=
|
||||
github.com/inconshreveable/mousetrap v1.1.0/go.mod h1:vpF70FUmC8bwa3OWnCshd2FqLfsEA9PFc4w1p2J65bw=
|
||||
github.com/russross/blackfriday/v2 v2.1.0/go.mod h1:+Rmxgy9KzJVeS9/2gXHxylqXiyQDYRxCVz55jmeOWTM=
|
||||
github.com/spf13/cobra v1.10.2 h1:DMTTonx5m65Ic0GOoRY2c16WCbHxOOw6xxezuLaBpcU=
|
||||
github.com/spf13/cobra v1.10.2/go.mod h1:7C1pvHqHw5A4vrJfjNwvOdzYu0Gml16OCs2GRiTUUS4=
|
||||
github.com/spf13/pflag v1.0.9 h1:9exaQaMOCwffKiiiYk6/BndUBv+iRViNW+4lEMi0PvY=
|
||||
github.com/spf13/pflag v1.0.9/go.mod h1:McXfInJRrz4CZXVZOBLb0bTZqETkiAhM9Iw0y3An2Bg=
|
||||
go.yaml.in/yaml/v3 v3.0.4/go.mod h1:DhzuOOF2ATzADvBadXxruRBLzYTpT36CKvDb3+aBEFg=
|
||||
golang.org/x/crypto v0.47.0 h1:V6e3FRj+n4dbpw86FJ8Fv7XVOql7TEwpHapKoMJ/GO8=
|
||||
golang.org/x/crypto v0.47.0/go.mod h1:ff3Y9VzzKbwSSEzWqJsJVBnWmRwRSHt/6Op5n9bQc4A=
|
||||
golang.org/x/sys v0.40.0 h1:DBZZqJ2Rkml6QMQsZywtnjnnGvHza6BTfYFWY9kjEWQ=
|
||||
golang.org/x/sys v0.40.0/go.mod h1:OgkHotnGiDImocRcuBABYBEXf8A9a87e/uXjp9XT3ks=
|
||||
gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
|
||||
911
manual.html
Normal file
911
manual.html
Normal file
|
|
@ -0,0 +1,911 @@
|
|||
<!DOCTYPE html>
|
||||
<html lang="en">
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
||||
<title>Operator Manual -- Swiss Post E-Voting Go PoC</title>
|
||||
<style>
|
||||
@page {
|
||||
size: A4;
|
||||
margin: 25mm 20mm 25mm 20mm;
|
||||
}
|
||||
@media print {
|
||||
body { font-size: 10pt; }
|
||||
.no-print { display: none !important; }
|
||||
.page-break { page-break-before: always; }
|
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h2 { page-break-before: always; }
|
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h2:first-of-type { page-break-before: avoid; }
|
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pre, .code-block { font-size: 8.5pt; }
|
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.cover-page { page-break-after: always; height: 100vh; }
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||||
.toc { page-break-after: always; }
|
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}
|
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|
||||
* { margin: 0; padding: 0; box-sizing: border-box; }
|
||||
body {
|
||||
font-family: 'Georgia', 'Times New Roman', serif;
|
||||
font-size: 11pt;
|
||||
line-height: 1.6;
|
||||
color: #1a1a1a;
|
||||
background: #fff;
|
||||
max-width: 210mm;
|
||||
margin: 0 auto;
|
||||
padding: 20mm;
|
||||
}
|
||||
|
||||
/* Cover page */
|
||||
.cover-page {
|
||||
display: flex;
|
||||
flex-direction: column;
|
||||
justify-content: center;
|
||||
align-items: center;
|
||||
text-align: center;
|
||||
min-height: 80vh;
|
||||
border: 3px double #333;
|
||||
padding: 40px;
|
||||
margin-bottom: 40px;
|
||||
}
|
||||
.cover-page .swiss-cross { font-size: 48px; margin-bottom: 20px; }
|
||||
.cover-page h1 { font-size: 24pt; margin-bottom: 8px; color: #111; }
|
||||
.cover-page .cover-sub { font-size: 14pt; color: #444; margin-bottom: 30px; }
|
||||
.cover-page .cover-detail { font-size: 10pt; color: #666; line-height: 1.8; }
|
||||
.cover-page .cover-line { width: 60%; height: 1px; background: #999; margin: 20px auto; }
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||||
|
||||
/* Table of Contents */
|
||||
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|
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||||
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||||
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||||
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|
||||
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|
||||
|
||||
/* Chapter headings */
|
||||
h2 {
|
||||
font-size: 18pt;
|
||||
color: #111;
|
||||
border-bottom: 2px solid #333;
|
||||
padding-bottom: 8px;
|
||||
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|
||||
margin-top: 40px;
|
||||
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|
||||
h3 {
|
||||
font-size: 13pt;
|
||||
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|
||||
margin-top: 24px;
|
||||
margin-bottom: 10px;
|
||||
border-bottom: 1px solid #ddd;
|
||||
padding-bottom: 4px;
|
||||
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|
||||
h4 {
|
||||
font-size: 11pt;
|
||||
color: #333;
|
||||
margin-top: 16px;
|
||||
margin-bottom: 8px;
|
||||
font-style: italic;
|
||||
}
|
||||
p { margin-bottom: 10px; text-align: justify; }
|
||||
ul, ol { margin: 8px 0 12px 24px; }
|
||||
li { margin-bottom: 4px; }
|
||||
|
||||
/* Role header boxes */
|
||||
.role-header {
|
||||
background: #f5f5f0;
|
||||
border: 1px solid #ccc;
|
||||
border-left: 4px solid #333;
|
||||
padding: 12px 16px;
|
||||
margin: 16px 0;
|
||||
}
|
||||
.role-header .role-name { font-weight: 700; font-size: 12pt; }
|
||||
.role-header .role-desc { font-size: 10pt; color: #555; margin-top: 4px; }
|
||||
|
||||
/* Code blocks */
|
||||
.code-block {
|
||||
font-family: 'SF Mono', 'Consolas', 'Courier New', monospace;
|
||||
background: #f8f8f8;
|
||||
border: 1px solid #ddd;
|
||||
border-radius: 3px;
|
||||
padding: 10px 14px;
|
||||
margin: 10px 0;
|
||||
font-size: 9.5pt;
|
||||
line-height: 1.4;
|
||||
overflow-x: auto;
|
||||
white-space: pre;
|
||||
}
|
||||
|
||||
/* Step boxes */
|
||||
.step {
|
||||
border: 1px solid #ddd;
|
||||
border-radius: 4px;
|
||||
padding: 12px 16px;
|
||||
margin: 12px 0;
|
||||
background: #fafafa;
|
||||
}
|
||||
.step-num {
|
||||
display: inline-block;
|
||||
background: #333;
|
||||
color: #fff;
|
||||
width: 24px; height: 24px;
|
||||
border-radius: 50%;
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|
||||
line-height: 24px;
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||||
font-size: 9pt;
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||||
font-weight: 700;
|
||||
margin-right: 8px;
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||||
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||||
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|
||||
.step-title { font-weight: 700; display: inline; }
|
||||
|
||||
/* Warning/note boxes */
|
||||
.warning {
|
||||
background: #fff8f0;
|
||||
border-left: 4px solid #e67e22;
|
||||
padding: 10px 14px;
|
||||
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|
||||
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|
||||
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|
||||
.warning::before { content: 'Warning: '; font-weight: 700; color: #e67e22; }
|
||||
|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
background: #f5f0f5;
|
||||
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|
||||
padding: 10px 14px;
|
||||
margin: 12px 0;
|
||||
font-size: 10pt;
|
||||
font-style: italic;
|
||||
}
|
||||
.legal-box::before { content: 'Legal basis: '; font-weight: 700; font-style: normal; color: #666; }
|
||||
|
||||
/* Tables */
|
||||
table {
|
||||
width: 100%;
|
||||
border-collapse: collapse;
|
||||
margin: 12px 0;
|
||||
font-size: 10pt;
|
||||
}
|
||||
th, td {
|
||||
padding: 6px 10px;
|
||||
border: 1px solid #ccc;
|
||||
text-align: left;
|
||||
}
|
||||
th { background: #f0f0f0; font-weight: 700; }
|
||||
|
||||
/* Checklist */
|
||||
.checklist { list-style: none; margin-left: 0; }
|
||||
.checklist li::before { content: '\2610\00a0'; font-size: 13pt; }
|
||||
|
||||
/* Print hint */
|
||||
.print-hint {
|
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background: #e8f4e8;
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font-size: 10pt;
|
||||
line-height: 1.6;
|
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|
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|
||||
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|
||||
|
||||
strong { color: #111; }
|
||||
em { color: #333; }
|
||||
</style>
|
||||
</head>
|
||||
<body>
|
||||
|
||||
<!-- PRINT HINT (screen only) -->
|
||||
<div class="print-hint no-print">
|
||||
<strong>To save as PDF:</strong> Safari → File → Print → Save as PDF<br>
|
||||
Or: Cmd+P → select "Save as PDF" in the bottom-left dropdown.
|
||||
</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- COVER PAGE -->
|
||||
<!-- ============================================================ -->
|
||||
<div class="cover-page">
|
||||
<div class="swiss-cross">🇨🇭</div>
|
||||
<h1>Operator Manual</h1>
|
||||
<div class="cover-sub">Swiss Post E-Voting System<br>Go Proof-of-Concept Implementation</div>
|
||||
<div class="cover-line"></div>
|
||||
<div class="cover-detail">
|
||||
Version 1.0<br>
|
||||
February 2026<br><br>
|
||||
This manual describes the operational procedures for all roles<br>
|
||||
participating in the e-voting election ceremony, mapped to the<br>
|
||||
Go PoC command-line tool <code>evote</code>.<br><br>
|
||||
The role structure follows the Ordinance on Electronic Voting (OEV/VEleS)<br>
|
||||
as mandated by the Federal Chancellery.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- TABLE OF CONTENTS -->
|
||||
<!-- ============================================================ -->
|
||||
<div class="toc">
|
||||
<h2>Table of Contents</h2>
|
||||
<div class="toc-entry toc-chapter"><span>1. Introduction</span></div>
|
||||
<div class="toc-entry toc-section"><span>1.1 Purpose of This Manual</span></div>
|
||||
<div class="toc-entry toc-section"><span>1.2 System Overview</span></div>
|
||||
<div class="toc-entry toc-section"><span>1.3 Role Structure & Legal Basis</span></div>
|
||||
<div class="toc-entry toc-section"><span>1.4 Prerequisites</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>2. Cantonal Administrator</span></div>
|
||||
<div class="toc-entry toc-section"><span>2.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>2.2 Day 1 -- Configuration Phase</span></div>
|
||||
<div class="toc-entry toc-section"><span>2.3 Day 2 -- Release Phase</span></div>
|
||||
<div class="toc-entry toc-section"><span>2.4 Day 3 -- Tally Phase</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>3. Electoral Board</span></div>
|
||||
<div class="toc-entry toc-section"><span>3.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>3.2 Constituting the Board (Day 2)</span></div>
|
||||
<div class="toc-entry toc-section"><span>3.3 Authorizing Decryption (Day 3)</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>4. Swiss Post -- System Provider</span></div>
|
||||
<div class="toc-entry toc-section"><span>4.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>4.2 Infrastructure & Central Services</span></div>
|
||||
<div class="toc-entry toc-section"><span>4.3 Red Phase (Voting Period)</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>5. Control Component Operators</span></div>
|
||||
<div class="toc-entry toc-section"><span>5.1 Role Description & Split Trust</span></div>
|
||||
<div class="toc-entry toc-section"><span>5.2 Key Generation (Setup Phase)</span></div>
|
||||
<div class="toc-entry toc-section"><span>5.3 Shuffle & Partial Decryption (Tally Phase)</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>6. Printing Office</span></div>
|
||||
<div class="toc-entry toc-section"><span>6.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>6.2 Voting Card Generation & Distribution</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>7. Voter</span></div>
|
||||
<div class="toc-entry toc-section"><span>7.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>7.2 Voting Procedure</span></div>
|
||||
<div class="toc-entry toc-section"><span>7.3 Verifying Your Vote (Individual Verifiability)</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>8. Independent Verifier</span></div>
|
||||
<div class="toc-entry toc-section"><span>8.1 Role Description</span></div>
|
||||
<div class="toc-entry toc-section"><span>8.2 Setup Verification (Day 2)</span></div>
|
||||
<div class="toc-entry toc-section"><span>8.3 Tally Verification (Day 3)</span></div>
|
||||
<div class="toc-entry toc-section"><span>8.4 Interpreting Verification Results</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>9. Federal Chancellery & External Examiners</span></div>
|
||||
<div class="toc-entry toc-section"><span>9.1 Oversight Role</span></div>
|
||||
<div class="toc-entry toc-section"><span>9.2 Four Audit Scopes</span></div>
|
||||
|
||||
<div class="toc-entry toc-chapter"><span>Appendix A: Command Reference</span></div>
|
||||
<div class="toc-entry toc-chapter"><span>Appendix B: Ceremony Checklist</span></div>
|
||||
<div class="toc-entry toc-chapter"><span>Appendix C: Mapping -- Production System vs. Go PoC</span></div>
|
||||
</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 1: INTRODUCTION -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>1. Introduction</h2>
|
||||
|
||||
<h3>1.1 Purpose of This Manual</h3>
|
||||
<p>This manual provides step-by-step operational procedures for all participants in the Swiss Post e-voting election ceremony, as implemented in the Go proof-of-concept (PoC) system <code>evote</code>.</p>
|
||||
<p>The Go PoC reimplements the cryptographic core of the production Swiss Post e-voting system in approximately 6,500 lines of Go. It uses the same algorithms (ElGamal encryption, Schnorr proofs, Bayer-Groth verifiable shuffle) but operates as a single-machine, command-line tool rather than a distributed multi-server deployment.</p>
|
||||
<p>Despite the simplified infrastructure, the Go PoC preserves the <strong>same role structure</strong> as the production system. Each role's responsibilities, trust boundaries, and ceremony steps are faithfully reproduced. This ensures operational familiarity and avoids disrupting the agreed-upon organizational framework with its legal underpinnings.</p>
|
||||
|
||||
<h3>1.2 System Overview</h3>
|
||||
<p>The e-voting system operates in three phases across three days:</p>
|
||||
<table>
|
||||
<tr><th>Phase</th><th>Day</th><th>Key Operations</th><th>Primary Roles</th></tr>
|
||||
<tr><td>Configuration</td><td>Day 1</td><td>Key generation, voting card creation, system setup</td><td>Cantonal Admin, CC Operators</td></tr>
|
||||
<tr><td>Release & Voting</td><td>Day 2 + Voting Period</td><td>Electoral Board constitution, setup verification, voter portal activation, ballot casting</td><td>Electoral Board, Verifier, Voters</td></tr>
|
||||
<tr><td>Tally</td><td>Day 3</td><td>Mixing, decryption, tally verification, result publication</td><td>CC Operators, Electoral Board, Verifier</td></tr>
|
||||
</table>
|
||||
|
||||
<h3>1.3 Role Structure & Legal Basis</h3>
|
||||
<div class="legal-box">The role structure follows the Ordinance on Electronic Voting (OEV/VEleS) issued by the Federal Chancellery (Bundeskanzlei). All operational roles, trust boundaries, and separation-of-duties requirements are mandated by law. Deviating from the agreed role structure may have legal implications for the authorization of e-voting channels.</div>
|
||||
|
||||
<p>The following organizational hierarchy applies:</p>
|
||||
<div class="code-block">Federal Chancellery (Bundeskanzlei)
|
||||
|-- Issues OEV Ordinance, commissions independent examiners
|
||||
|
|
||||
+-- Cantons (each independent)
|
||||
|-- Electoral Board (>= 2 members)
|
||||
| +-- Verifier Operator
|
||||
|
|
||||
|-- Cantonal Administrator
|
||||
| +-- Operates SDM (Setup, Online, Tally)
|
||||
| +-- Manages 1 Control Component
|
||||
| +-- Manages Printing Office
|
||||
|
|
||||
+-- Contracts with Swiss Post (System Provider)
|
||||
|-- Operates Voting Server, Access Layer
|
||||
+-- Operates 3 of 4 Control Components (separate teams)</div>
|
||||
|
||||
<div class="note-box">In the Go PoC, all roles are exercised by the same person on the same machine via different <code>evote</code> subcommands. In production, these roles are performed by <strong>different people on different machines</strong> with strict access controls and the four-eyes principle.</div>
|
||||
|
||||
<h3>1.4 Prerequisites</h3>
|
||||
<p>To operate the Go PoC system, you need:</p>
|
||||
<ul>
|
||||
<li>The <code>evote</code> binary (build with <code>go build ./cmd/evote</code> from the <code>evote/</code> directory)</li>
|
||||
<li>Go 1.21 or later (only for building; the binary is self-contained)</li>
|
||||
<li>A terminal (macOS Terminal, Linux shell, or Windows command prompt)</li>
|
||||
<li>No network access, database, or external services required</li>
|
||||
</ul>
|
||||
<div class="code-block"># Build the binary
|
||||
cd evote/
|
||||
go build -o evote ./cmd/evote
|
||||
|
||||
# Verify it works
|
||||
./evote --help</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 2: CANTONAL ADMINISTRATOR -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>2. Cantonal Administrator</h2>
|
||||
|
||||
<h3>2.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Cantonal Administrator (Kantonale/r Administrator/in)</div>
|
||||
<div class="role-desc">Operates the Secure Data Manager (SDM) and coordinates the election ceremony. Responsible for processing electoral data, managing the key generation ceremony, generating voting cards, and coordinating between all other roles.</div>
|
||||
</div>
|
||||
|
||||
<div class="legal-box">The Cantonal Administrator operates the SDM under cantonal authority, <strong>not</strong> under Swiss Post. All personal data (electoral registers) remains exclusively at the canton. The four-eyes principle applies to all SDM operations.</div>
|
||||
|
||||
<p>In the Go PoC, the Cantonal Administrator's role corresponds to initiating the election setup and configuring the system parameters.</p>
|
||||
|
||||
<h3>2.2 Day 1 -- Configuration Phase</h3>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Initialize the election and generate cryptographic parameters</div>
|
||||
<p style="margin-top:8px;">Decide on the number of voters and ballot options. The system will generate a safe prime group, encode the candidates, and begin the key generation ceremony.</p>
|
||||
<div class="code-block"># Full automated ceremony (all roles in one command):
|
||||
./evote demo --voters=6 --options=2</div>
|
||||
<p>The <code>demo</code> command performs:</p>
|
||||
<ul>
|
||||
<li>Safe prime group generation (p = 2q + 1, both prime, 256-bit)</li>
|
||||
<li>Generator selection (g = 4, verified as quadratic residue)</li>
|
||||
<li>Candidate encoding (Alice = 2² = 4, Bob = 3² = 9, etc.)</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Coordinate Control Component key generation</div>
|
||||
<p style="margin-top:8px;">The system generates key pairs for all 4 Control Components and the Electoral Board. Each CC generates a Schnorr proof of knowledge for its secret key. The Cantonal Administrator verifies these proofs are present.</p>
|
||||
<p>Expected output:</p>
|
||||
<div class="code-block"> CC0 (Bern): Key generated, Schnorr proof VALID
|
||||
CC1 (Zurich): Key generated, Schnorr proof VALID
|
||||
CC2 (Geneva): Key generated, Schnorr proof VALID
|
||||
CC3 (Lugano): Key generated, Schnorr proof VALID</div>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Combine public keys into Election Public Key</div>
|
||||
<p style="margin-top:8px;">The 5 public keys (4 CCs + Electoral Board) are multiplied together to form the joint Election Public Key. This key locks the ballot box -- all 5 key holders must cooperate to decrypt.</p>
|
||||
<div class="code-block"> ElectionPK = PK0 * PK1 * PK2 * PK3 * PK_EB mod p</div>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Generate voting cards</div>
|
||||
<p style="margin-top:8px;">The system generates a unique voting card for each registered voter containing:</p>
|
||||
<ul>
|
||||
<li><strong>Start Voting Key (SVK)</strong> -- used for authentication</li>
|
||||
<li><strong>Ballot Casting Key (BCK)</strong> -- used to confirm the vote</li>
|
||||
<li><strong>Choice Return Codes</strong> -- one per candidate, used for individual verifiability</li>
|
||||
<li><strong>Vote Cast Code (VCC)</strong> -- confirms the vote is sealed</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div class="warning">In the Go PoC, voting cards are displayed on screen. In production, these are printed on physical paper and mailed to voters. The codes must <strong>never</strong> be transmitted electronically.</div>
|
||||
|
||||
<h3>2.3 Day 2 -- Release Phase</h3>
|
||||
<p>The Cantonal Administrator coordinates the Electoral Board constitution (see Chapter 3) and triggers the setup verification (see Chapter 8). Once verification passes, the voter portal URL is configured and published.</p>
|
||||
|
||||
<h3>2.4 Day 3 -- Tally Phase</h3>
|
||||
<p>The Cantonal Administrator initiates the mixing process, coordinates Electoral Board password entry for decryption (see Chapter 3), and triggers the tally verification (see Chapter 8). Upon successful verification, the results are exported.</p>
|
||||
|
||||
<div class="code-block"># In the Go PoC, the demo command runs all three days automatically:
|
||||
./evote demo --voters=6 --options=2
|
||||
|
||||
# For the step-by-step theatrical version:
|
||||
./evote present</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 3: ELECTORAL BOARD -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>3. Electoral Board</h2>
|
||||
|
||||
<h3>3.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Electoral Board (Wahlbehörde / Commission électorale)</div>
|
||||
<div class="role-desc">A group of at least 2 board members who collectively hold the 5th encryption key. Each member sets a password during setup; all members must enter their passwords to authorize decryption on election night. The Electoral Board is the final safeguard against unauthorized decryption.</div>
|
||||
</div>
|
||||
|
||||
<div class="legal-box">The Ordinance requires a minimum of 2 Electoral Board members. Each member's password must meet complexity requirements (minimum 24 characters in production). The board operates on air-gapped machines under the four-eyes principle.</div>
|
||||
|
||||
<h3>3.2 Constituting the Board (Day 2)</h3>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Each board member sets a password</div>
|
||||
<p style="margin-top:8px;">On the Setup SDM (an air-gapped machine), each board member enters a strong password. The combined passwords are used to derive the Electoral Board's secret key via Argon2id (a memory-hard key derivation function).</p>
|
||||
<div class="code-block"> EB member 1: enters password --> |
|
||||
EB member 2: enters password --> |-- Argon2id --> sk_EB
|
||||
EB member 3: enters password --> |
|
||||
|
||||
pk_EB = g^sk_EB mod p (published as part of the Election Public Key)</div>
|
||||
</div>
|
||||
|
||||
<div class="warning">If any board member forgets their password, the ballot box <strong>cannot be decrypted</strong>. There is no recovery mechanism. This is by design: it prevents any single party from decrypting without the board's collective authorization.</div>
|
||||
|
||||
<p>In the Go PoC, the Electoral Board key is generated automatically during the <code>demo</code> command. The system simulates the password entry process.</p>
|
||||
|
||||
<h3>3.3 Authorizing Decryption (Day 3)</h3>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Enter passwords on the Tally SDM</div>
|
||||
<p style="margin-top:8px;">After the 4 Control Components have completed their shuffles, the Electoral Board performs the final shuffle and decryption on an air-gapped Tally SDM. Each board member enters their password to reconstruct the EB secret key.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Authorize the final shuffle and decryption</div>
|
||||
<p style="margin-top:8px;">The system performs the 5th Bayer-Groth shuffle, generates its proof, and removes the last encryption layer. The decrypted votes appear in random order.</p>
|
||||
</div>
|
||||
|
||||
<div class="note-box">The Electoral Board never sees which voter cast which vote. The 5 independent shuffles have permanently destroyed the link between voter identities and ballot contents.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 4: SWISS POST -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>4. Swiss Post -- System Provider</h2>
|
||||
|
||||
<h3>4.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Swiss Post (Schweizerische Post / System Provider)</div>
|
||||
<div class="role-desc">Develops and maintains the e-voting software. Operates the central infrastructure including the Voting Server, Access Layer, message broker, databases, and 3 of the 4 Control Components. Swiss Post does <strong>not</strong> operate the SDM, Verifier, or the cantonal Control Component.</div>
|
||||
</div>
|
||||
|
||||
<h3>4.2 Infrastructure & Central Services</h3>
|
||||
<p>In the production system, Swiss Post operates:</p>
|
||||
<table>
|
||||
<tr><th>Component</th><th>Technology</th><th>Purpose</th></tr>
|
||||
<tr><td>Access Layer</td><td>WAF, TLS termination</td><td>Protects the Voting Server from direct internet access</td></tr>
|
||||
<tr><td>Voting Server</td><td>Spring Boot, Kubernetes</td><td>Processes vote submissions, relays to CCs</td></tr>
|
||||
<tr><td>3 Control Components</td><td>Bare metal, diverse OS</td><td>Distributed key generation, return codes, shuffle</td></tr>
|
||||
<tr><td>Message Broker</td><td>Apache ActiveMQ Artemis</td><td>Asynchronous communication between Server and CCs</td></tr>
|
||||
<tr><td>Databases</td><td>PostgreSQL</td><td>Stores encrypted ballots, configuration, audit logs</td></tr>
|
||||
</table>
|
||||
|
||||
<p>In the Go PoC, all of Swiss Post's infrastructure is simulated within the <code>evote</code> binary. The Voting Server, message broker, and database are replaced by in-memory data structures. The cryptographic operations are identical.</p>
|
||||
|
||||
<h3>4.3 Red Phase (Voting Period)</h3>
|
||||
<p>During the voting period, Swiss Post enforces a "red phase":</p>
|
||||
<ul>
|
||||
<li>No system modifications are permitted</li>
|
||||
<li>Infrastructure access is strictly controlled</li>
|
||||
<li>SIEM monitoring is active for anomaly detection</li>
|
||||
<li>Only pre-authorized personnel may access the systems</li>
|
||||
</ul>
|
||||
|
||||
<div class="note-box">In the Go PoC, there is no persistent infrastructure. The "red phase" is conceptual: once the <code>demo</code> command enters the voting phase, the system processes all ballots without interruption.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 5: CONTROL COMPONENT OPERATORS -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>5. Control Component Operators</h2>
|
||||
|
||||
<h3>5.1 Role Description & Split Trust</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Control Component Operator (CC-Betreiber/in)</div>
|
||||
<div class="role-desc">Each of the 4 Control Components is operated by a separate team. No person with access to one CC may have access to any other CC. The CCs collectively ensure ballot secrecy (privacy) and election integrity (correctness). The system's security guarantees hold as long as at least one CC is honest.</div>
|
||||
</div>
|
||||
|
||||
<div class="legal-box">OEV Art. 3.15: "If a person has physical or logical access to a control component, that person may not have access to any other control component." The 4 CCs use maximally diverse hardware and operating systems to reduce common-mode failures.</div>
|
||||
|
||||
<p>In the production system, the 4 CCs are deployed on bare-metal servers:</p>
|
||||
<table>
|
||||
<tr><th>CC</th><th>Location</th><th>Hardware</th><th>OS</th><th>Operated By</th></tr>
|
||||
<tr><td>CC0</td><td>Canton premises</td><td>ProLiant BL460c</td><td>RHEL 9.6</td><td>Canton</td></tr>
|
||||
<tr><td>CC1</td><td>Swiss Post DC</td><td>ProLiant BL460c</td><td>Debian 12.12</td><td>Swiss Post Team A</td></tr>
|
||||
<tr><td>CC2</td><td>Swiss Post DC</td><td>ProLiant BL460c</td><td>Ubuntu 24.04</td><td>Swiss Post Team B</td></tr>
|
||||
<tr><td>CC3</td><td>Swiss Post DC</td><td>ProLiant DL385</td><td>Windows Server 2022</td><td>Swiss Post Team C</td></tr>
|
||||
</table>
|
||||
|
||||
<p>In the Go PoC, all 4 CCs are simulated within the same process. They are named CC0 (Bern), CC1 (Zurich), CC2 (Geneva), CC3 (Lugano) and behave identically to the production CCs cryptographically.</p>
|
||||
|
||||
<h3>5.2 Key Generation (Setup Phase)</h3>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Generate the key pair</div>
|
||||
<p style="margin-top:8px;">Each CC generates a secret key vector sk = (sk[0], sk[1]) by sampling uniformly at random from Z_q. The corresponding public key pk = (g^sk[0], g^sk[1]) is computed and published.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Generate the Schnorr proof of knowledge</div>
|
||||
<p style="margin-top:8px;">For each key component, the CC generates a non-interactive Schnorr proof (Fiat-Shamir heuristic) demonstrating knowledge of the secret key without revealing it. The proof consists of two values (e, z) that anyone can verify.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Publish public key and proof</div>
|
||||
<p style="margin-top:8px;">The public key and Schnorr proof are transmitted to the central system for combination with the other CCs' keys.</p>
|
||||
</div>
|
||||
|
||||
<h3>5.3 Shuffle & Partial Decryption (Tally Phase)</h3>
|
||||
|
||||
<p>On Day 3, each CC performs the following operations in sequence (CC0 first, then CC1, CC2, CC3):</p>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Receive the current ciphertext batch</div>
|
||||
<p style="margin-top:8px;">CC0 receives the original encrypted ballots from the ballot box. Subsequent CCs receive the output of the previous CC's shuffle.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Generate a random permutation</div>
|
||||
<p style="margin-top:8px;">Sample a uniformly random permutation π of {0, ..., N-1}. This permutation determines the new order of the ballots.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Re-encrypt and shuffle</div>
|
||||
<p style="margin-top:8px;">For each output slot k, re-encrypt the permuted input ciphertext with fresh randomness. The resulting ciphertexts encrypt the same votes but are computationally unlinkable to the inputs.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Generate the Bayer-Groth shuffle proof</div>
|
||||
<p style="margin-top:8px;">Generate a zero-knowledge proof that the output is a valid permutation + re-encryption of the input. The proof has sub-linear O(√N) size and consists of nested sub-arguments: ProductArgument, HadamardArgument, ZeroArgument, SingleValueProductArgument, and MultiExponentiationArgument.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">5</span>
|
||||
<div class="step-title">Destroy the permutation</div>
|
||||
<p style="margin-top:8px;">Securely erase the permutation π and all re-encryption randomness. After this step, <strong>even the CC operator cannot determine the correspondence</strong> between input and output ciphertexts.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">6</span>
|
||||
<div class="step-title">Perform partial decryption</div>
|
||||
<p style="margin-top:8px;">Remove this CC's encryption layer by computing γ^sk for each ciphertext and dividing from the phi components. This reduces the number of remaining encryption layers by one.</p>
|
||||
</div>
|
||||
|
||||
<div class="warning">The permutation must be destroyed <strong>immediately</strong> after the proof is generated. If any CC retains its permutation, the privacy guarantee for that shuffle step is compromised.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 6: PRINTING OFFICE -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>6. Printing Office</h2>
|
||||
|
||||
<h3>6.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Printing Office (Druckerei)</div>
|
||||
<div class="role-desc">Prints and mails the physical voting cards to eligible voters. The voting card is the root of individual verifiability: it contains secret codes that enable the voter to verify that their vote was recorded correctly.</div>
|
||||
</div>
|
||||
|
||||
<h3>6.2 Voting Card Generation & Distribution</h3>
|
||||
<p>The Cantonal Administrator generates voting card data during the Configuration Phase. The Printing Office receives the data and produces physical cards.</p>
|
||||
|
||||
<p>Each voting card contains:</p>
|
||||
<table>
|
||||
<tr><th>Field</th><th>Purpose</th><th>Example</th></tr>
|
||||
<tr><td>Start Voting Key (SVK)</td><td>Authentication credential</td><td>SVK-0000</td></tr>
|
||||
<tr><td>Ballot Casting Key (BCK)</td><td>Vote confirmation credential</td><td>BCK-0000</td></tr>
|
||||
<tr><td>Choice Return Codes</td><td>Verify correct recording (one per candidate)</td><td>CC00 (Alice), CC01 (Bob)</td></tr>
|
||||
<tr><td>Vote Cast Code (VCC)</td><td>Confirm vote is sealed</td><td>VCC00</td></tr>
|
||||
</table>
|
||||
|
||||
<p>In the Go PoC, the <code>demo</code> command displays all voting cards on screen:</p>
|
||||
<div class="code-block"> +------------------------------------------------------+
|
||||
| SWISS CONFEDERATION |
|
||||
| Electronic Voting Card |
|
||||
| |
|
||||
| Voter ID: voter-0000 |
|
||||
| Start Voting Key: SVK-0000 |
|
||||
| Ballot Casting Key: BCK-0000 |
|
||||
| |
|
||||
| Choice Return Codes: |
|
||||
| Alice: CC00 |
|
||||
| Bob: CC01 |
|
||||
| |
|
||||
| Vote Cast Code: VCC00 |
|
||||
+------------------------------------------------------+</div>
|
||||
|
||||
<div class="warning">Voting cards must be printed on physical paper and delivered via postal mail. The codes must <strong>never</strong> be transmitted electronically (no email, no SMS, no online download). The physical card is the out-of-band channel that enables individual verifiability even if the voting device is compromised.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 7: VOTER -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>7. Voter</h2>
|
||||
|
||||
<h3>7.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Voter (Stimmberechtigte/r)</div>
|
||||
<div class="role-desc">An eligible citizen who casts a vote using the e-voting system. The voter interacts with the system through a web browser and verifies correct recording using the physical voting card received by mail.</div>
|
||||
</div>
|
||||
|
||||
<h3>7.2 Voting Procedure</h3>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Open the voting portal</div>
|
||||
<p style="margin-top:8px;">Navigate to the official URL provided on your voting card or the cantonal website. Verify the TLS certificate. Accept the legal terms.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Authenticate</div>
|
||||
<p style="margin-top:8px;">Enter your <strong>Start Voting Key (SVK)</strong> and <strong>date of birth</strong>. The server verifies your identity using an Argon2id hash (the SVK is never stored in plaintext).</p>
|
||||
<p>In the Go PoC, authentication is simulated automatically.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Cast your vote</div>
|
||||
<p style="margin-top:8px;">Select your candidate(s) on the ballot. Your browser encrypts the vote locally using ElGamal encryption under the Election Public Key. <strong>The plaintext vote never leaves your device.</strong></p>
|
||||
<p>The browser sends two large numbers (γ, φ) to the server -- pure noise to anyone without all 5 secret keys.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">4</span>
|
||||
<div class="step-title">Verify the Choice Return Code</div>
|
||||
<p style="margin-top:8px;">The server displays a <strong>Choice Return Code</strong>. Compare it to the code on your physical voting card for the candidate you selected.</p>
|
||||
<ul>
|
||||
<li>If the codes <strong>match</strong>: your vote was recorded correctly. Proceed to confirm.</li>
|
||||
<li>If the codes <strong>do not match</strong>: <strong>STOP. Do not confirm.</strong> Contact the cantonal authority. Your vote may have been intercepted or modified.</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">5</span>
|
||||
<div class="step-title">Confirm with the Ballot Casting Key</div>
|
||||
<p style="margin-top:8px;">Enter your <strong>Ballot Casting Key (BCK)</strong> to finalize your vote. This is the second factor that prevents the server from confirming a vote without your explicit action.</p>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">6</span>
|
||||
<div class="step-title">Verify the Vote Cast Code</div>
|
||||
<p style="margin-top:8px;">The server displays a <strong>Vote Cast Code (VCC)</strong>. Compare it to your voting card. If it matches, your vote is sealed and confirmed.</p>
|
||||
</div>
|
||||
|
||||
<h3>7.3 Verifying Your Vote (Individual Verifiability)</h3>
|
||||
<p>The return code mechanism provides <strong>individual verifiability</strong>: each voter can personally verify that their vote was cast as intended and recorded as cast, without needing to trust any single system component.</p>
|
||||
<p>The security guarantee: if the Choice Return Code matches the code on your physical card, then the ciphertext stored on the server encrypts the candidate you selected. This holds under the assumption that at least 1 of the 4 Control Components is honest (since all 4 contribute to computing the return code).</p>
|
||||
|
||||
<div class="note-box">Even if your computer is compromised with malware, the return codes on the physical card were generated during setup by the 4 CCs -- independently of your browser. A malware-modified vote would produce the wrong return code.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 8: INDEPENDENT VERIFIER -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>8. Independent Verifier</h2>
|
||||
|
||||
<h3>8.1 Role Description</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Verifier Operator (Prüfer/in / Independent Auditor)</div>
|
||||
<div class="role-desc">Operates the verification software that independently checks whether all protocol participants faithfully executed their operations. The Verifier runs on an offline, hardened machine under cantonal authority -- <strong>not</strong> under Swiss Post. The Verifier requires no secret keys and uses only publicly available data.</div>
|
||||
</div>
|
||||
|
||||
<div class="legal-box">The Verifier is operated by the electoral commission under the responsibility of the cantons. It provides <strong>universal verifiability</strong>: any party can audit the election result using only public data and mathematics.</div>
|
||||
|
||||
<h3>8.2 Setup Verification (Day 2)</h3>
|
||||
<p>After the Configuration Phase, the Verifier checks that the setup was performed correctly:</p>
|
||||
<ul>
|
||||
<li><strong>Key proofs:</strong> Verify the Schnorr proof for each CC's public key (proves the CC knows the corresponding secret key)</li>
|
||||
<li><strong>Key combination:</strong> Verify the Election Public Key is the correct product of all 5 individual keys</li>
|
||||
<li><strong>Voting card integrity:</strong> Verify return code mappings are consistent</li>
|
||||
</ul>
|
||||
|
||||
<p>In the Go PoC, setup verification is performed automatically as part of the <code>demo</code> command.</p>
|
||||
|
||||
<h3>8.3 Tally Verification (Day 3)</h3>
|
||||
<p>After tallying, the Verifier performs the most critical checks:</p>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">1</span>
|
||||
<div class="step-title">Verify all Schnorr proofs (4 key proofs)</div>
|
||||
<p style="margin-top:8px;">For each CC, recompute the Schnorr verification equation: g<sup>z</sup> · pk<sup>-e</sup> should reconstruct the commitment c, and H(p, q, g, pk, c) should equal e.</p>
|
||||
<div class="code-block"> CC0 (Bern): [PASS]
|
||||
CC1 (Zurich): [PASS]
|
||||
CC2 (Geneva): [PASS]
|
||||
CC3 (Lugano): [PASS]</div>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">2</span>
|
||||
<div class="step-title">Verify all Bayer-Groth shuffle proofs (5 shuffle proofs)</div>
|
||||
<p style="margin-top:8px;">For each of the 5 shuffles (4 CCs + Electoral Board), verify all sub-arguments of the Bayer-Groth shuffle proof. This confirms each shuffle was a valid permutation + re-encryption.</p>
|
||||
<div class="code-block"> Shuffle 0 (CC0, Bern):
|
||||
ProductArgument .............. PASS
|
||||
HadamardArgument ........... PASS
|
||||
ZeroArgument ............. PASS
|
||||
SingleValueProduct ......... PASS
|
||||
MultiExponentiationArgument .. PASS
|
||||
==> VERIFIED
|
||||
|
||||
Shuffle 1 (CC1, Zurich): ==> VERIFIED
|
||||
Shuffle 2 (CC2, Geneva): ==> VERIFIED
|
||||
Shuffle 3 (CC3, Lugano): ==> VERIFIED
|
||||
Shuffle 4 (Electoral Board): ==> VERIFIED</div>
|
||||
</div>
|
||||
|
||||
<div class="step">
|
||||
<span class="step-num">3</span>
|
||||
<div class="step-title">Verify ballot count consistency</div>
|
||||
<p style="margin-top:8px;">Confirm that the number of ballots is preserved at every stage: input to the first shuffle = output of the last shuffle = number of decrypted votes.</p>
|
||||
<div class="code-block"> Ballots submitted: 6
|
||||
Ballots decrypted: 6
|
||||
==> PASS: Every ballot is accounted for.</div>
|
||||
</div>
|
||||
|
||||
<h3>8.4 Interpreting Verification Results</h3>
|
||||
<p>If all checks pass, the Verifier provides mathematical certainty that:</p>
|
||||
<ol>
|
||||
<li>All key holders proved knowledge of their secret keys</li>
|
||||
<li>All shuffles were honest permutations + re-encryptions (no votes added, removed, or changed)</li>
|
||||
<li>The ballot count is consistent throughout the pipeline</li>
|
||||
<li>The final tally correctly reflects the decrypted ballots</li>
|
||||
</ol>
|
||||
|
||||
<div class="warning">If <strong>any</strong> check fails, the election result <strong>must not be published</strong>. A failed shuffle proof indicates that a CC may have tampered with the ballots. Contact the Federal Chancellery and the cantonal authority immediately.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- CHAPTER 9: FEDERAL CHANCELLERY -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>9. Federal Chancellery & External Examiners</h2>
|
||||
|
||||
<h3>9.1 Oversight Role</h3>
|
||||
<div class="role-header">
|
||||
<div class="role-name">Federal Chancellery (Bundeskanzlei)</div>
|
||||
<div class="role-desc">The highest authority overseeing the e-voting system. Issues the Ordinance on Electronic Voting (OEV), commissions independent examinations, approves cantons for e-voting, and publishes examination reports.</div>
|
||||
</div>
|
||||
|
||||
<p>The Federal Chancellery does not directly operate any component of the e-voting system. Its role is regulatory and supervisory.</p>
|
||||
|
||||
<h3>9.2 Four Audit Scopes</h3>
|
||||
<p>The Federal Chancellery commissions independent examiners across 4 scopes:</p>
|
||||
<table>
|
||||
<tr><th>Scope</th><th>Subject</th><th>Examiner</th></tr>
|
||||
<tr><td>Scope 1</td><td>Cryptographic protocol</td><td>Academic cryptographers</td></tr>
|
||||
<tr><td>Scope 2</td><td>System software</td><td>Software security auditors</td></tr>
|
||||
<tr><td>Scope 3</td><td>Infrastructure & operations</td><td>Infrastructure security auditors</td></tr>
|
||||
<tr><td>Scope 4</td><td>Penetration testing</td><td>Penetration testers + bug bounty community</td></tr>
|
||||
</table>
|
||||
|
||||
<p>Additionally, Swiss Post publishes all source code and documentation, and runs a permanent bug bounty programme through YesWeHack, allowing the public to scrutinize the system.</p>
|
||||
|
||||
<div class="note-box">The Go PoC is a reimplementation for educational and demonstration purposes. It has not undergone the formal examination process. In a production deployment, all four audit scopes would need to be passed before the system is approved for use in federal elections.</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- APPENDIX A: COMMAND REFERENCE -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>Appendix A: Command Reference</h2>
|
||||
|
||||
<table>
|
||||
<tr><th>Command</th><th>Description</th><th>Key Flags</th></tr>
|
||||
<tr>
|
||||
<td><code>evote demo</code></td>
|
||||
<td>Run a full election ceremony: setup → vote → tally → verify</td>
|
||||
<td><code>--voters=N</code> (default 10)<br><code>--options=N</code> (default 2)</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>evote present</code></td>
|
||||
<td>Interactive step-by-step presentation mode with role-play narration</td>
|
||||
<td>(same as demo)</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>evote serve</code></td>
|
||||
<td>Serve web presentations on local network (iPad-optimized)</td>
|
||||
<td><code>--port=N</code> (default 8080)</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><code>evote --help</code></td>
|
||||
<td>Show available commands and flags</td>
|
||||
<td>--</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<h3>Example Sessions</h3>
|
||||
<div class="code-block"># Minimal election: 3 voters, 2 candidates
|
||||
./evote demo --voters=3 --options=2
|
||||
|
||||
# Larger election: 100 voters, 5 candidates
|
||||
./evote demo --voters=100 --options=5
|
||||
|
||||
# Step-by-step theatrical presentation
|
||||
./evote present
|
||||
|
||||
# Serve web presentations on local network
|
||||
./evote serve --port=8080</div>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- APPENDIX B: CEREMONY CHECKLIST -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>Appendix B: Ceremony Checklist</h2>
|
||||
|
||||
<h3>Day 1 -- Configuration</h3>
|
||||
<ul class="checklist">
|
||||
<li>Cantonal Administrator: election parameters defined (voters, options)</li>
|
||||
<li>Cantonal Administrator: cryptographic group generated (safe prime p = 2q + 1)</li>
|
||||
<li>CC0: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC1: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC2: key pair generated, Schnorr proof valid</li>
|
||||
<li>CC3: key pair generated, Schnorr proof valid</li>
|
||||
<li>Cantonal Administrator: Election Public Key computed (product of 5 keys)</li>
|
||||
<li>Cantonal Administrator: candidate encoding computed</li>
|
||||
<li>Cantonal Administrator: voting cards generated for all voters</li>
|
||||
</ul>
|
||||
|
||||
<h3>Day 2 -- Release</h3>
|
||||
<ul class="checklist">
|
||||
<li>Electoral Board: minimum 2 members constituted, passwords set</li>
|
||||
<li>Electoral Board: EB key pair generated from passwords</li>
|
||||
<li>Verifier: setup verification run -- all checks PASS</li>
|
||||
<li>Cantonal Administrator: voter portal activated</li>
|
||||
<li>Printing Office: voting cards printed and mailed</li>
|
||||
</ul>
|
||||
|
||||
<h3>Voting Period</h3>
|
||||
<ul class="checklist">
|
||||
<li>All voters: authenticated, voted, verified return codes, confirmed</li>
|
||||
<li>Swiss Post: system monitoring active, no modifications (red phase)</li>
|
||||
</ul>
|
||||
|
||||
<h3>Day 3 -- Tally</h3>
|
||||
<ul class="checklist">
|
||||
<li>CC0: shuffle + re-encrypt + Bayer-Groth proof + partial decrypt</li>
|
||||
<li>CC1: shuffle + re-encrypt + Bayer-Groth proof + partial decrypt</li>
|
||||
<li>CC2: shuffle + re-encrypt + Bayer-Groth proof + partial decrypt</li>
|
||||
<li>CC3: shuffle + re-encrypt + Bayer-Groth proof + partial decrypt</li>
|
||||
<li>Electoral Board: final shuffle + proof + full decryption (passwords entered)</li>
|
||||
<li>Cantonal Administrator: votes decoded, result tallied</li>
|
||||
<li>Verifier: 4 key proofs verified -- all PASS</li>
|
||||
<li>Verifier: 5 shuffle proofs verified -- all PASS</li>
|
||||
<li>Verifier: ballot count consistency -- PASS</li>
|
||||
<li>Cantonal Administrator: result published</li>
|
||||
</ul>
|
||||
|
||||
<!-- ============================================================ -->
|
||||
<!-- APPENDIX C: MAPPING -->
|
||||
<!-- ============================================================ -->
|
||||
<h2>Appendix C: Mapping -- Production System vs. Go PoC</h2>
|
||||
|
||||
<table>
|
||||
<tr><th>Aspect</th><th>Production System</th><th>Go PoC</th></tr>
|
||||
<tr><td>Language</td><td>Java 21 + TypeScript + C#</td><td>Go</td></tr>
|
||||
<tr><td>Prime size</td><td>3072 bits (128-bit security)</td><td>256 bits (demo only)</td></tr>
|
||||
<tr><td>Infrastructure</td><td>Kubernetes cluster + 4 bare-metal CCs + SDM machines</td><td>Single binary, single machine</td></tr>
|
||||
<tr><td>Networking</td><td>HTTPS/TLS, RSocket/CBOR, ActiveMQ</td><td>In-memory (no network)</td></tr>
|
||||
<tr><td>Persistence</td><td>PostgreSQL databases</td><td>In-memory (no persistence)</td></tr>
|
||||
<tr><td>SDM</td><td>Electron desktop app, air-gapped Windows machines</td><td>CLI commands</td></tr>
|
||||
<tr><td>Voter Portal</td><td>Angular SPA, 4 languages</td><td>Simulated in CLI</td></tr>
|
||||
<tr><td>Verifier</td><td>Standalone Java application, 50 checks</td><td>Built into <code>demo</code> command</td></tr>
|
||||
<tr><td>Electoral Board</td><td>Physical password entry on air-gapped machine</td><td>Simulated key derivation</td></tr>
|
||||
<tr><td>Voting cards</td><td>Printed on paper, mailed by post</td><td>Displayed on screen</td></tr>
|
||||
<tr><td>ElGamal encryption</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Schnorr proofs</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Bayer-Groth shuffle</td><td>Identical algorithm</td><td>Identical algorithm</td></tr>
|
||||
<tr><td>Fiat-Shamir heuristic</td><td>SHA3-256 recursive hash</td><td>SHA3-256 recursive hash</td></tr>
|
||||
<tr><td>Role structure</td><td>Distributed across organizations</td><td>Same roles, single operator</td></tr>
|
||||
<tr><td>Four-eyes principle</td><td>Enforced physically</td><td>Organizational (not enforced by software)</td></tr>
|
||||
<tr><td>Source code</td><td>~500,000 lines across 14 repos</td><td>~6,500 lines, 1 module</td></tr>
|
||||
<tr><td>Dependencies</td><td>BouncyCastle, Spring, Angular, Electron, ...</td><td>Cobra + x/crypto</td></tr>
|
||||
</table>
|
||||
|
||||
<div class="separator"></div>
|
||||
|
||||
<p style="text-align:center; color:#888; font-size:9pt; margin-top:30px;">
|
||||
End of Manual<br>
|
||||
Swiss Post E-Voting Go PoC -- Operator Manual v1.0<br>
|
||||
February 2026
|
||||
</p>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
131
pkg/elgamal/ciphertext.go
Normal file
131
pkg/elgamal/ciphertext.go
Normal file
|
|
@ -0,0 +1,131 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Ciphertext represents an ElGamal multi-recipient ciphertext.
|
||||
// Gamma is the shared randomness component g^r.
|
||||
// Phis are the per-recipient encrypted message components pk_i^r * m_i.
|
||||
type Ciphertext struct {
|
||||
Gamma emath.GqElement
|
||||
Phis *emath.GqVector
|
||||
}
|
||||
|
||||
// NewCiphertext creates a new ciphertext.
|
||||
func NewCiphertext(gamma emath.GqElement, phis *emath.GqVector) Ciphertext {
|
||||
return Ciphertext{Gamma: gamma, Phis: phis}
|
||||
}
|
||||
|
||||
// Size returns the number of phi elements (recipients).
|
||||
func (c Ciphertext) Size() int {
|
||||
return c.Phis.Size()
|
||||
}
|
||||
|
||||
// GetPhi returns the i-th phi element.
|
||||
func (c Ciphertext) GetPhi(i int) emath.GqElement {
|
||||
return c.Phis.Get(i)
|
||||
}
|
||||
|
||||
// Group returns the GqGroup of this ciphertext.
|
||||
func (c Ciphertext) Group() *emath.GqGroup {
|
||||
return c.Gamma.Group()
|
||||
}
|
||||
|
||||
// Multiply returns the component-wise product of two ciphertexts.
|
||||
// (a.gamma * b.gamma, a.phi_i * b.phi_i)
|
||||
func (c Ciphertext) Multiply(other Ciphertext) Ciphertext {
|
||||
if c.Size() != other.Size() {
|
||||
panic("ciphertexts must have the same size")
|
||||
}
|
||||
return Ciphertext{
|
||||
Gamma: c.Gamma.Multiply(other.Gamma),
|
||||
Phis: c.Phis.Multiply(other.Phis),
|
||||
}
|
||||
}
|
||||
|
||||
// Exponentiate returns this ciphertext raised to the power e.
|
||||
// (gamma^e, phi_i^e)
|
||||
func (c Ciphertext) Exponentiate(e emath.ZqElement) Ciphertext {
|
||||
return Ciphertext{
|
||||
Gamma: c.Gamma.Exponentiate(e),
|
||||
Phis: c.Phis.ExpScalar(e),
|
||||
}
|
||||
}
|
||||
|
||||
// CiphertextVector is a vector of Ciphertexts.
|
||||
type CiphertextVector struct {
|
||||
elements []Ciphertext
|
||||
group *emath.GqGroup
|
||||
}
|
||||
|
||||
// NewCiphertextVector creates a vector of ciphertexts.
|
||||
func NewCiphertextVector(elements []Ciphertext) *CiphertextVector {
|
||||
if len(elements) == 0 {
|
||||
return &CiphertextVector{elements: []Ciphertext{}}
|
||||
}
|
||||
copied := make([]Ciphertext, len(elements))
|
||||
copy(copied, elements)
|
||||
return &CiphertextVector{elements: copied, group: elements[0].Group()}
|
||||
}
|
||||
|
||||
// CiphertextVectorOf creates a vector from variadic ciphertexts.
|
||||
func CiphertextVectorOf(cts ...Ciphertext) *CiphertextVector {
|
||||
return NewCiphertextVector(cts)
|
||||
}
|
||||
|
||||
// Size returns the number of ciphertexts.
|
||||
func (v *CiphertextVector) Size() int {
|
||||
return len(v.elements)
|
||||
}
|
||||
|
||||
// Get returns the i-th ciphertext.
|
||||
func (v *CiphertextVector) Get(i int) Ciphertext {
|
||||
return v.elements[i]
|
||||
}
|
||||
|
||||
// Group returns the common group.
|
||||
func (v *CiphertextVector) Group() *emath.GqGroup {
|
||||
return v.group
|
||||
}
|
||||
|
||||
// Elements returns a copy of the elements.
|
||||
func (v *CiphertextVector) Elements() []Ciphertext {
|
||||
copied := make([]Ciphertext, len(v.elements))
|
||||
copy(copied, v.elements)
|
||||
return copied
|
||||
}
|
||||
|
||||
// Append creates a new vector with the ciphertext appended.
|
||||
func (v *CiphertextVector) Append(ct Ciphertext) *CiphertextVector {
|
||||
newElems := make([]Ciphertext, len(v.elements)+1)
|
||||
copy(newElems, v.elements)
|
||||
newElems[len(v.elements)] = ct
|
||||
return NewCiphertextVector(newElems)
|
||||
}
|
||||
|
||||
// PhiSize returns the size of the phi vectors (all must be the same).
|
||||
func (v *CiphertextVector) PhiSize() int {
|
||||
if len(v.elements) == 0 {
|
||||
return 0
|
||||
}
|
||||
return v.elements[0].Size()
|
||||
}
|
||||
|
||||
// Gammas returns a vector of all gamma values.
|
||||
func (v *CiphertextVector) Gammas() *emath.GqVector {
|
||||
elems := make([]emath.GqElement, len(v.elements))
|
||||
for i, ct := range v.elements {
|
||||
elems[i] = ct.Gamma
|
||||
}
|
||||
return emath.GqVectorOf(elems...)
|
||||
}
|
||||
|
||||
// GetPhiColumn returns a vector of the j-th phi from each ciphertext.
|
||||
func (v *CiphertextVector) GetPhiColumn(j int) *emath.GqVector {
|
||||
elems := make([]emath.GqElement, len(v.elements))
|
||||
for i, ct := range v.elements {
|
||||
elems[i] = ct.GetPhi(j)
|
||||
}
|
||||
return emath.GqVectorOf(elems...)
|
||||
}
|
||||
49
pkg/elgamal/decrypt.go
Normal file
49
pkg/elgamal/decrypt.go
Normal file
|
|
@ -0,0 +1,49 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Decrypt computes the ElGamal decryption of a ciphertext.
|
||||
// m_i = phi_i / gamma^sk_i = phi_i * gamma^(-sk_i)
|
||||
func Decrypt(ct Ciphertext, sk PrivateKey) Message {
|
||||
if ct.Size() != sk.Size() {
|
||||
panic("ciphertext size must match secret key size")
|
||||
}
|
||||
|
||||
elems := make([]emath.GqElement, ct.Size())
|
||||
for i := 0; i < ct.Size(); i++ {
|
||||
// gamma^sk_i
|
||||
gammaSk := ct.Gamma.Exponentiate(sk.Get(i))
|
||||
// m_i = phi_i / gamma^sk_i
|
||||
elems[i] = ct.GetPhi(i).Divide(gammaSk)
|
||||
}
|
||||
|
||||
return Message{Elements: emath.GqVectorOf(elems...)}
|
||||
}
|
||||
|
||||
// PartialDecrypt computes partial decryption using one key share.
|
||||
// For each phi: phi_i' = phi_i / gamma^sk_i
|
||||
// The gamma is left unchanged for further partial decryptions.
|
||||
func PartialDecrypt(ct Ciphertext, sk PrivateKey) Ciphertext {
|
||||
if ct.Size() != sk.Size() {
|
||||
panic("ciphertext size must match secret key size")
|
||||
}
|
||||
|
||||
phis := make([]emath.GqElement, ct.Size())
|
||||
for i := 0; i < ct.Size(); i++ {
|
||||
gammaSk := ct.Gamma.Exponentiate(sk.Get(i))
|
||||
phis[i] = ct.GetPhi(i).Divide(gammaSk)
|
||||
}
|
||||
|
||||
return Ciphertext{
|
||||
Gamma: ct.Gamma,
|
||||
Phis: emath.GqVectorOf(phis...),
|
||||
}
|
||||
}
|
||||
|
||||
// ExtractMessage extracts the plaintext from a fully decrypted ciphertext.
|
||||
// After all partial decryptions, the phis contain the plaintext directly.
|
||||
func ExtractMessage(ct Ciphertext) Message {
|
||||
return Message{Elements: ct.Phis}
|
||||
}
|
||||
50
pkg/elgamal/encrypt.go
Normal file
50
pkg/elgamal/encrypt.go
Normal file
|
|
@ -0,0 +1,50 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Encrypt computes the ElGamal encryption of a message.
|
||||
// gamma = g^r
|
||||
// phi_i = pk_i^r * m_i
|
||||
func Encrypt(msg Message, r emath.ZqElement, pk PublicKey) Ciphertext {
|
||||
if msg.Size() != pk.Size() {
|
||||
panic("message size must match public key size")
|
||||
}
|
||||
|
||||
group := pk.Group()
|
||||
g := group.Generator()
|
||||
|
||||
// gamma = g^r
|
||||
gamma := g.Exponentiate(r)
|
||||
|
||||
// phi_i = pk_i^r * m_i
|
||||
phis := make([]emath.GqElement, msg.Size())
|
||||
for i := 0; i < msg.Size(); i++ {
|
||||
pkR := pk.Get(i).Exponentiate(r)
|
||||
phis[i] = pkR.Multiply(msg.Get(i))
|
||||
}
|
||||
|
||||
return Ciphertext{
|
||||
Gamma: gamma,
|
||||
Phis: emath.GqVectorOf(phis...),
|
||||
}
|
||||
}
|
||||
|
||||
// EncryptOnes encrypts an all-ones message (used for trivial ciphertexts).
|
||||
// gamma = g^r, phi_i = pk_i^r
|
||||
func EncryptOnes(r emath.ZqElement, pk PublicKey) Ciphertext {
|
||||
group := pk.Group()
|
||||
g := group.Generator()
|
||||
gamma := g.Exponentiate(r)
|
||||
|
||||
phis := make([]emath.GqElement, pk.Size())
|
||||
for i := 0; i < pk.Size(); i++ {
|
||||
phis[i] = pk.Get(i).Exponentiate(r)
|
||||
}
|
||||
|
||||
return Ciphertext{
|
||||
Gamma: gamma,
|
||||
Phis: emath.GqVectorOf(phis...),
|
||||
}
|
||||
}
|
||||
77
pkg/elgamal/keys.go
Normal file
77
pkg/elgamal/keys.go
Normal file
|
|
@ -0,0 +1,77 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// PrivateKey is a vector of Z_q elements.
|
||||
type PrivateKey struct {
|
||||
Elements *emath.ZqVector
|
||||
}
|
||||
|
||||
// PublicKey is a vector of G_q elements.
|
||||
type PublicKey struct {
|
||||
Elements *emath.GqVector
|
||||
}
|
||||
|
||||
// KeyPair holds a matching private and public key.
|
||||
type KeyPair struct {
|
||||
SK PrivateKey
|
||||
PK PublicKey
|
||||
}
|
||||
|
||||
// GenKeyPair generates an ElGamal key pair with l elements.
|
||||
// sk = [x_0, ..., x_{l-1}] random in Z_q
|
||||
// pk = [g^x_0, ..., g^x_{l-1}]
|
||||
func GenKeyPair(group *emath.GqGroup, l int) KeyPair {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
skElements := emath.RandomZqVector(l, zqGroup)
|
||||
|
||||
g := group.Generator()
|
||||
pkElems := make([]emath.GqElement, l)
|
||||
for i := 0; i < l; i++ {
|
||||
pkElems[i] = g.Exponentiate(skElements.Get(i))
|
||||
}
|
||||
|
||||
return KeyPair{
|
||||
SK: PrivateKey{Elements: skElements},
|
||||
PK: PublicKey{Elements: emath.GqVectorOf(pkElems...)},
|
||||
}
|
||||
}
|
||||
|
||||
// CombinePublicKeys computes the element-wise product of multiple public keys.
|
||||
func CombinePublicKeys(keys ...PublicKey) PublicKey {
|
||||
if len(keys) == 0 {
|
||||
panic("must provide at least one key")
|
||||
}
|
||||
result := keys[0].Elements
|
||||
for i := 1; i < len(keys); i++ {
|
||||
result = result.Multiply(keys[i].Elements)
|
||||
}
|
||||
return PublicKey{Elements: result}
|
||||
}
|
||||
|
||||
// Size returns the number of key elements.
|
||||
func (pk PublicKey) Size() int {
|
||||
return pk.Elements.Size()
|
||||
}
|
||||
|
||||
// Get returns the i-th element of the public key.
|
||||
func (pk PublicKey) Get(i int) emath.GqElement {
|
||||
return pk.Elements.Get(i)
|
||||
}
|
||||
|
||||
// Size returns the number of key elements.
|
||||
func (sk PrivateKey) Size() int {
|
||||
return sk.Elements.Size()
|
||||
}
|
||||
|
||||
// Get returns the i-th element of the private key.
|
||||
func (sk PrivateKey) Get(i int) emath.ZqElement {
|
||||
return sk.Elements.Get(i)
|
||||
}
|
||||
|
||||
// Group returns the GqGroup associated with this public key.
|
||||
func (pk PublicKey) Group() *emath.GqGroup {
|
||||
return pk.Elements.Group()
|
||||
}
|
||||
51
pkg/elgamal/message.go
Normal file
51
pkg/elgamal/message.go
Normal file
|
|
@ -0,0 +1,51 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Message represents a multi-recipient plaintext message (vector of G_q elements).
|
||||
type Message struct {
|
||||
Elements *emath.GqVector
|
||||
}
|
||||
|
||||
// NewMessage creates a Message from a GqVector.
|
||||
func NewMessage(elements *emath.GqVector) Message {
|
||||
return Message{Elements: elements}
|
||||
}
|
||||
|
||||
// OnesMessage creates a message of all 1s (identity elements).
|
||||
func OnesMessage(size int, group *emath.GqGroup) Message {
|
||||
return Message{Elements: emath.GqVectorOfIdentities(size, group)}
|
||||
}
|
||||
|
||||
// Size returns the number of message elements.
|
||||
func (m Message) Size() int {
|
||||
return m.Elements.Size()
|
||||
}
|
||||
|
||||
// Get returns the i-th message element.
|
||||
func (m Message) Get(i int) emath.GqElement {
|
||||
return m.Elements.Get(i)
|
||||
}
|
||||
|
||||
// IsOnes checks if all elements are the identity (1).
|
||||
func (m Message) IsOnes() bool {
|
||||
for i := 0; i < m.Size(); i++ {
|
||||
if !m.Get(i).IsIdentity() {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// MessageFromBigInts creates a message from big.Int values.
|
||||
func MessageFromBigInts(values []*big.Int, group *emath.GqGroup) (Message, error) {
|
||||
v, err := emath.GqVectorFromBigInts(values, group)
|
||||
if err != nil {
|
||||
return Message{}, err
|
||||
}
|
||||
return Message{Elements: v}, nil
|
||||
}
|
||||
65
pkg/elgamal/ops.go
Normal file
65
pkg/elgamal/ops.go
Normal file
|
|
@ -0,0 +1,65 @@
|
|||
package elgamal
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// CiphertextProduct computes the component-wise product of a vector of ciphertexts.
|
||||
// Returns a single ciphertext: (Π gamma_i, Π phi_i,j for each j)
|
||||
func CiphertextProduct(cts *CiphertextVector) Ciphertext {
|
||||
if cts.Size() == 0 {
|
||||
panic("cannot compute product of empty vector")
|
||||
}
|
||||
result := cts.Get(0)
|
||||
for i := 1; i < cts.Size(); i++ {
|
||||
result = result.Multiply(cts.Get(i))
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// CiphertextVectorExponentiate exponentiates each ciphertext by the corresponding exponent.
|
||||
func CiphertextVectorExponentiate(cts *CiphertextVector, exps *emath.ZqVector) *CiphertextVector {
|
||||
if cts.Size() != exps.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]Ciphertext, cts.Size())
|
||||
for i := 0; i < cts.Size(); i++ {
|
||||
result[i] = cts.Get(i).Exponentiate(exps.Get(i))
|
||||
}
|
||||
return NewCiphertextVector(result)
|
||||
}
|
||||
|
||||
// CiphertextVectorMultiply multiplies two ciphertext vectors element-wise.
|
||||
func CiphertextVectorMultiply(a, b *CiphertextVector) *CiphertextVector {
|
||||
if a.Size() != b.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]Ciphertext, a.Size())
|
||||
for i := 0; i < a.Size(); i++ {
|
||||
result[i] = a.Get(i).Multiply(b.Get(i))
|
||||
}
|
||||
return NewCiphertextVector(result)
|
||||
}
|
||||
|
||||
// ReEncrypt re-encrypts a ciphertext with fresh randomness.
|
||||
// C' = C * Enc(1^l, r', pk) = (gamma * g^r', phi_i * pk_i^r')
|
||||
func ReEncrypt(ct Ciphertext, rPrime emath.ZqElement, pk PublicKey) Ciphertext {
|
||||
enc := EncryptOnes(rPrime, pk)
|
||||
return ct.Multiply(enc)
|
||||
}
|
||||
|
||||
// MultiExponentiation computes the multi-exponentiation of ciphertexts.
|
||||
// Returns Π C_i^e_i = (Π gamma_i^e_i, Π phi_i,j^e_i for each j)
|
||||
func MultiExponentiation(cts *CiphertextVector, exps *emath.ZqVector) Ciphertext {
|
||||
if cts.Size() != exps.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
if cts.Size() == 0 {
|
||||
panic("vectors must not be empty")
|
||||
}
|
||||
result := cts.Get(0).Exponentiate(exps.Get(0))
|
||||
for i := 1; i < cts.Size(); i++ {
|
||||
result = result.Multiply(cts.Get(i).Exponentiate(exps.Get(i)))
|
||||
}
|
||||
return result
|
||||
}
|
||||
73
pkg/hash/conversions.go
Normal file
73
pkg/hash/conversions.go
Normal file
|
|
@ -0,0 +1,73 @@
|
|||
package hash
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// IntegerToByteArray converts a non-negative big.Int to unsigned big-endian bytes.
|
||||
// This matches Java's behavior: strip sign byte from BigInteger.toByteArray().
|
||||
// Go's big.Int.Bytes() already returns unsigned big-endian, so this is a direct match.
|
||||
// Zero produces an empty byte array.
|
||||
func IntegerToByteArray(x *big.Int) []byte {
|
||||
if x.Sign() < 0 {
|
||||
panic("value must be non-negative")
|
||||
}
|
||||
return x.Bytes() // Go big.Int.Bytes() returns unsigned big-endian
|
||||
}
|
||||
|
||||
// IntegerToFixedLengthByteArray converts a non-negative big.Int to a fixed-length
|
||||
// unsigned big-endian byte array, zero-padded on the left.
|
||||
func IntegerToFixedLengthByteArray(x *big.Int, length int) []byte {
|
||||
if x.Sign() < 0 {
|
||||
panic("value must be non-negative")
|
||||
}
|
||||
b := x.Bytes()
|
||||
if len(b) > length {
|
||||
panic("value too large for requested length")
|
||||
}
|
||||
if len(b) == length {
|
||||
return b
|
||||
}
|
||||
result := make([]byte, length)
|
||||
copy(result[length-len(b):], b)
|
||||
return result
|
||||
}
|
||||
|
||||
// ByteArrayToInteger converts unsigned big-endian bytes to a non-negative big.Int.
|
||||
// This matches Java's new BigInteger(1, bytes).
|
||||
func ByteArrayToInteger(b []byte) *big.Int {
|
||||
return new(big.Int).SetBytes(b)
|
||||
}
|
||||
|
||||
// StringToByteArray converts a string to UTF-8 bytes.
|
||||
func StringToByteArray(s string) []byte {
|
||||
return []byte(s)
|
||||
}
|
||||
|
||||
// ByteLength returns the byte length of a big.Int: ceil(bitLength / 8).
|
||||
func ByteLength(x *big.Int) int {
|
||||
bits := x.BitLen()
|
||||
if bits == 0 {
|
||||
return 0
|
||||
}
|
||||
return (bits + 7) / 8
|
||||
}
|
||||
|
||||
// CutToBitLength extracts the rightmost n bits from a byte array B.
|
||||
// Returns a byte array of ceil(n/8) bytes with only the rightmost n bits set.
|
||||
func CutToBitLength(b []byte, n int) []byte {
|
||||
if n == 0 {
|
||||
return []byte{}
|
||||
}
|
||||
length := (n + 7) / 8 // ceil(n/8)
|
||||
offset := len(b) - length
|
||||
result := make([]byte, length)
|
||||
copy(result, b[offset:])
|
||||
// Mask the leftmost byte if n is not byte-aligned
|
||||
remainder := n % 8
|
||||
if remainder != 0 {
|
||||
mask := byte((1 << remainder) - 1)
|
||||
result[0] &= mask
|
||||
}
|
||||
return result
|
||||
}
|
||||
66
pkg/hash/hashable.go
Normal file
66
pkg/hash/hashable.go
Normal file
|
|
@ -0,0 +1,66 @@
|
|||
package hash
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// Tag bytes for the Hashable type system
|
||||
const (
|
||||
TagBytes byte = 0x00
|
||||
TagBigInt byte = 0x01
|
||||
TagString byte = 0x02
|
||||
TagList byte = 0x03
|
||||
)
|
||||
|
||||
// Hashable represents a value that can be recursively hashed.
|
||||
type Hashable interface {
|
||||
hashableTag() byte
|
||||
hashableData() interface{}
|
||||
}
|
||||
|
||||
// HashableBytes wraps a byte slice.
|
||||
type HashableBytes struct {
|
||||
Data []byte
|
||||
}
|
||||
|
||||
func (h HashableBytes) hashableTag() byte { return TagBytes }
|
||||
func (h HashableBytes) hashableData() interface{} { return h.Data }
|
||||
|
||||
// HashableBigInt wraps a non-negative big.Int.
|
||||
type HashableBigInt struct {
|
||||
Value *big.Int
|
||||
}
|
||||
|
||||
func (h HashableBigInt) hashableTag() byte { return TagBigInt }
|
||||
func (h HashableBigInt) hashableData() interface{} { return h.Value }
|
||||
|
||||
// HashableString wraps a string.
|
||||
type HashableString struct {
|
||||
Value string
|
||||
}
|
||||
|
||||
func (h HashableString) hashableTag() byte { return TagString }
|
||||
func (h HashableString) hashableData() interface{} { return h.Value }
|
||||
|
||||
// HashableList wraps a list of Hashable values.
|
||||
type HashableList struct {
|
||||
Elements []Hashable
|
||||
}
|
||||
|
||||
func (h HashableList) hashableTag() byte { return TagList }
|
||||
func (h HashableList) hashableData() interface{} { return h.Elements }
|
||||
|
||||
// RawBigIntToHashable converts big.Int to HashableBigInt.
|
||||
func RawBigIntToHashable(v *big.Int) Hashable {
|
||||
return HashableBigInt{Value: v}
|
||||
}
|
||||
|
||||
// RawStringToHashable converts string to HashableString.
|
||||
func RawStringToHashable(s string) Hashable {
|
||||
return HashableString{Value: s}
|
||||
}
|
||||
|
||||
// RawBytesToHashable converts bytes to HashableBytes.
|
||||
func RawBytesToHashable(b []byte) Hashable {
|
||||
return HashableBytes{Data: b}
|
||||
}
|
||||
25
pkg/hash/hashandsquare.go
Normal file
25
pkg/hash/hashandsquare.go
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
package hash
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// HashAndSquare hashes a value x to a GqElement by:
|
||||
// 1. Computing h = RecursiveHashToZq(q, "HashAndSquare", x)
|
||||
// 2. Adding 1: h_plus_one = h + 1
|
||||
// 3. Squaring: result = (h+1)^2 mod p (guaranteed to be in G_q)
|
||||
func HashAndSquare(x *big.Int, group *emath.GqGroup) emath.GqElement {
|
||||
q := group.Q()
|
||||
// Hash to Z_q with "HashAndSquare" label
|
||||
h := RecursiveHashToZq(q, HashableString{Value: "HashAndSquare"}, HashableBigInt{Value: x})
|
||||
// Add 1
|
||||
hPlusOne := new(big.Int).Add(h, big.NewInt(1))
|
||||
// Square mod p to get element of G_q
|
||||
elem, err := emath.GqElementFromSquareRoot(hPlusOne, group)
|
||||
if err != nil {
|
||||
panic("HashAndSquare: failed to create GqElement: " + err.Error())
|
||||
}
|
||||
return elem
|
||||
}
|
||||
132
pkg/hash/recursive.go
Normal file
132
pkg/hash/recursive.go
Normal file
|
|
@ -0,0 +1,132 @@
|
|||
package hash
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"golang.org/x/crypto/sha3"
|
||||
)
|
||||
|
||||
// SecurityLambda is the security parameter (128 bits).
|
||||
const SecurityLambda = 128
|
||||
|
||||
// RecursiveHash computes the recursive hash using SHA3-256.
|
||||
// If multiple values are provided, they are wrapped in a HashableList.
|
||||
func RecursiveHash(values ...Hashable) []byte {
|
||||
if len(values) == 0 {
|
||||
panic("values must not be empty")
|
||||
}
|
||||
if len(values) > 1 {
|
||||
return RecursiveHash(HashableList{Elements: values})
|
||||
}
|
||||
|
||||
v := values[0]
|
||||
switch h := v.(type) {
|
||||
case HashableBytes:
|
||||
return sha3Hash256(TagBytes, h.Data)
|
||||
|
||||
case HashableBigInt:
|
||||
if h.Value.Sign() < 0 {
|
||||
panic("big.Int must be non-negative")
|
||||
}
|
||||
return sha3Hash256(TagBigInt, IntegerToByteArray(h.Value))
|
||||
|
||||
case HashableString:
|
||||
return sha3Hash256(TagString, StringToByteArray(h.Value))
|
||||
|
||||
case HashableList:
|
||||
// Recursively hash each element to 256 bits, then concatenate
|
||||
var data []byte
|
||||
for _, elem := range h.Elements {
|
||||
data = append(data, RecursiveHash(elem)...)
|
||||
}
|
||||
return sha3Hash256(TagList, data)
|
||||
|
||||
default:
|
||||
panic("unknown Hashable type")
|
||||
}
|
||||
}
|
||||
|
||||
// sha3Hash256 computes SHA3-256(tag || data).
|
||||
func sha3Hash256(tag byte, data []byte) []byte {
|
||||
h := sha3.New256()
|
||||
h.Write([]byte{tag})
|
||||
h.Write(data)
|
||||
return h.Sum(nil)
|
||||
}
|
||||
|
||||
// RecursiveHashOfLength computes the recursive hash using SHAKE-256 XOF,
|
||||
// producing output of the requested bit length.
|
||||
// For lists, each element is recursively hashed to the REQUESTED bit length (not 256 bits).
|
||||
func RecursiveHashOfLength(requestedBitLength int, values ...Hashable) []byte {
|
||||
if len(values) == 0 {
|
||||
panic("values must not be empty")
|
||||
}
|
||||
if requestedBitLength < 512 {
|
||||
panic("requested bit length must be >= 512")
|
||||
}
|
||||
if len(values) > 1 {
|
||||
return RecursiveHashOfLength(requestedBitLength, HashableList{Elements: values})
|
||||
}
|
||||
|
||||
v := values[0]
|
||||
byteLen := (requestedBitLength + 7) / 8 // ceil(bitLength/8)
|
||||
|
||||
switch h := v.(type) {
|
||||
case HashableBytes:
|
||||
return CutToBitLength(shake256XOF(byteLen, TagBytes, h.Data), requestedBitLength)
|
||||
|
||||
case HashableBigInt:
|
||||
if h.Value.Sign() < 0 {
|
||||
panic("big.Int must be non-negative")
|
||||
}
|
||||
return CutToBitLength(shake256XOF(byteLen, TagBigInt, IntegerToByteArray(h.Value)), requestedBitLength)
|
||||
|
||||
case HashableString:
|
||||
return CutToBitLength(shake256XOF(byteLen, TagString, StringToByteArray(h.Value)), requestedBitLength)
|
||||
|
||||
case HashableList:
|
||||
// CRITICAL: For lists, each element is recursively hashed to the REQUESTED bit length
|
||||
var data []byte
|
||||
for _, elem := range h.Elements {
|
||||
data = append(data, RecursiveHashOfLength(requestedBitLength, elem)...)
|
||||
}
|
||||
return CutToBitLength(shake256XOF(byteLen, TagList, data), requestedBitLength)
|
||||
|
||||
default:
|
||||
panic("unknown Hashable type")
|
||||
}
|
||||
}
|
||||
|
||||
// shake256XOF computes SHAKE-256 XOF with the specified output length.
|
||||
func shake256XOF(outputLen int, tag byte, data []byte) []byte {
|
||||
h := sha3.NewShake256()
|
||||
h.Write([]byte{tag})
|
||||
h.Write(data)
|
||||
output := make([]byte, outputLen)
|
||||
h.Read(output)
|
||||
return output
|
||||
}
|
||||
|
||||
// RecursiveHashToZq hashes values to an element of Z_q.
|
||||
// Prepends q and "RecursiveHash" to the input, then reduces modulo q.
|
||||
func RecursiveHashToZq(q *big.Int, values ...Hashable) *big.Int {
|
||||
if q.Sign() <= 0 {
|
||||
panic("q must be positive")
|
||||
}
|
||||
|
||||
// Target bit length: q.BitLen() + 2*lambda
|
||||
targetBits := q.BitLen() + 2*SecurityLambda
|
||||
|
||||
// Construct extended input: [q, "RecursiveHash", values...]
|
||||
extended := make([]Hashable, 0, len(values)+2)
|
||||
extended = append(extended, HashableBigInt{Value: q})
|
||||
extended = append(extended, HashableString{Value: "RecursiveHash"})
|
||||
extended = append(extended, values...)
|
||||
|
||||
// Hash to extended length
|
||||
hashBytes := RecursiveHashOfLength(targetBits, extended...)
|
||||
|
||||
// Convert to integer and reduce mod q
|
||||
hPrime := ByteArrayToInteger(hashBytes)
|
||||
return new(big.Int).Mod(hPrime, q)
|
||||
}
|
||||
63
pkg/kdf/hkdf.go
Normal file
63
pkg/kdf/hkdf.go
Normal file
|
|
@ -0,0 +1,63 @@
|
|||
package kdf
|
||||
|
||||
import (
|
||||
"crypto/sha256"
|
||||
"io"
|
||||
"math/big"
|
||||
|
||||
"golang.org/x/crypto/argon2"
|
||||
"golang.org/x/crypto/hkdf"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// DeriveKey derives a key using HKDF-SHA256.
|
||||
func DeriveKey(prk, info []byte, length int) []byte {
|
||||
reader := hkdf.Expand(sha256.New, prk, info)
|
||||
key := make([]byte, length)
|
||||
_, err := io.ReadFull(reader, key)
|
||||
if err != nil {
|
||||
panic("HKDF expand failed: " + err.Error())
|
||||
}
|
||||
return key
|
||||
}
|
||||
|
||||
// KDFToZq derives a Z_q element using HKDF-SHA256.
|
||||
// PRK is the pseudorandom key, info is the context info, q is the modulus.
|
||||
func KDFToZq(prk []byte, info []byte, q *big.Int) *big.Int {
|
||||
// Derive enough bytes: ceil(q.BitLen() / 8) + extra for uniformity
|
||||
byteLen := (q.BitLen()+7)/8 + 16 // extra 16 bytes for rejection sampling avoidance
|
||||
derived := DeriveKey(prk, info, byteLen)
|
||||
val := new(big.Int).SetBytes(derived)
|
||||
return val.Mod(val, q)
|
||||
}
|
||||
|
||||
// KDFToZqElement derives a ZqElement using HKDF-SHA256.
|
||||
func KDFToZqElement(prk []byte, info []byte, group *emath.ZqGroup) emath.ZqElement {
|
||||
val := KDFToZq(prk, info, group.Q())
|
||||
e, err := emath.NewZqElement(val, group)
|
||||
if err != nil {
|
||||
panic("KDFToZqElement: " + err.Error())
|
||||
}
|
||||
return e
|
||||
}
|
||||
|
||||
// BuildKDFInfo builds a KDF info string from label and context parts.
|
||||
func BuildKDFInfo(parts ...string) []byte {
|
||||
var info []byte
|
||||
for _, p := range parts {
|
||||
info = append(info, []byte(p)...)
|
||||
}
|
||||
return info
|
||||
}
|
||||
|
||||
// Argon2id derives a key using Argon2id.
|
||||
func Argon2id(password, salt []byte, time, memory uint32, threads uint8, keyLen uint32) []byte {
|
||||
return argon2.IDKey(password, salt, time, memory, threads, keyLen)
|
||||
}
|
||||
|
||||
// DefaultArgon2id uses the default parameters from the Swiss Post e-voting system.
|
||||
func DefaultArgon2id(password, salt []byte) []byte {
|
||||
// Typical parameters from the protocol
|
||||
return Argon2id(password, salt, 3, 64*1024, 4, 32)
|
||||
}
|
||||
126
pkg/math/gqelement.go
Normal file
126
pkg/math/gqelement.go
Normal file
|
|
@ -0,0 +1,126 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// GqElement represents an element of the quadratic residue group G_q.
|
||||
// Immutable: all operations return new instances.
|
||||
type GqElement struct {
|
||||
value *big.Int
|
||||
group *GqGroup
|
||||
}
|
||||
|
||||
// NewGqElement creates a GqElement from a value, validating group membership.
|
||||
func NewGqElement(value *big.Int, group *GqGroup) (GqElement, error) {
|
||||
if value == nil || group == nil {
|
||||
return GqElement{}, fmt.Errorf("value and group must not be nil")
|
||||
}
|
||||
if !group.IsGroupMember(value) {
|
||||
return GqElement{}, fmt.Errorf("value %v is not a member of the group", value)
|
||||
}
|
||||
return GqElement{value: new(big.Int).Set(value), group: group}, nil
|
||||
}
|
||||
|
||||
// GqElementFromSquareRoot creates a GqElement by squaring a value, guaranteeing group membership.
|
||||
// The input element must be in [1, q).
|
||||
func GqElementFromSquareRoot(element *big.Int, group *GqGroup) (GqElement, error) {
|
||||
if element == nil || group == nil {
|
||||
return GqElement{}, fmt.Errorf("element and group must not be nil")
|
||||
}
|
||||
if element.Sign() < 1 || element.Cmp(group.q) >= 0 {
|
||||
return GqElement{}, fmt.Errorf("element must be in [1, q)")
|
||||
}
|
||||
// element^2 mod p is guaranteed to be a quadratic residue
|
||||
squared := new(big.Int).Exp(element, big.NewInt(2), group.p)
|
||||
return GqElement{value: squared, group: group}, nil
|
||||
}
|
||||
|
||||
// gqElementUnchecked creates a GqElement without validation.
|
||||
// Only use when the value is mathematically guaranteed to be in the group.
|
||||
func gqElementUnchecked(value *big.Int, group *GqGroup) GqElement {
|
||||
return GqElement{value: new(big.Int).Set(value), group: group}
|
||||
}
|
||||
|
||||
// Value returns the element's value as a new big.Int.
|
||||
func (e GqElement) Value() *big.Int {
|
||||
return new(big.Int).Set(e.value)
|
||||
}
|
||||
|
||||
// Group returns the element's group.
|
||||
func (e GqElement) Group() *GqGroup {
|
||||
return e.group
|
||||
}
|
||||
|
||||
// Multiply returns (this * other) mod p.
|
||||
func (e GqElement) Multiply(other GqElement) GqElement {
|
||||
e.checkSameGroup(other)
|
||||
result := new(big.Int).Mul(e.value, other.value)
|
||||
result.Mod(result, e.group.p)
|
||||
return GqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Exponentiate returns this^exponent mod p.
|
||||
func (e GqElement) Exponentiate(exponent ZqElement) GqElement {
|
||||
result := new(big.Int).Exp(e.value, exponent.value, e.group.p)
|
||||
return GqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// ExpBigInt returns this^exponent mod p where exponent is a raw big.Int.
|
||||
func (e GqElement) ExpBigInt(exponent *big.Int) GqElement {
|
||||
result := new(big.Int).Exp(e.value, exponent, e.group.p)
|
||||
return GqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Invert returns this^(-1) mod p.
|
||||
func (e GqElement) Invert() GqElement {
|
||||
result := new(big.Int).ModInverse(e.value, e.group.p)
|
||||
return GqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Divide returns this / divisor = this * divisor^(-1) mod p.
|
||||
func (e GqElement) Divide(divisor GqElement) GqElement {
|
||||
e.checkSameGroup(divisor)
|
||||
inv := divisor.Invert()
|
||||
return e.Multiply(inv)
|
||||
}
|
||||
|
||||
// Equals checks if two elements have the same value and group.
|
||||
func (e GqElement) Equals(other GqElement) bool {
|
||||
return e.value.Cmp(other.value) == 0 && e.group.Equals(other.group)
|
||||
}
|
||||
|
||||
// IsIdentity checks if this element is the group identity (1).
|
||||
func (e GqElement) IsIdentity() bool {
|
||||
return e.value.Cmp(big.NewInt(1)) == 0
|
||||
}
|
||||
|
||||
// MultiModExp computes Π(bases[i]^exponents[i]) mod p.
|
||||
func MultiModExp(bases []GqElement, exponents []ZqElement) GqElement {
|
||||
if len(bases) == 0 {
|
||||
panic("bases must not be empty")
|
||||
}
|
||||
if len(bases) != len(exponents) {
|
||||
panic("bases and exponents must have the same length")
|
||||
}
|
||||
group := bases[0].group
|
||||
result := new(big.Int).Set(big.NewInt(1))
|
||||
for i := range bases {
|
||||
term := new(big.Int).Exp(bases[i].value, exponents[i].value, group.p)
|
||||
result.Mul(result, term)
|
||||
result.Mod(result, group.p)
|
||||
}
|
||||
return GqElement{value: result, group: group}
|
||||
}
|
||||
|
||||
func (e GqElement) checkSameGroup(other GqElement) {
|
||||
if !e.group.Equals(other.group) {
|
||||
panic(fmt.Sprintf("elements must be from the same group"))
|
||||
}
|
||||
}
|
||||
|
||||
// String returns the string representation of the element value.
|
||||
func (e GqElement) String() string {
|
||||
return e.value.String()
|
||||
}
|
||||
103
pkg/math/gqgroup.go
Normal file
103
pkg/math/gqgroup.go
Normal file
|
|
@ -0,0 +1,103 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// GqGroup represents the quadratic residue group of integers modulo p,
|
||||
// where p is a safe prime (p = 2q + 1) and q is the group order.
|
||||
type GqGroup struct {
|
||||
p *big.Int
|
||||
q *big.Int
|
||||
generator GqElement
|
||||
identity GqElement
|
||||
}
|
||||
|
||||
// NewGqGroup creates a new GqGroup with the given parameters.
|
||||
// Validates that p and q are prime, p = 2q + 1, and g is a group member.
|
||||
func NewGqGroup(p, q, g *big.Int) (*GqGroup, error) {
|
||||
if p == nil || q == nil || g == nil {
|
||||
return nil, fmt.Errorf("parameters must not be nil")
|
||||
}
|
||||
|
||||
// Validate p is prime
|
||||
if !p.ProbablyPrime(64) {
|
||||
return nil, fmt.Errorf("p is not prime")
|
||||
}
|
||||
|
||||
// Validate q is prime
|
||||
if !q.ProbablyPrime(64) {
|
||||
return nil, fmt.Errorf("q is not prime")
|
||||
}
|
||||
|
||||
// Validate p = 2q + 1
|
||||
twoQPlusOne := new(big.Int).Mul(big.NewInt(2), q)
|
||||
twoQPlusOne.Add(twoQPlusOne, big.NewInt(1))
|
||||
if p.Cmp(twoQPlusOne) != 0 {
|
||||
return nil, fmt.Errorf("p != 2q + 1")
|
||||
}
|
||||
|
||||
// Validate g is in range [2, p)
|
||||
if g.Cmp(big.NewInt(2)) < 0 || g.Cmp(p) >= 0 {
|
||||
return nil, fmt.Errorf("g must be in range [2, p)")
|
||||
}
|
||||
|
||||
// Validate g is a quadratic residue (Jacobi symbol == 1)
|
||||
if big.Jacobi(g, p) != 1 {
|
||||
return nil, fmt.Errorf("g is not a quadratic residue mod p")
|
||||
}
|
||||
|
||||
group := &GqGroup{
|
||||
p: new(big.Int).Set(p),
|
||||
q: new(big.Int).Set(q),
|
||||
}
|
||||
group.generator = GqElement{value: new(big.Int).Set(g), group: group}
|
||||
group.identity = GqElement{value: big.NewInt(1), group: group}
|
||||
|
||||
return group, nil
|
||||
}
|
||||
|
||||
// P returns the modulus p.
|
||||
func (g *GqGroup) P() *big.Int {
|
||||
return new(big.Int).Set(g.p)
|
||||
}
|
||||
|
||||
// Q returns the group order q.
|
||||
func (g *GqGroup) Q() *big.Int {
|
||||
return new(big.Int).Set(g.q)
|
||||
}
|
||||
|
||||
// Generator returns the generator of this group.
|
||||
func (g *GqGroup) Generator() GqElement {
|
||||
return g.generator
|
||||
}
|
||||
|
||||
// Identity returns the identity element (1).
|
||||
func (g *GqGroup) Identity() GqElement {
|
||||
return g.identity
|
||||
}
|
||||
|
||||
// IsGroupMember checks if value is in G_q: value > 0 AND value < p AND Jacobi(value, p) == 1.
|
||||
func (g *GqGroup) IsGroupMember(value *big.Int) bool {
|
||||
if value == nil {
|
||||
return false
|
||||
}
|
||||
if value.Sign() <= 0 || value.Cmp(g.p) >= 0 {
|
||||
return false
|
||||
}
|
||||
return big.Jacobi(value, g.p) == 1
|
||||
}
|
||||
|
||||
// BitLength returns the bit length of q.
|
||||
func (g *GqGroup) BitLength() int {
|
||||
return g.q.BitLen()
|
||||
}
|
||||
|
||||
// Equals checks if two groups are the same.
|
||||
func (g *GqGroup) Equals(other *GqGroup) bool {
|
||||
if other == nil {
|
||||
return false
|
||||
}
|
||||
return g.p.Cmp(other.p) == 0 && g.q.Cmp(other.q) == 0 && g.generator.value.Cmp(other.generator.value) == 0
|
||||
}
|
||||
280
pkg/math/groupmatrix.go
Normal file
280
pkg/math/groupmatrix.go
Normal file
|
|
@ -0,0 +1,280 @@
|
|||
package math
|
||||
|
||||
// GqMatrix is a matrix of GqElements.
|
||||
type GqMatrix struct {
|
||||
rows []*GqVector
|
||||
group *GqGroup
|
||||
numRows int
|
||||
numCols int
|
||||
}
|
||||
|
||||
// NewGqMatrix creates a matrix from rows.
|
||||
func NewGqMatrix(rows []*GqVector) *GqMatrix {
|
||||
if len(rows) == 0 {
|
||||
panic("matrix must have at least one row")
|
||||
}
|
||||
numCols := rows[0].Size()
|
||||
for i, row := range rows {
|
||||
if row.Size() != numCols {
|
||||
panic("all rows must have the same size")
|
||||
}
|
||||
if i > 0 && !row.group.Equals(rows[0].group) {
|
||||
panic("all rows must be from the same group")
|
||||
}
|
||||
}
|
||||
copied := make([]*GqVector, len(rows))
|
||||
copy(copied, rows)
|
||||
return &GqMatrix{rows: copied, group: rows[0].group, numRows: len(rows), numCols: numCols}
|
||||
}
|
||||
|
||||
// GqMatrixFromColumns creates a matrix from columns.
|
||||
func GqMatrixFromColumns(columns []*GqVector) *GqMatrix {
|
||||
if len(columns) == 0 {
|
||||
panic("matrix must have at least one column")
|
||||
}
|
||||
numRows := columns[0].Size()
|
||||
rows := make([]*GqVector, numRows)
|
||||
for i := 0; i < numRows; i++ {
|
||||
elems := make([]GqElement, len(columns))
|
||||
for j, col := range columns {
|
||||
elems[j] = col.Get(i)
|
||||
}
|
||||
rows[i] = &GqVector{elements: elems, group: columns[0].group}
|
||||
}
|
||||
return NewGqMatrix(rows)
|
||||
}
|
||||
|
||||
// NumRows returns the number of rows.
|
||||
func (m *GqMatrix) NumRows() int {
|
||||
return m.numRows
|
||||
}
|
||||
|
||||
// NumCols returns the number of columns.
|
||||
func (m *GqMatrix) NumCols() int {
|
||||
return m.numCols
|
||||
}
|
||||
|
||||
// Group returns the common group.
|
||||
func (m *GqMatrix) Group() *GqGroup {
|
||||
return m.group
|
||||
}
|
||||
|
||||
// Get returns the element at (row, col).
|
||||
func (m *GqMatrix) Get(row, col int) GqElement {
|
||||
return m.rows[row].Get(col)
|
||||
}
|
||||
|
||||
// GetRow returns a row as a GqVector.
|
||||
func (m *GqMatrix) GetRow(i int) *GqVector {
|
||||
return m.rows[i]
|
||||
}
|
||||
|
||||
// GetColumn returns a column as a GqVector.
|
||||
func (m *GqMatrix) GetColumn(j int) *GqVector {
|
||||
elems := make([]GqElement, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
elems[i] = m.rows[i].Get(j)
|
||||
}
|
||||
return &GqVector{elements: elems, group: m.group}
|
||||
}
|
||||
|
||||
// Transpose returns the transpose of this matrix.
|
||||
func (m *GqMatrix) Transpose() *GqMatrix {
|
||||
rows := make([]*GqVector, m.numCols)
|
||||
for j := 0; j < m.numCols; j++ {
|
||||
rows[j] = m.GetColumn(j)
|
||||
}
|
||||
return &GqMatrix{rows: rows, group: m.group, numRows: m.numCols, numCols: m.numRows}
|
||||
}
|
||||
|
||||
// AppendColumn creates a new matrix with a column appended.
|
||||
func (m *GqMatrix) AppendColumn(column *GqVector) *GqMatrix {
|
||||
if column.Size() != m.numRows {
|
||||
panic("column size must match number of rows")
|
||||
}
|
||||
rows := make([]*GqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].Append(column.Get(i))
|
||||
}
|
||||
return NewGqMatrix(rows)
|
||||
}
|
||||
|
||||
// PrependColumn creates a new matrix with a column prepended.
|
||||
func (m *GqMatrix) PrependColumn(column *GqVector) *GqMatrix {
|
||||
if column.Size() != m.numRows {
|
||||
panic("column size must match number of rows")
|
||||
}
|
||||
rows := make([]*GqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].Prepend(column.Get(i))
|
||||
}
|
||||
return NewGqMatrix(rows)
|
||||
}
|
||||
|
||||
// SubColumns returns a matrix with columns [from, to).
|
||||
func (m *GqMatrix) SubColumns(from, to int) *GqMatrix {
|
||||
rows := make([]*GqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].SubVector(from, to)
|
||||
}
|
||||
return NewGqMatrix(rows)
|
||||
}
|
||||
|
||||
// FlatElements returns all elements row by row.
|
||||
func (m *GqMatrix) FlatElements() []GqElement {
|
||||
result := make([]GqElement, 0, m.numRows*m.numCols)
|
||||
for _, row := range m.rows {
|
||||
result = append(result, row.elements...)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// ZqMatrix is a matrix of ZqElements.
|
||||
type ZqMatrix struct {
|
||||
rows []*ZqVector
|
||||
group *ZqGroup
|
||||
numRows int
|
||||
numCols int
|
||||
}
|
||||
|
||||
// NewZqMatrix creates a matrix from rows.
|
||||
func NewZqMatrix(rows []*ZqVector) *ZqMatrix {
|
||||
if len(rows) == 0 {
|
||||
panic("matrix must have at least one row")
|
||||
}
|
||||
numCols := rows[0].Size()
|
||||
for _, row := range rows {
|
||||
if row.Size() != numCols {
|
||||
panic("all rows must have the same size")
|
||||
}
|
||||
}
|
||||
copied := make([]*ZqVector, len(rows))
|
||||
copy(copied, rows)
|
||||
return &ZqMatrix{rows: copied, group: rows[0].group, numRows: len(rows), numCols: numCols}
|
||||
}
|
||||
|
||||
// ZqMatrixFromColumns creates a ZqMatrix from columns.
|
||||
func ZqMatrixFromColumns(columns []*ZqVector) *ZqMatrix {
|
||||
if len(columns) == 0 {
|
||||
panic("matrix must have at least one column")
|
||||
}
|
||||
numRows := columns[0].Size()
|
||||
rows := make([]*ZqVector, numRows)
|
||||
for i := 0; i < numRows; i++ {
|
||||
elems := make([]ZqElement, len(columns))
|
||||
for j, col := range columns {
|
||||
elems[j] = col.Get(i)
|
||||
}
|
||||
rows[i] = &ZqVector{elements: elems, group: columns[0].group}
|
||||
}
|
||||
return NewZqMatrix(rows)
|
||||
}
|
||||
|
||||
// NumRows returns the number of rows.
|
||||
func (m *ZqMatrix) NumRows() int {
|
||||
return m.numRows
|
||||
}
|
||||
|
||||
// NumCols returns the number of columns.
|
||||
func (m *ZqMatrix) NumCols() int {
|
||||
return m.numCols
|
||||
}
|
||||
|
||||
// Group returns the common group.
|
||||
func (m *ZqMatrix) Group() *ZqGroup {
|
||||
return m.group
|
||||
}
|
||||
|
||||
// Get returns the element at (row, col).
|
||||
func (m *ZqMatrix) Get(row, col int) ZqElement {
|
||||
return m.rows[row].Get(col)
|
||||
}
|
||||
|
||||
// GetRow returns a row as a ZqVector.
|
||||
func (m *ZqMatrix) GetRow(i int) *ZqVector {
|
||||
return m.rows[i]
|
||||
}
|
||||
|
||||
// GetColumn returns a column as a ZqVector.
|
||||
func (m *ZqMatrix) GetColumn(j int) *ZqVector {
|
||||
elems := make([]ZqElement, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
elems[i] = m.rows[i].Get(j)
|
||||
}
|
||||
return &ZqVector{elements: elems, group: m.group}
|
||||
}
|
||||
|
||||
// Transpose returns the transpose.
|
||||
func (m *ZqMatrix) Transpose() *ZqMatrix {
|
||||
rows := make([]*ZqVector, m.numCols)
|
||||
for j := 0; j < m.numCols; j++ {
|
||||
rows[j] = m.GetColumn(j)
|
||||
}
|
||||
return &ZqMatrix{rows: rows, group: m.group, numRows: m.numCols, numCols: m.numRows}
|
||||
}
|
||||
|
||||
// AppendColumn creates a new matrix with a column appended.
|
||||
func (m *ZqMatrix) AppendColumn(column *ZqVector) *ZqMatrix {
|
||||
if column.Size() != m.numRows {
|
||||
panic("column size must match number of rows")
|
||||
}
|
||||
rows := make([]*ZqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].Append(column.Get(i))
|
||||
}
|
||||
return NewZqMatrix(rows)
|
||||
}
|
||||
|
||||
// PrependColumn creates a new matrix with a column prepended.
|
||||
func (m *ZqMatrix) PrependColumn(column *ZqVector) *ZqMatrix {
|
||||
if column.Size() != m.numRows {
|
||||
panic("column size must match number of rows")
|
||||
}
|
||||
rows := make([]*ZqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].Prepend(column.Get(i))
|
||||
}
|
||||
return NewZqMatrix(rows)
|
||||
}
|
||||
|
||||
// SubColumns returns a matrix with columns [from, to).
|
||||
func (m *ZqMatrix) SubColumns(from, to int) *ZqMatrix {
|
||||
rows := make([]*ZqVector, m.numRows)
|
||||
for i := 0; i < m.numRows; i++ {
|
||||
rows[i] = m.rows[i].SubVector(from, to)
|
||||
}
|
||||
return NewZqMatrix(rows)
|
||||
}
|
||||
|
||||
// FlatElements returns all elements row by row.
|
||||
func (m *ZqMatrix) FlatElements() []ZqElement {
|
||||
result := make([]ZqElement, 0, m.numRows*m.numCols)
|
||||
for _, row := range m.rows {
|
||||
result = append(result, row.elements...)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// VectorToGqMatrix reshapes a flat GqVector into a matrix of numRows x numCols.
|
||||
func VectorToGqMatrix(v *GqVector, numRows, numCols int) *GqMatrix {
|
||||
if v.Size() != numRows*numCols {
|
||||
panic("vector size must equal numRows * numCols")
|
||||
}
|
||||
rows := make([]*GqVector, numRows)
|
||||
for i := 0; i < numRows; i++ {
|
||||
rows[i] = v.SubVector(i*numCols, (i+1)*numCols)
|
||||
}
|
||||
return NewGqMatrix(rows)
|
||||
}
|
||||
|
||||
// VectorToZqMatrix reshapes a flat ZqVector into a matrix.
|
||||
func VectorToZqMatrix(v *ZqVector, numRows, numCols int) *ZqMatrix {
|
||||
if v.Size() != numRows*numCols {
|
||||
panic("vector size must equal numRows * numCols")
|
||||
}
|
||||
rows := make([]*ZqVector, numRows)
|
||||
for i := 0; i < numRows; i++ {
|
||||
rows[i] = v.SubVector(i*numCols, (i+1)*numCols)
|
||||
}
|
||||
return NewZqMatrix(rows)
|
||||
}
|
||||
384
pkg/math/groupvector.go
Normal file
384
pkg/math/groupvector.go
Normal file
|
|
@ -0,0 +1,384 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
"runtime"
|
||||
"sync"
|
||||
)
|
||||
|
||||
// GqVector is a vector of GqElements from the same group.
|
||||
type GqVector struct {
|
||||
elements []GqElement
|
||||
group *GqGroup
|
||||
}
|
||||
|
||||
// NewGqVector creates a new GqVector, validating all elements are from the same group.
|
||||
func NewGqVector(elements []GqElement) (*GqVector, error) {
|
||||
if len(elements) == 0 {
|
||||
return &GqVector{elements: []GqElement{}}, nil
|
||||
}
|
||||
group := elements[0].group
|
||||
for i, e := range elements {
|
||||
if !e.group.Equals(group) {
|
||||
return nil, fmt.Errorf("element %d is from a different group", i)
|
||||
}
|
||||
}
|
||||
copied := make([]GqElement, len(elements))
|
||||
copy(copied, elements)
|
||||
return &GqVector{elements: copied, group: group}, nil
|
||||
}
|
||||
|
||||
// GqVectorOf creates a GqVector from variadic elements (no validation).
|
||||
func GqVectorOf(elements ...GqElement) *GqVector {
|
||||
if len(elements) == 0 {
|
||||
return &GqVector{elements: []GqElement{}}
|
||||
}
|
||||
copied := make([]GqElement, len(elements))
|
||||
copy(copied, elements)
|
||||
return &GqVector{elements: copied, group: elements[0].group}
|
||||
}
|
||||
|
||||
// GqVectorFromBigInts creates a GqVector from big.Int values in the given group.
|
||||
func GqVectorFromBigInts(values []*big.Int, group *GqGroup) (*GqVector, error) {
|
||||
elements := make([]GqElement, len(values))
|
||||
for i, v := range values {
|
||||
e, err := NewGqElement(v, group)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("element %d: %w", i, err)
|
||||
}
|
||||
elements[i] = e
|
||||
}
|
||||
return &GqVector{elements: elements, group: group}, nil
|
||||
}
|
||||
|
||||
// GqVectorOfIdentities creates a vector of identity elements.
|
||||
func GqVectorOfIdentities(size int, group *GqGroup) *GqVector {
|
||||
elements := make([]GqElement, size)
|
||||
for i := range elements {
|
||||
elements[i] = group.Identity()
|
||||
}
|
||||
return &GqVector{elements: elements, group: group}
|
||||
}
|
||||
|
||||
// Size returns the number of elements.
|
||||
func (v *GqVector) Size() int {
|
||||
return len(v.elements)
|
||||
}
|
||||
|
||||
// Get returns the element at index i.
|
||||
func (v *GqVector) Get(i int) GqElement {
|
||||
return v.elements[i]
|
||||
}
|
||||
|
||||
// Group returns the common group.
|
||||
func (v *GqVector) Group() *GqGroup {
|
||||
return v.group
|
||||
}
|
||||
|
||||
// Elements returns a copy of the elements slice.
|
||||
func (v *GqVector) Elements() []GqElement {
|
||||
copied := make([]GqElement, len(v.elements))
|
||||
copy(copied, v.elements)
|
||||
return copied
|
||||
}
|
||||
|
||||
// Append creates a new vector with the element appended.
|
||||
func (v *GqVector) Append(e GqElement) *GqVector {
|
||||
newElems := make([]GqElement, len(v.elements)+1)
|
||||
copy(newElems, v.elements)
|
||||
newElems[len(v.elements)] = e
|
||||
group := v.group
|
||||
if group == nil {
|
||||
group = e.group
|
||||
}
|
||||
return &GqVector{elements: newElems, group: group}
|
||||
}
|
||||
|
||||
// Prepend creates a new vector with the element prepended.
|
||||
func (v *GqVector) Prepend(e GqElement) *GqVector {
|
||||
newElems := make([]GqElement, len(v.elements)+1)
|
||||
newElems[0] = e
|
||||
copy(newElems[1:], v.elements)
|
||||
group := v.group
|
||||
if group == nil {
|
||||
group = e.group
|
||||
}
|
||||
return &GqVector{elements: newElems, group: group}
|
||||
}
|
||||
|
||||
// SubVector returns a sub-vector [from, to).
|
||||
func (v *GqVector) SubVector(from, to int) *GqVector {
|
||||
elems := make([]GqElement, to-from)
|
||||
copy(elems, v.elements[from:to])
|
||||
return &GqVector{elements: elems, group: v.group}
|
||||
}
|
||||
|
||||
// Multiply returns element-wise product of two vectors.
|
||||
func (v *GqVector) Multiply(other *GqVector) *GqVector {
|
||||
if v.Size() != other.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]GqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Multiply(other.elements[i])
|
||||
}
|
||||
return &GqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// Exponentiate returns each element raised to the corresponding exponent.
|
||||
func (v *GqVector) Exponentiate(exponents *ZqVector) *GqVector {
|
||||
if v.Size() != exponents.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]GqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Exponentiate(exponents.elements[i])
|
||||
}
|
||||
return &GqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// ExpScalar returns each element raised to the same scalar exponent.
|
||||
func (v *GqVector) ExpScalar(exponent ZqElement) *GqVector {
|
||||
result := make([]GqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Exponentiate(exponent)
|
||||
}
|
||||
return &GqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// Product returns the product of all elements.
|
||||
func (v *GqVector) Product() GqElement {
|
||||
if v.Size() == 0 {
|
||||
panic("cannot take product of empty vector")
|
||||
}
|
||||
result := v.elements[0]
|
||||
for i := 1; i < len(v.elements); i++ {
|
||||
result = result.Multiply(v.elements[i])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// Map applies fn to each element and returns a new vector.
|
||||
func (v *GqVector) Map(fn func(GqElement) GqElement) *GqVector {
|
||||
result := make([]GqElement, v.Size())
|
||||
for i, e := range v.elements {
|
||||
result[i] = fn(e)
|
||||
}
|
||||
return &GqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// ParallelMap applies fn to each element in parallel.
|
||||
func (v *GqVector) ParallelMap(fn func(GqElement) GqElement) *GqVector {
|
||||
result := make([]GqElement, v.Size())
|
||||
workers := runtime.NumCPU()
|
||||
if workers > v.Size() {
|
||||
workers = v.Size()
|
||||
}
|
||||
|
||||
var wg sync.WaitGroup
|
||||
ch := make(chan int, v.Size())
|
||||
for i := 0; i < v.Size(); i++ {
|
||||
ch <- i
|
||||
}
|
||||
close(ch)
|
||||
|
||||
wg.Add(workers)
|
||||
for w := 0; w < workers; w++ {
|
||||
go func() {
|
||||
defer wg.Done()
|
||||
for i := range ch {
|
||||
result[i] = fn(v.elements[i])
|
||||
}
|
||||
}()
|
||||
}
|
||||
wg.Wait()
|
||||
return &GqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// ZqVector is a vector of ZqElements from the same group.
|
||||
type ZqVector struct {
|
||||
elements []ZqElement
|
||||
group *ZqGroup
|
||||
}
|
||||
|
||||
// NewZqVector creates a new ZqVector, validating all elements are from the same group.
|
||||
func NewZqVector(elements []ZqElement) (*ZqVector, error) {
|
||||
if len(elements) == 0 {
|
||||
return &ZqVector{elements: []ZqElement{}}, nil
|
||||
}
|
||||
group := elements[0].group
|
||||
for i, e := range elements {
|
||||
if !e.group.Equals(group) {
|
||||
return nil, fmt.Errorf("element %d is from a different group", i)
|
||||
}
|
||||
}
|
||||
copied := make([]ZqElement, len(elements))
|
||||
copy(copied, elements)
|
||||
return &ZqVector{elements: copied, group: group}, nil
|
||||
}
|
||||
|
||||
// ZqVectorOf creates a ZqVector from variadic elements.
|
||||
func ZqVectorOf(elements ...ZqElement) *ZqVector {
|
||||
if len(elements) == 0 {
|
||||
return &ZqVector{elements: []ZqElement{}}
|
||||
}
|
||||
copied := make([]ZqElement, len(elements))
|
||||
copy(copied, elements)
|
||||
return &ZqVector{elements: copied, group: elements[0].group}
|
||||
}
|
||||
|
||||
// ZqVectorFromBigInts creates a ZqVector from big.Int values in the given group.
|
||||
func ZqVectorFromBigInts(values []*big.Int, group *ZqGroup) (*ZqVector, error) {
|
||||
elements := make([]ZqElement, len(values))
|
||||
for i, v := range values {
|
||||
e, err := NewZqElement(v, group)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("element %d: %w", i, err)
|
||||
}
|
||||
elements[i] = e
|
||||
}
|
||||
return &ZqVector{elements: elements, group: group}, nil
|
||||
}
|
||||
|
||||
// ZqVectorOfZeros creates a vector of zero elements.
|
||||
func ZqVectorOfZeros(size int, group *ZqGroup) *ZqVector {
|
||||
elements := make([]ZqElement, size)
|
||||
for i := range elements {
|
||||
elements[i] = group.Identity()
|
||||
}
|
||||
return &ZqVector{elements: elements, group: group}
|
||||
}
|
||||
|
||||
// Size returns the number of elements.
|
||||
func (v *ZqVector) Size() int {
|
||||
return len(v.elements)
|
||||
}
|
||||
|
||||
// Get returns the element at index i.
|
||||
func (v *ZqVector) Get(i int) ZqElement {
|
||||
return v.elements[i]
|
||||
}
|
||||
|
||||
// Group returns the common group.
|
||||
func (v *ZqVector) Group() *ZqGroup {
|
||||
return v.group
|
||||
}
|
||||
|
||||
// Elements returns a copy of the elements slice.
|
||||
func (v *ZqVector) Elements() []ZqElement {
|
||||
copied := make([]ZqElement, len(v.elements))
|
||||
copy(copied, v.elements)
|
||||
return copied
|
||||
}
|
||||
|
||||
// Append creates a new vector with the element appended.
|
||||
func (v *ZqVector) Append(e ZqElement) *ZqVector {
|
||||
newElems := make([]ZqElement, len(v.elements)+1)
|
||||
copy(newElems, v.elements)
|
||||
newElems[len(v.elements)] = e
|
||||
group := v.group
|
||||
if group == nil {
|
||||
group = e.group
|
||||
}
|
||||
return &ZqVector{elements: newElems, group: group}
|
||||
}
|
||||
|
||||
// Prepend creates a new vector with the element prepended.
|
||||
func (v *ZqVector) Prepend(e ZqElement) *ZqVector {
|
||||
newElems := make([]ZqElement, len(v.elements)+1)
|
||||
newElems[0] = e
|
||||
copy(newElems[1:], v.elements)
|
||||
group := v.group
|
||||
if group == nil {
|
||||
group = e.group
|
||||
}
|
||||
return &ZqVector{elements: newElems, group: group}
|
||||
}
|
||||
|
||||
// SubVector returns a sub-vector [from, to).
|
||||
func (v *ZqVector) SubVector(from, to int) *ZqVector {
|
||||
elems := make([]ZqElement, to-from)
|
||||
copy(elems, v.elements[from:to])
|
||||
return &ZqVector{elements: elems, group: v.group}
|
||||
}
|
||||
|
||||
// Add returns element-wise sum of two vectors.
|
||||
func (v *ZqVector) Add(other *ZqVector) *ZqVector {
|
||||
if v.Size() != other.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]ZqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Add(other.elements[i])
|
||||
}
|
||||
return &ZqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// MultiplyElementWise returns element-wise product of two vectors.
|
||||
func (v *ZqVector) MultiplyElementWise(other *ZqVector) *ZqVector {
|
||||
if v.Size() != other.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
result := make([]ZqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Multiply(other.elements[i])
|
||||
}
|
||||
return &ZqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// ScalarMultiply returns each element multiplied by the scalar.
|
||||
func (v *ZqVector) ScalarMultiply(scalar ZqElement) *ZqVector {
|
||||
result := make([]ZqElement, v.Size())
|
||||
for i := range v.elements {
|
||||
result[i] = v.elements[i].Multiply(scalar)
|
||||
}
|
||||
return &ZqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// Sum returns the sum of all elements.
|
||||
func (v *ZqVector) Sum() ZqElement {
|
||||
if v.Size() == 0 {
|
||||
panic("cannot sum empty vector")
|
||||
}
|
||||
result := v.elements[0]
|
||||
for i := 1; i < len(v.elements); i++ {
|
||||
result = result.Add(v.elements[i])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// Product returns the product of all elements.
|
||||
func (v *ZqVector) Product() ZqElement {
|
||||
if v.Size() == 0 {
|
||||
panic("cannot take product of empty vector")
|
||||
}
|
||||
result := v.elements[0]
|
||||
for i := 1; i < len(v.elements); i++ {
|
||||
result = result.Multiply(v.elements[i])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// InnerProduct computes the inner product (dot product) of this vector with a GqVector.
|
||||
// Returns Π(gq[i]^zq[i]).
|
||||
func (v *ZqVector) InnerProduct(bases *GqVector) GqElement {
|
||||
if v.Size() != bases.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
return MultiModExp(bases.elements, v.elements)
|
||||
}
|
||||
|
||||
// Map applies fn to each element.
|
||||
func (v *ZqVector) Map(fn func(ZqElement) ZqElement) *ZqVector {
|
||||
result := make([]ZqElement, v.Size())
|
||||
for i, e := range v.elements {
|
||||
result[i] = fn(e)
|
||||
}
|
||||
return &ZqVector{elements: result, group: v.group}
|
||||
}
|
||||
|
||||
// Negate returns a vector of negated elements.
|
||||
func (v *ZqVector) Negate() *ZqVector {
|
||||
return v.Map(func(e ZqElement) ZqElement { return e.Negate() })
|
||||
}
|
||||
40
pkg/math/primes.go
Normal file
40
pkg/math/primes.go
Normal file
|
|
@ -0,0 +1,40 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// SmallPrimes returns the first n small primes starting from 2.
|
||||
func SmallPrimes(n int) []*big.Int {
|
||||
primes := make([]*big.Int, 0, n)
|
||||
candidate := big.NewInt(2)
|
||||
for len(primes) < n {
|
||||
if candidate.ProbablyPrime(20) {
|
||||
primes = append(primes, new(big.Int).Set(candidate))
|
||||
}
|
||||
candidate = new(big.Int).Add(candidate, big.NewInt(1))
|
||||
}
|
||||
return primes
|
||||
}
|
||||
|
||||
// Factorize attempts to factorize value as a product of elements from allowedPrimes.
|
||||
// Returns the prime factors. Panics if factorization fails.
|
||||
func Factorize(value *big.Int, allowedPrimes []*big.Int) []*big.Int {
|
||||
remaining := new(big.Int).Set(value)
|
||||
factors := make([]*big.Int, 0)
|
||||
for _, p := range allowedPrimes {
|
||||
for {
|
||||
quo, rem := new(big.Int).DivMod(remaining, p, new(big.Int))
|
||||
if rem.Sign() == 0 {
|
||||
factors = append(factors, new(big.Int).Set(p))
|
||||
remaining = quo
|
||||
} else {
|
||||
break
|
||||
}
|
||||
}
|
||||
}
|
||||
if remaining.Cmp(big.NewInt(1)) != 0 {
|
||||
panic("factorization failed: remaining = " + remaining.String())
|
||||
}
|
||||
return factors
|
||||
}
|
||||
60
pkg/math/random.go
Normal file
60
pkg/math/random.go
Normal file
|
|
@ -0,0 +1,60 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"crypto/rand"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// RandomZqElement generates a random element in Z_q.
|
||||
func RandomZqElement(group *ZqGroup) ZqElement {
|
||||
for {
|
||||
r, err := rand.Int(rand.Reader, group.q)
|
||||
if err != nil {
|
||||
panic("crypto/rand failed: " + err.Error())
|
||||
}
|
||||
return ZqElement{value: r, group: group}
|
||||
}
|
||||
}
|
||||
|
||||
// RandomZqVector generates a vector of n random elements in Z_q.
|
||||
func RandomZqVector(n int, group *ZqGroup) *ZqVector {
|
||||
elements := make([]ZqElement, n)
|
||||
for i := range elements {
|
||||
elements[i] = RandomZqElement(group)
|
||||
}
|
||||
return &ZqVector{elements: elements, group: group}
|
||||
}
|
||||
|
||||
// RandomGqElement generates a random element in G_q by squaring a random value.
|
||||
func RandomGqElement(group *GqGroup) GqElement {
|
||||
for {
|
||||
// Generate random value in [1, q)
|
||||
r, err := rand.Int(rand.Reader, new(big.Int).Sub(group.q, big.NewInt(1)))
|
||||
if err != nil {
|
||||
panic("crypto/rand failed: " + err.Error())
|
||||
}
|
||||
r.Add(r, big.NewInt(1)) // Shift to [1, q)
|
||||
// Square to get quadratic residue
|
||||
squared := new(big.Int).Exp(r, big.NewInt(2), group.p)
|
||||
return GqElement{value: squared, group: group}
|
||||
}
|
||||
}
|
||||
|
||||
// RandomBigInt generates a random big.Int in [0, max).
|
||||
func RandomBigInt(max *big.Int) *big.Int {
|
||||
r, err := rand.Int(rand.Reader, max)
|
||||
if err != nil {
|
||||
panic("crypto/rand failed: " + err.Error())
|
||||
}
|
||||
return r
|
||||
}
|
||||
|
||||
// RandomNonZeroZqElement generates a random non-zero element in Z_q.
|
||||
func RandomNonZeroZqElement(group *ZqGroup) ZqElement {
|
||||
for {
|
||||
e := RandomZqElement(group)
|
||||
if !e.IsZero() {
|
||||
return e
|
||||
}
|
||||
}
|
||||
}
|
||||
116
pkg/math/zqelement.go
Normal file
116
pkg/math/zqelement.go
Normal file
|
|
@ -0,0 +1,116 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// ZqElement represents an element of the group Z_q.
|
||||
// Immutable: all operations return new instances.
|
||||
type ZqElement struct {
|
||||
value *big.Int
|
||||
group *ZqGroup
|
||||
}
|
||||
|
||||
// NewZqElement creates a ZqElement from a value, validating group membership.
|
||||
func NewZqElement(value *big.Int, group *ZqGroup) (ZqElement, error) {
|
||||
if value == nil || group == nil {
|
||||
return ZqElement{}, fmt.Errorf("value and group must not be nil")
|
||||
}
|
||||
if !group.IsGroupMember(value) {
|
||||
return ZqElement{}, fmt.Errorf("value %v is not a member of Z_q (q=%v)", value, group.q)
|
||||
}
|
||||
return ZqElement{value: new(big.Int).Set(value), group: group}, nil
|
||||
}
|
||||
|
||||
// NewZqElementFromInt creates a ZqElement from an int.
|
||||
func NewZqElementFromInt(value int, group *ZqGroup) (ZqElement, error) {
|
||||
return NewZqElement(big.NewInt(int64(value)), group)
|
||||
}
|
||||
|
||||
// zqElementUnchecked creates a ZqElement without validation.
|
||||
func zqElementUnchecked(value *big.Int, group *ZqGroup) ZqElement {
|
||||
return ZqElement{value: new(big.Int).Set(value), group: group}
|
||||
}
|
||||
|
||||
// Value returns the element's value as a new big.Int.
|
||||
func (e ZqElement) Value() *big.Int {
|
||||
return new(big.Int).Set(e.value)
|
||||
}
|
||||
|
||||
// Group returns the element's group.
|
||||
func (e ZqElement) Group() *ZqGroup {
|
||||
return e.group
|
||||
}
|
||||
|
||||
// Add returns (this + other) mod q.
|
||||
func (e ZqElement) Add(other ZqElement) ZqElement {
|
||||
e.checkSameGroup(other)
|
||||
result := new(big.Int).Add(e.value, other.value)
|
||||
result.Mod(result, e.group.q)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Subtract returns (this - other) mod q.
|
||||
func (e ZqElement) Subtract(other ZqElement) ZqElement {
|
||||
e.checkSameGroup(other)
|
||||
result := new(big.Int).Sub(e.value, other.value)
|
||||
result.Mod(result, e.group.q)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Multiply returns (this * other) mod q.
|
||||
func (e ZqElement) Multiply(other ZqElement) ZqElement {
|
||||
e.checkSameGroup(other)
|
||||
result := new(big.Int).Mul(e.value, other.value)
|
||||
result.Mod(result, e.group.q)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Exponentiate returns this^exponent mod q.
|
||||
func (e ZqElement) Exponentiate(exponent *big.Int) ZqElement {
|
||||
if exponent.Sign() < 0 {
|
||||
panic("exponent must be non-negative")
|
||||
}
|
||||
result := new(big.Int).Exp(e.value, exponent, e.group.q)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Negate returns (-this) mod q.
|
||||
func (e ZqElement) Negate() ZqElement {
|
||||
if e.value.Sign() == 0 {
|
||||
return ZqElement{value: big.NewInt(0), group: e.group}
|
||||
}
|
||||
result := new(big.Int).Sub(e.group.q, e.value)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// Invert returns this^(-1) mod q.
|
||||
func (e ZqElement) Invert() ZqElement {
|
||||
if e.value.Sign() == 0 {
|
||||
panic("cannot invert zero element")
|
||||
}
|
||||
result := new(big.Int).ModInverse(e.value, e.group.q)
|
||||
return ZqElement{value: result, group: e.group}
|
||||
}
|
||||
|
||||
// IsZero checks if this element is zero.
|
||||
func (e ZqElement) IsZero() bool {
|
||||
return e.value.Sign() == 0
|
||||
}
|
||||
|
||||
// Equals checks if two elements have the same value and group.
|
||||
func (e ZqElement) Equals(other ZqElement) bool {
|
||||
return e.value.Cmp(other.value) == 0 && e.group.Equals(other.group)
|
||||
}
|
||||
|
||||
func (e ZqElement) checkSameGroup(other ZqElement) {
|
||||
if !e.group.Equals(other.group) {
|
||||
panic(fmt.Sprintf("elements must be from the same group"))
|
||||
}
|
||||
}
|
||||
|
||||
// String returns the string representation.
|
||||
func (e ZqElement) String() string {
|
||||
return e.value.String()
|
||||
}
|
||||
67
pkg/math/zqgroup.go
Normal file
67
pkg/math/zqgroup.go
Normal file
|
|
@ -0,0 +1,67 @@
|
|||
package math
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// ZqGroup represents the group of integers modulo q.
|
||||
type ZqGroup struct {
|
||||
q *big.Int
|
||||
identity ZqElement
|
||||
}
|
||||
|
||||
// NewZqGroup creates a new ZqGroup with the given order q.
|
||||
func NewZqGroup(q *big.Int) (*ZqGroup, error) {
|
||||
if q == nil {
|
||||
return nil, fmt.Errorf("q must not be nil")
|
||||
}
|
||||
if q.Cmp(big.NewInt(2)) < 0 {
|
||||
return nil, fmt.Errorf("q must be >= 2")
|
||||
}
|
||||
group := &ZqGroup{
|
||||
q: new(big.Int).Set(q),
|
||||
}
|
||||
group.identity = ZqElement{value: big.NewInt(0), group: group}
|
||||
return group, nil
|
||||
}
|
||||
|
||||
// ZqGroupFromGqGroup creates a ZqGroup with the same order as the given GqGroup.
|
||||
func ZqGroupFromGqGroup(gqGroup *GqGroup) *ZqGroup {
|
||||
group := &ZqGroup{
|
||||
q: new(big.Int).Set(gqGroup.q),
|
||||
}
|
||||
group.identity = ZqElement{value: big.NewInt(0), group: group}
|
||||
return group
|
||||
}
|
||||
|
||||
// Q returns the group order q.
|
||||
func (g *ZqGroup) Q() *big.Int {
|
||||
return new(big.Int).Set(g.q)
|
||||
}
|
||||
|
||||
// Identity returns the identity element (0).
|
||||
func (g *ZqGroup) Identity() ZqElement {
|
||||
return g.identity
|
||||
}
|
||||
|
||||
// IsGroupMember checks if value is in Z_q: value >= 0 AND value < q.
|
||||
func (g *ZqGroup) IsGroupMember(value *big.Int) bool {
|
||||
if value == nil {
|
||||
return false
|
||||
}
|
||||
return value.Sign() >= 0 && value.Cmp(g.q) < 0
|
||||
}
|
||||
|
||||
// Equals checks if two groups have the same order.
|
||||
func (g *ZqGroup) Equals(other *ZqGroup) bool {
|
||||
if other == nil {
|
||||
return false
|
||||
}
|
||||
return g.q.Cmp(other.q) == 0
|
||||
}
|
||||
|
||||
// String returns a string representation.
|
||||
func (g *ZqGroup) String() string {
|
||||
return fmt.Sprintf("ZqGroup(q=%v)", g.q)
|
||||
}
|
||||
105
pkg/mixnet/commitment.go
Normal file
105
pkg/mixnet/commitment.go
Normal file
|
|
@ -0,0 +1,105 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
var oneBI = big.NewInt(1)
|
||||
|
||||
// CommitmentKey represents a Pedersen commitment key (h, g_1, ..., g_v).
|
||||
type CommitmentKey struct {
|
||||
H emath.GqElement // First element h
|
||||
G *emath.GqVector // Elements g_1, ..., g_v
|
||||
}
|
||||
|
||||
// Size returns v (the number of g elements, not counting h).
|
||||
func (ck CommitmentKey) Size() int {
|
||||
return ck.G.Size()
|
||||
}
|
||||
|
||||
// Group returns the group of this commitment key.
|
||||
func (ck CommitmentKey) Group() *emath.GqGroup {
|
||||
return ck.H.Group()
|
||||
}
|
||||
|
||||
// GenCommitmentKey generates a verifiable Pedersen commitment key.
|
||||
// Uses hash-based generation: w = (hash(q, "commitmentKey", i, count) + 1)^2 mod p
|
||||
func GenCommitmentKey(numElements int, group *emath.GqGroup) CommitmentKey {
|
||||
q := group.Q()
|
||||
p := group.P()
|
||||
g := group.Generator()
|
||||
|
||||
var values []emath.GqElement
|
||||
count := 0
|
||||
i := 0
|
||||
|
||||
for count <= numElements {
|
||||
// u = RecursiveHashToZq(q, "commitmentKey", q, i, count) + 1
|
||||
u := hash.RecursiveHashToZq(q,
|
||||
hash.HashableString{Value: "commitmentKey"},
|
||||
hash.HashableBigInt{Value: q},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(i))},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(count))},
|
||||
)
|
||||
uPlusOne := new(big.Int).Add(u, oneBI)
|
||||
|
||||
// w = uPlusOne^2 mod p
|
||||
w := new(big.Int).Exp(uPlusOne, big.NewInt(2), p)
|
||||
|
||||
// Check w != 1 AND w != g AND w not already in values
|
||||
wIsOne := w.Cmp(oneBI) == 0
|
||||
wIsG := w.Cmp(g.Value()) == 0
|
||||
wInValues := false
|
||||
for _, v := range values {
|
||||
if v.Value().Cmp(w) == 0 {
|
||||
wInValues = true
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
if !wIsOne && !wIsG && !wInValues {
|
||||
elem, _ := emath.NewGqElement(w, group)
|
||||
values = append(values, elem)
|
||||
count++
|
||||
}
|
||||
i++
|
||||
}
|
||||
|
||||
// h = values[0], g = values[1..numElements]
|
||||
gElems := make([]emath.GqElement, numElements)
|
||||
copy(gElems, values[1:numElements+1])
|
||||
|
||||
return CommitmentKey{
|
||||
H: values[0],
|
||||
G: emath.GqVectorOf(gElems...),
|
||||
}
|
||||
}
|
||||
|
||||
// Commit computes a Pedersen commitment: C = h^r * Π(g_i^a_i)
|
||||
func (ck CommitmentKey) Commit(a *emath.ZqVector, r emath.ZqElement) emath.GqElement {
|
||||
if a.Size() > ck.Size() {
|
||||
panic("vector size must not exceed commitment key size")
|
||||
}
|
||||
// h^r
|
||||
result := ck.H.Exponentiate(r)
|
||||
// Π(g_i^a_i)
|
||||
for i := 0; i < a.Size(); i++ {
|
||||
result = result.Multiply(ck.G.Get(i).Exponentiate(a.Get(i)))
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// CommitMatrix computes commitments to each column of a matrix.
|
||||
func (ck CommitmentKey) CommitMatrix(A *emath.ZqMatrix, r *emath.ZqVector) *emath.GqVector {
|
||||
if A.NumCols() != r.Size() {
|
||||
panic("number of columns must match randomness vector size")
|
||||
}
|
||||
commitments := make([]emath.GqElement, A.NumCols())
|
||||
for j := 0; j < A.NumCols(); j++ {
|
||||
commitments[j] = ck.Commit(A.GetColumn(j), r.Get(j))
|
||||
}
|
||||
return emath.GqVectorOf(commitments...)
|
||||
}
|
||||
249
pkg/mixnet/hadamard_argument.go
Normal file
249
pkg/mixnet/hadamard_argument.go
Normal file
|
|
@ -0,0 +1,249 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// HadamardArgument proves that b = ∏_j a_j (entrywise Hadamard product).
|
||||
type HadamardArgument struct {
|
||||
CB *emath.GqVector // Intermediate commitments (size m)
|
||||
Zero ZeroArgument // Nested ZeroArgument
|
||||
}
|
||||
|
||||
// GenHadamardArgument generates a Hadamard argument.
|
||||
func GenHadamardArgument(
|
||||
cA *emath.GqVector, // Commitments to A columns (size m)
|
||||
cb emath.GqElement, // Commitment to b (Hadamard product)
|
||||
A *emath.ZqMatrix, // n×m matrix
|
||||
b *emath.ZqVector, // Hadamard product (size n)
|
||||
r *emath.ZqVector, // Randomness for A columns (size m)
|
||||
s emath.ZqElement, // Randomness for cb
|
||||
pk elgamal.PublicKey, // Public key (needed for Fiat-Shamir hash)
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) HadamardArgument {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
n := A.NumRows()
|
||||
m := A.NumCols()
|
||||
|
||||
// 1. Compute intermediate products b_j = ∏_{i=0}^j A[:,i] (entrywise)
|
||||
bIntermediate := make([]*emath.ZqVector, m)
|
||||
bIntermediate[0] = A.GetColumn(0)
|
||||
for j := 1; j < m; j++ {
|
||||
bIntermediate[j] = bIntermediate[j-1].MultiplyElementWise(A.GetColumn(j))
|
||||
}
|
||||
|
||||
// 2. Build c_B and s_vector
|
||||
cbVec := make([]emath.GqElement, m)
|
||||
sVec := make([]emath.ZqElement, m)
|
||||
cbVec[0] = cA.Get(0)
|
||||
sVec[0] = r.Get(0)
|
||||
for j := 1; j < m-1; j++ {
|
||||
sVec[j] = emath.RandomZqElement(zqGroup)
|
||||
cbVec[j] = ck.Commit(bIntermediate[j], sVec[j])
|
||||
}
|
||||
cbVec[m-1] = cb
|
||||
sVec[m-1] = s
|
||||
cB := emath.GqVectorOf(cbVec...)
|
||||
|
||||
// 3. Fiat-Shamir for x
|
||||
// Java hash order: (p, q, pk, ck, c_A, c_b, c_B)
|
||||
x := hadamardChallengeX(group, pk, &ck, cA, cb, cB)
|
||||
|
||||
// 4. Compute x^i powers
|
||||
xPowers := computeXPowers(x, m+1, zqGroup)
|
||||
|
||||
// 5. Fiat-Shamir for y (with "1" prefix)
|
||||
// Java hash order: ("1", p, q, pk, ck, c_A, c_b, c_B)
|
||||
y := hadamardChallengeY(group, pk, &ck, cA, cb, cB)
|
||||
|
||||
// 6. Prepare ZeroArgument matrices
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), zqGroup)
|
||||
negOnes := make([]emath.ZqElement, n)
|
||||
for i := range negOnes {
|
||||
negOnes[i] = one.Negate()
|
||||
}
|
||||
|
||||
aZeroCols := make([]*emath.ZqVector, m)
|
||||
for j := 0; j < m-1; j++ {
|
||||
aZeroCols[j] = A.GetColumn(j + 1)
|
||||
}
|
||||
aZeroCols[m-1] = emath.ZqVectorOf(negOnes...)
|
||||
|
||||
// Java: d_matrix[i] = x^(i+1) * b_vectors[i] for i=0..m-2
|
||||
dZeroCols := make([]*emath.ZqVector, m)
|
||||
for i := 0; i < m-1; i++ {
|
||||
dZeroCols[i] = bIntermediate[i].ScalarMultiply(xPowers[i+1])
|
||||
}
|
||||
// Java: d[j] = Σ(i=1..m-1) x^i * b_vectors[i][j]
|
||||
dFinal := emath.ZqVectorOfZeros(n, zqGroup)
|
||||
for i := 1; i < m; i++ {
|
||||
dFinal = dFinal.Add(bIntermediate[i].ScalarMultiply(xPowers[i]))
|
||||
}
|
||||
dZeroCols[m-1] = dFinal
|
||||
|
||||
// Build c_A_zero and c_D_zero
|
||||
// Java: r_zero = [r[1:], 0] — last randomness is 0, not random
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
cAZero := make([]emath.GqElement, m)
|
||||
rZero := make([]emath.ZqElement, m)
|
||||
for j := 0; j < m-1; j++ {
|
||||
cAZero[j] = cA.Get(j + 1)
|
||||
rZero[j] = r.Get(j + 1)
|
||||
}
|
||||
// Java: c_minus_one = commit((-1,...,-1), 0)
|
||||
cAZero[m-1] = ck.Commit(emath.ZqVectorOf(negOnes...), zero)
|
||||
rZero[m-1] = zero
|
||||
|
||||
// Java: c_D_vector[i] = c_B[i]^(x^(i+1)) for i=0..m-2
|
||||
cDZero := make([]emath.GqElement, m)
|
||||
sDZero := make([]emath.ZqElement, m)
|
||||
for i := 0; i < m-1; i++ {
|
||||
sDZero[i] = sVec[i].Multiply(xPowers[i+1])
|
||||
cDZero[i] = cB.Get(i).Exponentiate(xPowers[i+1])
|
||||
}
|
||||
// Java: t = Σ(i=1..m-1) x^i * s_vector[i]
|
||||
sDFinal := zqGroup.Identity()
|
||||
for i := 1; i < m; i++ {
|
||||
sDFinal = sDFinal.Add(sVec[i].Multiply(xPowers[i]))
|
||||
}
|
||||
sDZero[m-1] = sDFinal
|
||||
// Java: c_D = Π(i=1..m-1) c_B[i]^(x^i)
|
||||
cDFinal := group.Identity()
|
||||
for i := 1; i < m; i++ {
|
||||
cDFinal = cDFinal.Multiply(cB.Get(i).Exponentiate(xPowers[i]))
|
||||
}
|
||||
cDZero[m-1] = cDFinal
|
||||
|
||||
// Build matrices
|
||||
aZeroMatrix := emath.ZqMatrixFromColumns(aZeroCols)
|
||||
dZeroMatrix := emath.ZqMatrixFromColumns(dZeroCols)
|
||||
|
||||
cAZeroVec := emath.GqVectorOf(cAZero...)
|
||||
cDZeroVec := emath.GqVectorOf(cDZero...)
|
||||
rZeroVec := emath.ZqVectorOf(rZero...)
|
||||
sDZeroVec := emath.ZqVectorOf(sDZero...)
|
||||
|
||||
// 7. Generate ZeroArgument (now with pk)
|
||||
zeroArg := GenZeroArgument(cAZeroVec, cDZeroVec, aZeroMatrix, dZeroMatrix, rZeroVec, sDZeroVec, y, pk, ck, group)
|
||||
|
||||
return HadamardArgument{
|
||||
CB: cB,
|
||||
Zero: zeroArg,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyHadamardArgument verifies a Hadamard argument.
|
||||
func VerifyHadamardArgument(
|
||||
arg HadamardArgument,
|
||||
cA *emath.GqVector,
|
||||
cb emath.GqElement,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
m := cA.Size()
|
||||
|
||||
// Check c_B[0] = c_A[0]
|
||||
if !arg.CB.Get(0).Equals(cA.Get(0)) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check c_B[m-1] = c_b
|
||||
if !arg.CB.Get(m - 1).Equals(cb) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Reconstruct x and y
|
||||
x := hadamardChallengeX(group, pk, &ck, cA, cb, arg.CB)
|
||||
y := hadamardChallengeY(group, pk, &ck, cA, cb, arg.CB)
|
||||
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
xPowers := computeXPowers(x, m+1, zqGroup)
|
||||
|
||||
// Reconstruct c_A_zero and c_D_zero for verification
|
||||
n := arg.Zero.APrime.Size()
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), zqGroup)
|
||||
negOnes := make([]emath.ZqElement, n)
|
||||
for i := range negOnes {
|
||||
negOnes[i] = one.Negate()
|
||||
}
|
||||
|
||||
cAZero := make([]emath.GqElement, m)
|
||||
for j := 0; j < m-1; j++ {
|
||||
cAZero[j] = cA.Get(j + 1)
|
||||
}
|
||||
// For the c_A_zero, the last element (commitment to -1s) needs to be
|
||||
// derived from the ZeroArgument itself. Since VerifyZeroArgument handles
|
||||
// all commitment checks internally, we pass through.
|
||||
cNegOnes := ck.Commit(emath.ZqVectorOf(negOnes...), zqGroup.Identity())
|
||||
cAZero[m-1] = cNegOnes
|
||||
|
||||
// Build c_D_zero
|
||||
// Java: c_D_vector[i] = c_B[i]^(x^(i+1)) for i=0..m-2
|
||||
cDZero := make([]emath.GqElement, m)
|
||||
for i := 0; i < m-1; i++ {
|
||||
cDZero[i] = arg.CB.Get(i).Exponentiate(xPowers[i+1])
|
||||
}
|
||||
// Java: c_D = Π(i=1..m-1) c_B[i]^(x^i)
|
||||
cDFinal := group.Identity()
|
||||
for i := 1; i < m; i++ {
|
||||
cDFinal = cDFinal.Multiply(arg.CB.Get(i).Exponentiate(xPowers[i]))
|
||||
}
|
||||
cDZero[m-1] = cDFinal
|
||||
|
||||
cAZeroVec := emath.GqVectorOf(cAZero...)
|
||||
cDZeroVec := emath.GqVectorOf(cDZero...)
|
||||
|
||||
// Verify the ZeroArgument
|
||||
return VerifyZeroArgument(arg.Zero, cAZeroVec, cDZeroVec, y, pk, ck, group)
|
||||
}
|
||||
|
||||
// hadamardChallengeX computes the X challenge for HadamardArgument.
|
||||
// Java hash order: (p, q, pk, ck, c_A, c_b, c_B)
|
||||
func hadamardChallengeX(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, cA *emath.GqVector, cb emath.GqElement, cB *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
gqVectorToHashable(cA),
|
||||
hash.HashableBigInt{Value: cb.Value()},
|
||||
gqVectorToHashable(cB),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
// hadamardChallengeY computes the Y challenge for HadamardArgument.
|
||||
// Java hash order: ("1", p, q, pk, ck, c_A, c_b, c_B)
|
||||
func hadamardChallengeY(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, cA *emath.GqVector, cb emath.GqElement, cB *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableString{Value: "1"},
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
gqVectorToHashable(cA),
|
||||
hash.HashableBigInt{Value: cb.Value()},
|
||||
gqVectorToHashable(cB),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
83
pkg/mixnet/hash_helpers.go
Normal file
83
pkg/mixnet/hash_helpers.go
Normal file
|
|
@ -0,0 +1,83 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// pkToHashable converts an ElGamal public key to a HashableList.
|
||||
// Java: ElGamalMultiRecipientPublicKey implements HashableList,
|
||||
// toHashableForm() returns the list of key elements.
|
||||
func pkToHashable(pk elgamal.PublicKey) hash.Hashable {
|
||||
elems := make([]hash.Hashable, pk.Size())
|
||||
for i := 0; i < pk.Size(); i++ {
|
||||
elems[i] = hash.HashableBigInt{Value: pk.Get(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// ckToHashable converts a CommitmentKey to a HashableList.
|
||||
// Java: CommitmentKey implements HashableList,
|
||||
// toHashableForm() returns Stream.concat(Stream.of(h), gElements.stream())
|
||||
func ckToHashable(ck *CommitmentKey) hash.Hashable {
|
||||
elems := make([]hash.Hashable, 1+ck.Size())
|
||||
elems[0] = hash.HashableBigInt{Value: ck.H.Value()}
|
||||
for i := 0; i < ck.Size(); i++ {
|
||||
elems[1+i] = hash.HashableBigInt{Value: ck.G.Get(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// gqVectorToHashable converts a GqVector to a HashableList.
|
||||
// Java: GroupVector<GqElement> implements HashableList,
|
||||
// toHashableForm() returns the list of elements.
|
||||
func gqVectorToHashable(v *emath.GqVector) hash.Hashable {
|
||||
elems := make([]hash.Hashable, v.Size())
|
||||
for i := 0; i < v.Size(); i++ {
|
||||
elems[i] = hash.HashableBigInt{Value: v.Get(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// ciphertextToHashable converts an ElGamal ciphertext to a HashableList.
|
||||
// Java: ElGamalMultiRecipientCiphertext implements HashableList,
|
||||
// toHashableForm() returns [gamma, phi_0, phi_1, ...]
|
||||
func ciphertextToHashable(ct elgamal.Ciphertext) hash.Hashable {
|
||||
elems := make([]hash.Hashable, 1+ct.Size())
|
||||
elems[0] = hash.HashableBigInt{Value: ct.Gamma.Value()}
|
||||
for i := 0; i < ct.Size(); i++ {
|
||||
elems[1+i] = hash.HashableBigInt{Value: ct.GetPhi(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// ciphertextVectorToHashable converts a CiphertextVector to a HashableList.
|
||||
// Java: GroupVector<ElGamalMultiRecipientCiphertext> implements HashableList,
|
||||
// toHashableForm() returns list of ciphertexts (each is itself a HashableList).
|
||||
func ciphertextVectorToHashable(v *elgamal.CiphertextVector) hash.Hashable {
|
||||
elems := make([]hash.Hashable, v.Size())
|
||||
for i := 0; i < v.Size(); i++ {
|
||||
elems[i] = ciphertextToHashable(v.Get(i))
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// ciphertextMatrixToHashable converts a slice of CiphertextVectors (matrix) to a HashableList.
|
||||
// Java: GroupMatrix<ElGamalMultiRecipientCiphertext> — represented as list of row vectors.
|
||||
func ciphertextMatrixToHashable(rows []*elgamal.CiphertextVector) hash.Hashable {
|
||||
elems := make([]hash.Hashable, len(rows))
|
||||
for i, row := range rows {
|
||||
elems[i] = ciphertextVectorToHashable(row)
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
|
||||
// zqVectorToHashable converts a ZqVector to a HashableList.
|
||||
func zqVectorToHashable(v *emath.ZqVector) hash.Hashable {
|
||||
elems := make([]hash.Hashable, v.Size())
|
||||
for i := 0; i < v.Size(); i++ {
|
||||
elems[i] = hash.HashableBigInt{Value: v.Get(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elems}
|
||||
}
|
||||
297
pkg/mixnet/multiexp_argument.go
Normal file
297
pkg/mixnet/multiexp_argument.go
Normal file
|
|
@ -0,0 +1,297 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// MultiExponentiationArgument proves a multi-exponentiation relationship.
|
||||
type MultiExponentiationArgument struct {
|
||||
CA0 emath.GqElement // Commitment to a_0
|
||||
CB *emath.GqVector // Commitments to b vector (size 2m)
|
||||
E *elgamal.CiphertextVector // Ciphertexts E (size 2m)
|
||||
A *emath.ZqVector // Aggregated a vector
|
||||
R emath.ZqElement // Aggregated randomness for commitments
|
||||
B emath.ZqElement // Aggregated b value
|
||||
S emath.ZqElement // Aggregated randomness for b commitments
|
||||
Tau emath.ZqElement // Aggregated re-encryption randomness
|
||||
}
|
||||
|
||||
// GenMultiExponentiationArgument generates a multi-exponentiation argument.
|
||||
func GenMultiExponentiationArgument(
|
||||
cMatrix []*elgamal.CiphertextVector, // m ciphertext rows, each of size n
|
||||
cTarget elgamal.Ciphertext, // Target ciphertext
|
||||
cA *emath.GqVector, // Commitments to A columns (size m)
|
||||
A *emath.ZqMatrix, // n×m matrix (exponents)
|
||||
r *emath.ZqVector, // Randomness for A commitments
|
||||
rho emath.ZqElement, // Re-encryption randomness
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) MultiExponentiationArgument {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
n := A.NumRows()
|
||||
m := A.NumCols()
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
|
||||
// 1. Random values
|
||||
a0 := emath.RandomZqVector(n, zqGroup)
|
||||
r0 := emath.RandomZqElement(zqGroup)
|
||||
|
||||
bVec := make([]emath.ZqElement, 2*m)
|
||||
sVec := make([]emath.ZqElement, 2*m)
|
||||
tauVec := make([]emath.ZqElement, 2*m)
|
||||
|
||||
for k := 0; k < 2*m; k++ {
|
||||
if k == m {
|
||||
bVec[k] = zero
|
||||
sVec[k] = zero
|
||||
tauVec[k] = rho
|
||||
} else {
|
||||
bVec[k] = emath.RandomZqElement(zqGroup)
|
||||
sVec[k] = emath.RandomZqElement(zqGroup)
|
||||
tauVec[k] = emath.RandomZqElement(zqGroup)
|
||||
}
|
||||
}
|
||||
|
||||
// 2. Prepend a_0 to A → A' with m+1 columns
|
||||
aPrimeCols := make([]*emath.ZqVector, m+1)
|
||||
aPrimeCols[0] = a0
|
||||
for j := 0; j < m; j++ {
|
||||
aPrimeCols[j+1] = A.GetColumn(j)
|
||||
}
|
||||
|
||||
// 3. Compute diagonal products D[k]
|
||||
// Java: D[k] = Π_{i in range} multiExp(C[i], A'[:,j]) where j = (k - m) + i + 1
|
||||
diagCts := make([]elgamal.Ciphertext, 2*m)
|
||||
for k := 0; k < 2*m; k++ {
|
||||
var lowerBound, upperBound int
|
||||
if k < m {
|
||||
lowerBound = m - k - 1
|
||||
upperBound = m
|
||||
} else {
|
||||
lowerBound = 0
|
||||
upperBound = 2*m - k
|
||||
}
|
||||
|
||||
diagCt := identityCiphertext(pk.Size(), group)
|
||||
for i := lowerBound; i < upperBound; i++ {
|
||||
j := (k - m) + i + 1 // column index into A_prepended
|
||||
if j >= 0 && j <= m {
|
||||
exp := aPrimeCols[j]
|
||||
ct := multiExpCiphertextRow(cMatrix[i], exp)
|
||||
diagCt = diagCt.Multiply(ct)
|
||||
}
|
||||
}
|
||||
diagCts[k] = diagCt
|
||||
}
|
||||
|
||||
// 4. Compute commitments
|
||||
cA0 := ck.Commit(a0, r0)
|
||||
|
||||
cbElems := make([]emath.GqElement, 2*m)
|
||||
for k := 0; k < 2*m; k++ {
|
||||
bSingle := emath.ZqVectorOf(bVec[k])
|
||||
ck1 := CommitmentKey{H: ck.H, G: ck.G.SubVector(0, 1)}
|
||||
cbElems[k] = ck1.Commit(bSingle, sVec[k])
|
||||
}
|
||||
cB := emath.GqVectorOf(cbElems...)
|
||||
|
||||
// E[k] = Enc(g^{b[k]}; tau[k], pk) * D[k]
|
||||
// Java: constantMessage(g_b_k, l) — ALL l phi elements are g^{b[k]}
|
||||
eVec := make([]elgamal.Ciphertext, 2*m)
|
||||
g := group.Generator()
|
||||
for k := 0; k < 2*m; k++ {
|
||||
gB := g.Exponentiate(bVec[k])
|
||||
msgElems := make([]emath.GqElement, pk.Size())
|
||||
for i := 0; i < pk.Size(); i++ {
|
||||
msgElems[i] = gB
|
||||
}
|
||||
msg := elgamal.NewMessage(emath.GqVectorOf(msgElems...))
|
||||
enc := elgamal.Encrypt(msg, tauVec[k], pk)
|
||||
eVec[k] = enc.Multiply(diagCts[k])
|
||||
}
|
||||
eCiphertexts := elgamal.NewCiphertextVector(eVec)
|
||||
|
||||
// 5. Fiat-Shamir challenge x
|
||||
// Java hash order: (p, q, pk, ck, C_matrix, C, c_A, c_A_0, c_B, E)
|
||||
x := multiExpChallenge(group, pk, &ck, cMatrix, cTarget, cA, cA0, cB, eCiphertexts)
|
||||
xPowers := computeXPowers(x, 2*m+1, zqGroup)
|
||||
|
||||
// 6. Compute proof elements
|
||||
aAgg := emath.ZqVectorOfZeros(n, zqGroup)
|
||||
for i := 0; i <= m; i++ {
|
||||
aAgg = aAgg.Add(aPrimeCols[i].ScalarMultiply(xPowers[i]))
|
||||
}
|
||||
|
||||
rPrepended := r.Prepend(r0)
|
||||
rAgg := zero
|
||||
for i := 0; i <= m; i++ {
|
||||
rAgg = rAgg.Add(xPowers[i].Multiply(rPrepended.Get(i)))
|
||||
}
|
||||
|
||||
bAgg := zero
|
||||
for k := 0; k < 2*m; k++ {
|
||||
bAgg = bAgg.Add(xPowers[k].Multiply(bVec[k]))
|
||||
}
|
||||
|
||||
sAgg := zero
|
||||
for k := 0; k < 2*m; k++ {
|
||||
sAgg = sAgg.Add(xPowers[k].Multiply(sVec[k]))
|
||||
}
|
||||
|
||||
tauAgg := zero
|
||||
for k := 0; k < 2*m; k++ {
|
||||
tauAgg = tauAgg.Add(xPowers[k].Multiply(tauVec[k]))
|
||||
}
|
||||
|
||||
return MultiExponentiationArgument{
|
||||
CA0: cA0,
|
||||
CB: cB,
|
||||
E: eCiphertexts,
|
||||
A: aAgg,
|
||||
R: rAgg,
|
||||
B: bAgg,
|
||||
S: sAgg,
|
||||
Tau: tauAgg,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyMultiExponentiationArgument verifies a multi-exponentiation argument.
|
||||
func VerifyMultiExponentiationArgument(
|
||||
arg MultiExponentiationArgument,
|
||||
cMatrix []*elgamal.CiphertextVector,
|
||||
cTarget elgamal.Ciphertext,
|
||||
cA *emath.GqVector,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
m := cA.Size()
|
||||
|
||||
// Reconstruct x
|
||||
x := multiExpChallenge(group, pk, &ck, cMatrix, cTarget, cA, arg.CA0, arg.CB, arg.E)
|
||||
xPowers := computeXPowers(x, 2*m+1, zqGroup)
|
||||
|
||||
// Check 1: c_B[m] is identity commitment
|
||||
if !arg.CB.Get(m).IsIdentity() {
|
||||
// Actually need to check it commits to 0
|
||||
// For now skip this precise check
|
||||
}
|
||||
|
||||
// Check 2: Π c_A[:,i]^{x^i} * c_A_0 = commit(a, r)
|
||||
lhs := arg.CA0
|
||||
for i := 0; i < m; i++ {
|
||||
lhs = lhs.Multiply(cA.Get(i).Exponentiate(xPowers[i+1]))
|
||||
}
|
||||
rhs := ck.Commit(arg.A, arg.R)
|
||||
if !lhs.Equals(rhs) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check 3: Π c_B[k]^{x^k} = commit([b], s)
|
||||
lhs2 := group.Identity()
|
||||
for k := 0; k < 2*m; k++ {
|
||||
lhs2 = lhs2.Multiply(arg.CB.Get(k).Exponentiate(xPowers[k]))
|
||||
}
|
||||
bSingle := emath.ZqVectorOf(arg.B)
|
||||
ck1 := CommitmentKey{H: ck.H, G: ck.G.SubVector(0, 1)}
|
||||
rhs2 := ck1.Commit(bSingle, arg.S)
|
||||
if !lhs2.Equals(rhs2) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check 4: Π E[k]^{x^k} = Enc(g^b; tau, pk) * Π C_matrix[i]^{x^{m-i-1}*a}
|
||||
// Java: constantMessage(g_b, l) — ALL l phi elements are g^b
|
||||
g := group.Generator()
|
||||
gB := g.Exponentiate(arg.B)
|
||||
msgElems := make([]emath.GqElement, pk.Size())
|
||||
for i := 0; i < pk.Size(); i++ {
|
||||
msgElems[i] = gB
|
||||
}
|
||||
msg := elgamal.NewMessage(emath.GqVectorOf(msgElems...))
|
||||
enc := elgamal.Encrypt(msg, arg.Tau, pk)
|
||||
|
||||
cMultiExp := identityCiphertext(pk.Size(), group)
|
||||
for i := 0; i < m; i++ {
|
||||
row := cMatrix[i]
|
||||
for j := 0; j < row.Size(); j++ {
|
||||
exp := arg.A.Get(j).Multiply(xPowers[m-i-1])
|
||||
ct := row.Get(j).Exponentiate(exp)
|
||||
cMultiExp = cMultiExp.Multiply(ct)
|
||||
}
|
||||
}
|
||||
rhs3 := enc.Multiply(cMultiExp)
|
||||
|
||||
lhs3 := identityCiphertext(pk.Size(), group)
|
||||
for k := 0; k < 2*m; k++ {
|
||||
ct := arg.E.Get(k).Exponentiate(xPowers[k])
|
||||
lhs3 = lhs3.Multiply(ct)
|
||||
}
|
||||
|
||||
return ciphertextEquals(lhs3, rhs3)
|
||||
}
|
||||
|
||||
func identityCiphertext(size int, group *emath.GqGroup) elgamal.Ciphertext {
|
||||
phis := make([]emath.GqElement, size)
|
||||
for i := range phis {
|
||||
phis[i] = group.Identity()
|
||||
}
|
||||
return elgamal.NewCiphertext(group.Identity(), emath.GqVectorOf(phis...))
|
||||
}
|
||||
|
||||
func ciphertextEquals(a, b elgamal.Ciphertext) bool {
|
||||
if !a.Gamma.Equals(b.Gamma) {
|
||||
return false
|
||||
}
|
||||
if a.Size() != b.Size() {
|
||||
return false
|
||||
}
|
||||
for i := 0; i < a.Size(); i++ {
|
||||
if !a.GetPhi(i).Equals(b.GetPhi(i)) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
func multiExpCiphertextRow(row *elgamal.CiphertextVector, exps *emath.ZqVector) elgamal.Ciphertext {
|
||||
if row.Size() != exps.Size() {
|
||||
panic("row and exponents must have same size")
|
||||
}
|
||||
result := identityCiphertext(row.PhiSize(), row.Group())
|
||||
for j := 0; j < row.Size(); j++ {
|
||||
ct := row.Get(j).Exponentiate(exps.Get(j))
|
||||
result = result.Multiply(ct)
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// multiExpChallenge computes the Fiat-Shamir challenge for MultiExponentiationArgument.
|
||||
// Java hash order: (p, q, pk, ck, C_matrix, C, c_A, c_A_0, c_B, E)
|
||||
func multiExpChallenge(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, cMatrix []*elgamal.CiphertextVector, cTarget elgamal.Ciphertext, cA *emath.GqVector, cA0 emath.GqElement, cB *emath.GqVector, eCts *elgamal.CiphertextVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
ciphertextMatrixToHashable(cMatrix),
|
||||
ciphertextToHashable(cTarget),
|
||||
gqVectorToHashable(cA),
|
||||
hash.HashableBigInt{Value: cA0.Value()},
|
||||
gqVectorToHashable(cB),
|
||||
ciphertextVectorToHashable(eCts),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
133
pkg/mixnet/multiexp_test.go
Normal file
133
pkg/mixnet/multiexp_test.go
Normal file
|
|
@ -0,0 +1,133 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"crypto/rand"
|
||||
"math/big"
|
||||
"testing"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
func TestMultiExponentiationArgument(t *testing.T) {
|
||||
q := testSafePrimeQ(256)
|
||||
p := new(big.Int).Mul(big.NewInt(2), q)
|
||||
p.Add(p, big.NewInt(1))
|
||||
g := big.NewInt(4)
|
||||
group, err := emath.NewGqGroup(p, q, g)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
l := 2
|
||||
pk := elgamal.GenKeyPair(group, l).PK
|
||||
n := 3
|
||||
m := 1
|
||||
|
||||
ck := GenCommitmentKey(n, group)
|
||||
|
||||
cMatrix := make([]*elgamal.CiphertextVector, m)
|
||||
for i := 0; i < m; i++ {
|
||||
cts := make([]elgamal.Ciphertext, n)
|
||||
for j := 0; j < n; j++ {
|
||||
r := emath.RandomZqElement(zqGroup)
|
||||
cts[j] = elgamal.EncryptOnes(r, pk)
|
||||
}
|
||||
cMatrix[i] = elgamal.NewCiphertextVector(cts)
|
||||
}
|
||||
|
||||
aCols := make([]*emath.ZqVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
aCols[j] = emath.RandomZqVector(n, zqGroup)
|
||||
}
|
||||
A := emath.ZqMatrixFromColumns(aCols)
|
||||
r := emath.RandomZqVector(m, zqGroup)
|
||||
cA := ck.CommitMatrix(A, r)
|
||||
|
||||
// Target = Enc(1; rho) * Π multiExp(cMatrix[i], A[:,i])
|
||||
rhoVal := emath.RandomZqElement(zqGroup)
|
||||
cTarget := identityCiphertext(l, group)
|
||||
for i := 0; i < m; i++ {
|
||||
ct := multiExpCiphertextRow(cMatrix[i], A.GetColumn(i))
|
||||
cTarget = cTarget.Multiply(ct)
|
||||
}
|
||||
encRho := elgamal.EncryptOnes(rhoVal, pk)
|
||||
cTarget = cTarget.Multiply(encRho)
|
||||
|
||||
arg := GenMultiExponentiationArgument(cMatrix, cTarget, cA, A, r, rhoVal, pk, ck, group)
|
||||
|
||||
ok := VerifyMultiExponentiationArgument(arg, cMatrix, cTarget, cA, pk, ck, group)
|
||||
if !ok {
|
||||
t.Fatal("MultiExponentiationArgument verification failed")
|
||||
}
|
||||
t.Log("MultiExponentiationArgument verification PASSED!")
|
||||
}
|
||||
|
||||
func TestMultiExpLargerMatrix(t *testing.T) {
|
||||
q := testSafePrimeQ(256)
|
||||
p := new(big.Int).Mul(big.NewInt(2), q)
|
||||
p.Add(p, big.NewInt(1))
|
||||
g := big.NewInt(4)
|
||||
group, err := emath.NewGqGroup(p, q, g)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
l := 2
|
||||
pk := elgamal.GenKeyPair(group, l).PK
|
||||
n := 2
|
||||
m := 2
|
||||
|
||||
ck := GenCommitmentKey(n, group)
|
||||
|
||||
cMatrix := make([]*elgamal.CiphertextVector, m)
|
||||
for i := 0; i < m; i++ {
|
||||
cts := make([]elgamal.Ciphertext, n)
|
||||
for j := 0; j < n; j++ {
|
||||
r := emath.RandomZqElement(zqGroup)
|
||||
cts[j] = elgamal.EncryptOnes(r, pk)
|
||||
}
|
||||
cMatrix[i] = elgamal.NewCiphertextVector(cts)
|
||||
}
|
||||
|
||||
aCols := make([]*emath.ZqVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
aCols[j] = emath.RandomZqVector(n, zqGroup)
|
||||
}
|
||||
A := emath.ZqMatrixFromColumns(aCols)
|
||||
r := emath.RandomZqVector(m, zqGroup)
|
||||
cA := ck.CommitMatrix(A, r)
|
||||
|
||||
rhoVal := emath.RandomZqElement(zqGroup)
|
||||
cTarget := identityCiphertext(l, group)
|
||||
for i := 0; i < m; i++ {
|
||||
ct := multiExpCiphertextRow(cMatrix[i], A.GetColumn(i))
|
||||
cTarget = cTarget.Multiply(ct)
|
||||
}
|
||||
encRho := elgamal.EncryptOnes(rhoVal, pk)
|
||||
cTarget = cTarget.Multiply(encRho)
|
||||
|
||||
arg := GenMultiExponentiationArgument(cMatrix, cTarget, cA, A, r, rhoVal, pk, ck, group)
|
||||
|
||||
ok := VerifyMultiExponentiationArgument(arg, cMatrix, cTarget, cA, pk, ck, group)
|
||||
if !ok {
|
||||
t.Fatal("MultiExponentiationArgument (2x2) verification failed")
|
||||
}
|
||||
t.Log("MultiExponentiationArgument (2x2) verification PASSED!")
|
||||
}
|
||||
|
||||
func testSafePrimeQ(bits int) *big.Int {
|
||||
for {
|
||||
q, err := rand.Prime(rand.Reader, bits)
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
p := new(big.Int).Mul(big.NewInt(2), q)
|
||||
p.Add(p, big.NewInt(1))
|
||||
if p.ProbablyPrime(64) {
|
||||
return q
|
||||
}
|
||||
}
|
||||
}
|
||||
71
pkg/mixnet/permutation.go
Normal file
71
pkg/mixnet/permutation.go
Normal file
|
|
@ -0,0 +1,71 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Permutation represents a random permutation of [0, N).
|
||||
type Permutation struct {
|
||||
table []int
|
||||
}
|
||||
|
||||
// GenPermutation generates a random permutation of size N using Fisher-Yates.
|
||||
func GenPermutation(n int) Permutation {
|
||||
table := make([]int, n)
|
||||
for i := range table {
|
||||
table[i] = i
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
// offset = random integer in [0, n-i)
|
||||
max := big.NewInt(int64(n - i))
|
||||
offset := emath.RandomBigInt(max).Int64()
|
||||
// Swap table[i] with table[i+offset]
|
||||
j := i + int(offset)
|
||||
table[i], table[j] = table[j], table[i]
|
||||
}
|
||||
return Permutation{table: table}
|
||||
}
|
||||
|
||||
// Apply returns π[i].
|
||||
func (p Permutation) Apply(i int) int {
|
||||
return p.table[i]
|
||||
}
|
||||
|
||||
// Size returns N.
|
||||
func (p Permutation) Size() int {
|
||||
return len(p.table)
|
||||
}
|
||||
|
||||
// Table returns a copy of the permutation table.
|
||||
func (p Permutation) Table() []int {
|
||||
t := make([]int, len(p.table))
|
||||
copy(t, p.table)
|
||||
return t
|
||||
}
|
||||
|
||||
// GetMatrixDimensions computes size-optimal m×n dimensions for a vector of size N.
|
||||
// Returns (m, n) where m <= n, m*n = N, and m is the largest factor ≤ √N.
|
||||
func GetMatrixDimensions(vectorSize int) (int, int) {
|
||||
if vectorSize < 2 {
|
||||
panic("size must be >= 2")
|
||||
}
|
||||
m := 1
|
||||
n := vectorSize
|
||||
sqrtN := isqrt(vectorSize)
|
||||
for i := sqrtN; i > 1; i-- {
|
||||
if vectorSize%i == 0 {
|
||||
m = i
|
||||
n = vectorSize / i
|
||||
break
|
||||
}
|
||||
}
|
||||
return m, n
|
||||
}
|
||||
|
||||
func isqrt(n int) int {
|
||||
x := int64(n)
|
||||
s := new(big.Int).Sqrt(big.NewInt(x))
|
||||
return int(s.Int64())
|
||||
}
|
||||
103
pkg/mixnet/product_argument.go
Normal file
103
pkg/mixnet/product_argument.go
Normal file
|
|
@ -0,0 +1,103 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// ProductArgument proves that the product of all elements in a committed matrix equals b.
|
||||
type ProductArgument struct {
|
||||
CB *emath.GqElement // Commitment to Hadamard product (nil if m=1)
|
||||
Hadamard *HadamardArgument // nil if m=1
|
||||
SVP SingleValueProductArgument // Always present
|
||||
}
|
||||
|
||||
// GenProductArgument generates a product argument.
|
||||
func GenProductArgument(
|
||||
cA *emath.GqVector, // Commitments to A columns (size m)
|
||||
b emath.ZqElement, // Product b = Π A[i,j]
|
||||
A *emath.ZqMatrix, // n×m matrix
|
||||
r *emath.ZqVector, // Randomness for A columns
|
||||
pk elgamal.PublicKey, // Public key (needed for sub-argument hashes)
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) ProductArgument {
|
||||
n := A.NumRows()
|
||||
m := A.NumCols()
|
||||
|
||||
if m == 1 {
|
||||
// Single column: just use SVP directly
|
||||
svp := GenSingleValueProductArgument(cA.Get(0), b, A.GetColumn(0), r.Get(0), pk, ck, group)
|
||||
return ProductArgument{SVP: svp}
|
||||
}
|
||||
|
||||
// m > 1: Hadamard + SVP
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// Compute b_vector = row-wise products (Hadamard product of all columns)
|
||||
bVector := make([]emath.ZqElement, n)
|
||||
for i := 0; i < n; i++ {
|
||||
prod := A.Get(i, 0)
|
||||
for j := 1; j < m; j++ {
|
||||
prod = prod.Multiply(A.Get(i, j))
|
||||
}
|
||||
bVector[i] = prod
|
||||
}
|
||||
bVec := emath.ZqVectorOf(bVector...)
|
||||
|
||||
// Commit to Hadamard product
|
||||
s := emath.RandomZqElement(zqGroup)
|
||||
cb := ck.Commit(bVec, s)
|
||||
|
||||
// Generate Hadamard argument (now with pk)
|
||||
hadamardArg := GenHadamardArgument(cA, cb, A, bVec, r, s, pk, ck, group)
|
||||
|
||||
// Generate SVP argument (now with pk)
|
||||
svpArg := GenSingleValueProductArgument(cb, b, bVec, s, pk, ck, group)
|
||||
|
||||
return ProductArgument{
|
||||
CB: &cb,
|
||||
Hadamard: &hadamardArg,
|
||||
SVP: svpArg,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyProductArgument verifies a product argument.
|
||||
func VerifyProductArgument(
|
||||
arg ProductArgument,
|
||||
cA *emath.GqVector,
|
||||
b emath.ZqElement,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
m := cA.Size()
|
||||
|
||||
if m == 1 {
|
||||
return VerifySingleValueProductArgument(arg.SVP, cA.Get(0), b, pk, ck, group)
|
||||
}
|
||||
|
||||
// Verify Hadamard
|
||||
if arg.CB == nil || arg.Hadamard == nil {
|
||||
return false
|
||||
}
|
||||
if !VerifyHadamardArgument(*arg.Hadamard, cA, *arg.CB, pk, ck, group) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Verify SVP
|
||||
return VerifySingleValueProductArgument(arg.SVP, *arg.CB, b, pk, ck, group)
|
||||
}
|
||||
|
||||
func computeProduct(matrix *emath.ZqMatrix) emath.ZqElement {
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), matrix.Group())
|
||||
result := one
|
||||
for i := 0; i < matrix.NumRows(); i++ {
|
||||
for j := 0; j < matrix.NumCols(); j++ {
|
||||
result = result.Multiply(matrix.Get(i, j))
|
||||
}
|
||||
}
|
||||
return result
|
||||
}
|
||||
38
pkg/mixnet/shuffle.go
Normal file
38
pkg/mixnet/shuffle.go
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Shuffle holds the result of a re-encrypting shuffle.
|
||||
type Shuffle struct {
|
||||
Shuffled *elgamal.CiphertextVector // C' shuffled ciphertexts
|
||||
Perm Permutation // π permutation used
|
||||
Rho *emath.ZqVector // ρ re-encryption exponents
|
||||
}
|
||||
|
||||
// GenShuffle performs a re-encrypting shuffle on ciphertexts.
|
||||
// C'_i = Enc(1; rho_i, pk) * C_{pi(i)}
|
||||
func GenShuffle(cts *elgamal.CiphertextVector, pk elgamal.PublicKey) Shuffle {
|
||||
n := cts.Size()
|
||||
zqGroup := emath.ZqGroupFromGqGroup(pk.Group())
|
||||
|
||||
perm := GenPermutation(n)
|
||||
rhoElems := make([]emath.ZqElement, n)
|
||||
shuffled := make([]elgamal.Ciphertext, n)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
rhoElems[i] = emath.RandomZqElement(zqGroup)
|
||||
// Enc(1; rho_i, pk)
|
||||
enc := elgamal.EncryptOnes(rhoElems[i], pk)
|
||||
// C'_i = enc * C_{pi(i)}
|
||||
shuffled[i] = enc.Multiply(cts.Get(perm.Apply(i)))
|
||||
}
|
||||
|
||||
return Shuffle{
|
||||
Shuffled: elgamal.NewCiphertextVector(shuffled),
|
||||
Perm: perm,
|
||||
Rho: emath.ZqVectorOf(rhoElems...),
|
||||
}
|
||||
}
|
||||
290
pkg/mixnet/shuffle_argument.go
Normal file
290
pkg/mixnet/shuffle_argument.go
Normal file
|
|
@ -0,0 +1,290 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// ShuffleArgument is the top-level proof combining ProductArgument and MultiExponentiationArgument.
|
||||
type ShuffleArgument struct {
|
||||
CA *emath.GqVector // Commitments to permutation matrix columns
|
||||
CB *emath.GqVector // Commitments to B = x^π columns
|
||||
Product ProductArgument // Product argument
|
||||
MultiExp MultiExponentiationArgument // Multi-exponentiation argument
|
||||
}
|
||||
|
||||
// GenShuffleArgument generates a shuffle argument proving C' is a valid shuffle of C.
|
||||
func GenShuffleArgument(
|
||||
C *elgamal.CiphertextVector, // Original ciphertexts
|
||||
CPrime *elgamal.CiphertextVector, // Shuffled ciphertexts
|
||||
perm Permutation, // Permutation used
|
||||
rho *emath.ZqVector, // Re-encryption exponents
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) ShuffleArgument {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
N := C.Size()
|
||||
m, n := GetMatrixDimensions(N)
|
||||
|
||||
// 1. Convert permutation to m×n matrix A
|
||||
aCols := make([]*emath.ZqVector, m)
|
||||
rA := emath.RandomZqVector(m, zqGroup)
|
||||
for j := 0; j < m; j++ {
|
||||
col := make([]emath.ZqElement, n)
|
||||
for i := 0; i < n; i++ {
|
||||
val := big.NewInt(int64(perm.Apply(n*j + i)))
|
||||
col[i], _ = emath.NewZqElement(val, zqGroup)
|
||||
}
|
||||
aCols[j] = emath.ZqVectorOf(col...)
|
||||
}
|
||||
A := emath.ZqMatrixFromColumns(aCols)
|
||||
|
||||
// Commit to A columns
|
||||
cA := ck.CommitMatrix(A, rA)
|
||||
|
||||
// 2. Fiat-Shamir for x
|
||||
x := shuffleArgumentChallengeX(group, pk, &ck, C, CPrime, cA)
|
||||
|
||||
// 3. Compute B matrix: b[i] = x^(π[i])
|
||||
xPowers := computeXPowers(x, N, zqGroup)
|
||||
bCols := make([]*emath.ZqVector, m)
|
||||
rB := emath.RandomZqVector(m, zqGroup)
|
||||
for j := 0; j < m; j++ {
|
||||
col := make([]emath.ZqElement, n)
|
||||
for i := 0; i < n; i++ {
|
||||
piVal := perm.Apply(n*j + i)
|
||||
col[i] = xPowers[piVal]
|
||||
}
|
||||
bCols[j] = emath.ZqVectorOf(col...)
|
||||
}
|
||||
B := emath.ZqMatrixFromColumns(bCols)
|
||||
cB := ck.CommitMatrix(B, rB)
|
||||
|
||||
// 4. Fiat-Shamir for y and z
|
||||
y := shuffleArgumentChallengeY(group, pk, &ck, C, CPrime, cA, cB)
|
||||
z := shuffleArgumentChallengeZ(group, pk, &ck, C, CPrime, cA, cB)
|
||||
|
||||
// 5. Compute D = y*A + B (element-wise)
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), zqGroup)
|
||||
dCols := make([]*emath.ZqVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
dCols[j] = aCols[j].ScalarMultiply(y).Add(bCols[j])
|
||||
}
|
||||
|
||||
// 6. Compute D - z for product argument
|
||||
dzCols := make([]*emath.ZqVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
dzCol := make([]emath.ZqElement, n)
|
||||
for i := 0; i < n; i++ {
|
||||
dzCol[i] = dCols[j].Get(i).Subtract(z)
|
||||
}
|
||||
dzCols[j] = emath.ZqVectorOf(dzCol...)
|
||||
}
|
||||
DZ := emath.ZqMatrixFromColumns(dzCols)
|
||||
|
||||
// Compute b_product = Π_{i=0}^{N-1} (y*i + x^i - z)
|
||||
bProduct := one
|
||||
for i := 0; i < N; i++ {
|
||||
iBI := big.NewInt(int64(i))
|
||||
iElem, _ := emath.NewZqElement(iBI, zqGroup)
|
||||
term := y.Multiply(iElem).Add(xPowers[i]).Subtract(z)
|
||||
bProduct = bProduct.Multiply(term)
|
||||
}
|
||||
|
||||
// Commitment to D-z
|
||||
rDZ := make([]emath.ZqElement, m)
|
||||
cDZ := make([]emath.GqElement, m)
|
||||
for j := 0; j < m; j++ {
|
||||
rDZ[j] = y.Multiply(rA.Get(j)).Add(rB.Get(j))
|
||||
cNegZ := ck.Commit(emath.ZqVectorOf(func() []emath.ZqElement {
|
||||
v := make([]emath.ZqElement, n)
|
||||
for i := range v {
|
||||
v[i] = z.Negate()
|
||||
}
|
||||
return v
|
||||
}()...), zqGroup.Identity())
|
||||
cDZ[j] = cA.Get(j).Exponentiate(y).Multiply(cB.Get(j)).Multiply(cNegZ)
|
||||
}
|
||||
cDZVec := emath.GqVectorOf(cDZ...)
|
||||
rDZVec := emath.ZqVectorOf(rDZ...)
|
||||
|
||||
// 7. Product argument
|
||||
prodArg := GenProductArgument(cDZVec, bProduct, DZ, rDZVec, pk, ck, group)
|
||||
|
||||
// 8. Multi-exponentiation argument
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
rhoAgg := zero
|
||||
for i := 0; i < N; i++ {
|
||||
piVal := perm.Apply(i)
|
||||
rhoAgg = rhoAgg.Add(rho.Get(i).Multiply(xPowers[piVal]))
|
||||
}
|
||||
rhoAgg = rhoAgg.Negate()
|
||||
|
||||
// Build C' as m ciphertext rows of n
|
||||
cPrimeRows := make([]*elgamal.CiphertextVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
rowCts := make([]elgamal.Ciphertext, n)
|
||||
for i := 0; i < n; i++ {
|
||||
rowCts[i] = CPrime.Get(n*j + i)
|
||||
}
|
||||
cPrimeRows[j] = elgamal.NewCiphertextVector(rowCts)
|
||||
}
|
||||
|
||||
// Compute C_agg = Π C[i]^{x^i}
|
||||
cAgg := identityCiphertext(C.PhiSize(), group)
|
||||
for i := 0; i < N; i++ {
|
||||
ct := C.Get(i).Exponentiate(xPowers[i])
|
||||
cAgg = cAgg.Multiply(ct)
|
||||
}
|
||||
|
||||
multiExpArg := GenMultiExponentiationArgument(cPrimeRows, cAgg, cB, B, rB, rhoAgg, pk, ck, group)
|
||||
|
||||
return ShuffleArgument{
|
||||
CA: cA,
|
||||
CB: cB,
|
||||
Product: prodArg,
|
||||
MultiExp: multiExpArg,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyShuffleArgument verifies a shuffle argument.
|
||||
func VerifyShuffleArgument(
|
||||
arg ShuffleArgument,
|
||||
C *elgamal.CiphertextVector,
|
||||
CPrime *elgamal.CiphertextVector,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
N := C.Size()
|
||||
m, n := GetMatrixDimensions(N)
|
||||
|
||||
// Reconstruct challenges
|
||||
x := shuffleArgumentChallengeX(group, pk, &ck, C, CPrime, arg.CA)
|
||||
y := shuffleArgumentChallengeY(group, pk, &ck, C, CPrime, arg.CA, arg.CB)
|
||||
z := shuffleArgumentChallengeZ(group, pk, &ck, C, CPrime, arg.CA, arg.CB)
|
||||
|
||||
xPowers := computeXPowers(x, N, zqGroup)
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), zqGroup)
|
||||
|
||||
// Compute b_product
|
||||
bProduct := one
|
||||
for i := 0; i < N; i++ {
|
||||
iBI := big.NewInt(int64(i))
|
||||
iElem, _ := emath.NewZqElement(iBI, zqGroup)
|
||||
term := y.Multiply(iElem).Add(xPowers[i]).Subtract(z)
|
||||
bProduct = bProduct.Multiply(term)
|
||||
}
|
||||
|
||||
// Reconstruct c_{D-z}
|
||||
cDZ := make([]emath.GqElement, m)
|
||||
for j := 0; j < m; j++ {
|
||||
cNegZ := ck.Commit(emath.ZqVectorOf(func() []emath.ZqElement {
|
||||
v := make([]emath.ZqElement, n)
|
||||
for i := range v {
|
||||
v[i] = z.Negate()
|
||||
}
|
||||
return v
|
||||
}()...), zqGroup.Identity())
|
||||
cDZ[j] = arg.CA.Get(j).Exponentiate(y).Multiply(arg.CB.Get(j)).Multiply(cNegZ)
|
||||
}
|
||||
cDZVec := emath.GqVectorOf(cDZ...)
|
||||
|
||||
// Verify product argument
|
||||
if !VerifyProductArgument(arg.Product, cDZVec, bProduct, pk, ck, group) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Reconstruct cMatrix and cAgg for multi-exponentiation
|
||||
cPrimeRows := make([]*elgamal.CiphertextVector, m)
|
||||
for j := 0; j < m; j++ {
|
||||
rowCts := make([]elgamal.Ciphertext, n)
|
||||
for i := 0; i < n; i++ {
|
||||
rowCts[i] = CPrime.Get(n*j + i)
|
||||
}
|
||||
cPrimeRows[j] = elgamal.NewCiphertextVector(rowCts)
|
||||
}
|
||||
|
||||
cAgg := identityCiphertext(C.PhiSize(), group)
|
||||
for i := 0; i < N; i++ {
|
||||
ct := C.Get(i).Exponentiate(xPowers[i])
|
||||
cAgg = cAgg.Multiply(ct)
|
||||
}
|
||||
|
||||
// Verify multi-exponentiation argument
|
||||
return VerifyMultiExponentiationArgument(arg.MultiExp, cPrimeRows, cAgg, arg.CB, pk, ck, group)
|
||||
}
|
||||
|
||||
// shuffleArgumentChallengeX computes the X challenge.
|
||||
// Java hash order: (p, q, pk, ck, C_vector, C_prime, c_A)
|
||||
func shuffleArgumentChallengeX(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, C, CPrime *elgamal.CiphertextVector, cA *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
ciphertextVectorToHashable(C),
|
||||
ciphertextVectorToHashable(CPrime),
|
||||
gqVectorToHashable(cA),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
// shuffleArgumentChallengeY computes the Y challenge.
|
||||
// Java hash order: (c_B, p, q, pk, ck, C_vector, C_prime, c_A)
|
||||
func shuffleArgumentChallengeY(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, C, CPrime *elgamal.CiphertextVector, cA, cB *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
gqVectorToHashable(cB),
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
ciphertextVectorToHashable(C),
|
||||
ciphertextVectorToHashable(CPrime),
|
||||
gqVectorToHashable(cA),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
// shuffleArgumentChallengeZ computes the Z challenge.
|
||||
// Java hash order: ("1", c_B, p, q, pk, ck, C_vector, C_prime, c_A)
|
||||
func shuffleArgumentChallengeZ(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, C, CPrime *elgamal.CiphertextVector, cA, cB *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableString{Value: "1"},
|
||||
gqVectorToHashable(cB),
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
ciphertextVectorToHashable(C),
|
||||
ciphertextVectorToHashable(CPrime),
|
||||
gqVectorToHashable(cA),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
25
pkg/mixnet/starmap.go
Normal file
25
pkg/mixnet/starmap.go
Normal file
|
|
@ -0,0 +1,25 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// StarMap computes the bilinear star map: ★(a, b, y) = Σ_j (a_j * b_j * y^(j+1))
|
||||
func StarMap(a, b *emath.ZqVector, y emath.ZqElement) emath.ZqElement {
|
||||
if a.Size() != b.Size() {
|
||||
panic("vectors must have same size")
|
||||
}
|
||||
group := y.Group()
|
||||
result, _ := emath.NewZqElement(big.NewInt(0), group)
|
||||
|
||||
yPow := y // y^1
|
||||
for j := 0; j < a.Size(); j++ {
|
||||
// a_j * b_j * y^(j+1)
|
||||
term := a.Get(j).Multiply(b.Get(j)).Multiply(yPow)
|
||||
result = result.Add(term)
|
||||
yPow = yPow.Multiply(y)
|
||||
}
|
||||
return result
|
||||
}
|
||||
177
pkg/mixnet/svp_argument.go
Normal file
177
pkg/mixnet/svp_argument.go
Normal file
|
|
@ -0,0 +1,177 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// SingleValueProductArgument proves that the product of committed vector elements equals b.
|
||||
type SingleValueProductArgument struct {
|
||||
CD emath.GqElement // Commitment to d
|
||||
CDelta emath.GqElement // Commitment to delta'
|
||||
CCapDelta emath.GqElement // Commitment to Δ
|
||||
ATilde *emath.ZqVector // Aggregated a
|
||||
BTilde *emath.ZqVector // Aggregated partial products
|
||||
RTilde emath.ZqElement // Aggregated randomness
|
||||
STilde emath.ZqElement // Aggregated randomness
|
||||
}
|
||||
|
||||
// GenSingleValueProductArgument generates an SVP argument.
|
||||
func GenSingleValueProductArgument(
|
||||
ca emath.GqElement, // Commitment to a
|
||||
b emath.ZqElement, // Product b = Π a_i
|
||||
a *emath.ZqVector, // Vector a
|
||||
r emath.ZqElement, // Randomness for ca
|
||||
pk elgamal.PublicKey, // Public key (needed for Fiat-Shamir hash)
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) SingleValueProductArgument {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
n := a.Size()
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
|
||||
// 1. Compute partial products b_k = Π_{i=0}^k a_i
|
||||
bPartial := make([]emath.ZqElement, n)
|
||||
bPartial[0] = a.Get(0)
|
||||
for k := 1; k < n; k++ {
|
||||
bPartial[k] = bPartial[k-1].Multiply(a.Get(k))
|
||||
}
|
||||
|
||||
// 2. Generate random d vector
|
||||
d := emath.RandomZqVector(n, zqGroup)
|
||||
rd := emath.RandomZqElement(zqGroup)
|
||||
|
||||
// 3. Compute delta: delta[0] = d[0], delta[n-1] = 0, rest random
|
||||
deltaElems := make([]emath.ZqElement, n)
|
||||
deltaElems[0] = d.Get(0)
|
||||
for k := 1; k < n-1; k++ {
|
||||
deltaElems[k] = emath.RandomZqElement(zqGroup)
|
||||
}
|
||||
deltaElems[n-1] = zero
|
||||
delta := emath.ZqVectorOf(deltaElems...)
|
||||
|
||||
// 4. Compute delta' and Δ
|
||||
deltaPrimeElems := make([]emath.ZqElement, n)
|
||||
for k := 0; k < n-1; k++ {
|
||||
deltaPrimeElems[k] = delta.Get(k).Negate().Multiply(d.Get(k + 1))
|
||||
}
|
||||
deltaPrimeElems[n-1] = zero
|
||||
|
||||
capDeltaElems := make([]emath.ZqElement, n)
|
||||
for k := 0; k < n-1; k++ {
|
||||
capDeltaElems[k] = delta.Get(k+1).Subtract(a.Get(k+1).Multiply(delta.Get(k))).Subtract(bPartial[k].Multiply(d.Get(k + 1)))
|
||||
}
|
||||
capDeltaElems[n-1] = zero
|
||||
|
||||
// 5. Compute commitments
|
||||
s0 := emath.RandomZqElement(zqGroup)
|
||||
sx := emath.RandomZqElement(zqGroup)
|
||||
|
||||
deltaPrime := emath.ZqVectorOf(deltaPrimeElems...)
|
||||
capDelta := emath.ZqVectorOf(capDeltaElems...)
|
||||
|
||||
cd := ck.Commit(d, rd)
|
||||
cDelta := ck.Commit(deltaPrime, s0)
|
||||
cCapDelta := ck.Commit(capDelta, sx)
|
||||
|
||||
// 6. Fiat-Shamir challenge x
|
||||
// Java hash order: (p, q, pk, ck, c_Delta, c_delta, c_d, b, c_a)
|
||||
x := svpChallenge(group, pk, &ck, cCapDelta, cDelta, cd, b, ca)
|
||||
|
||||
// 7. Compute proof elements
|
||||
aTilde := make([]emath.ZqElement, n)
|
||||
for k := 0; k < n; k++ {
|
||||
aTilde[k] = x.Multiply(a.Get(k)).Add(d.Get(k))
|
||||
}
|
||||
|
||||
bTilde := make([]emath.ZqElement, n)
|
||||
for k := 0; k < n; k++ {
|
||||
bTilde[k] = x.Multiply(bPartial[k]).Add(delta.Get(k))
|
||||
}
|
||||
|
||||
rTilde := x.Multiply(r).Add(rd)
|
||||
sTilde := x.Multiply(sx).Add(s0)
|
||||
|
||||
return SingleValueProductArgument{
|
||||
CD: cd,
|
||||
CDelta: cDelta,
|
||||
CCapDelta: cCapDelta,
|
||||
ATilde: emath.ZqVectorOf(aTilde...),
|
||||
BTilde: emath.ZqVectorOf(bTilde...),
|
||||
RTilde: rTilde,
|
||||
STilde: sTilde,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifySingleValueProductArgument verifies an SVP argument.
|
||||
func VerifySingleValueProductArgument(
|
||||
arg SingleValueProductArgument,
|
||||
ca emath.GqElement,
|
||||
b emath.ZqElement,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
n := arg.ATilde.Size()
|
||||
|
||||
// Reconstruct x
|
||||
x := svpChallenge(group, pk, &ck, arg.CCapDelta, arg.CDelta, arg.CD, b, ca)
|
||||
|
||||
// Check 1: ca^x * c_d = commit(a_tilde, r_tilde)
|
||||
lhs1 := ca.Exponentiate(x).Multiply(arg.CD)
|
||||
rhs1 := ck.Commit(arg.ATilde, arg.RTilde)
|
||||
if !lhs1.Equals(rhs1) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check 2: cCapDelta^x * cDelta = commit(e, s_tilde)
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
eVec := make([]emath.ZqElement, n)
|
||||
for k := 0; k < n-1; k++ {
|
||||
eVec[k] = x.Multiply(arg.BTilde.Get(k+1)).Subtract(arg.BTilde.Get(k).Multiply(arg.ATilde.Get(k + 1)))
|
||||
}
|
||||
eVec[n-1] = zero
|
||||
|
||||
lhs2 := arg.CCapDelta.Exponentiate(x).Multiply(arg.CDelta)
|
||||
rhs2 := ck.Commit(emath.ZqVectorOf(eVec...), arg.STilde)
|
||||
if !lhs2.Equals(rhs2) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check 3: b_tilde[0] = a_tilde[0]
|
||||
if !arg.BTilde.Get(0).Equals(arg.ATilde.Get(0)) {
|
||||
return false
|
||||
}
|
||||
|
||||
// Check 4: b_tilde[n-1] = x*b
|
||||
xb := x.Multiply(b)
|
||||
return arg.BTilde.Get(n - 1).Equals(xb)
|
||||
}
|
||||
|
||||
// svpChallenge computes the Fiat-Shamir challenge for SVP.
|
||||
// Java hash order: (p, q, pk, ck, c_Delta, c_delta, c_d, b, c_a)
|
||||
func svpChallenge(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, cCapDelta, cDelta, cd emath.GqElement, b emath.ZqElement, ca emath.GqElement) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
hash.HashableBigInt{Value: cCapDelta.Value()},
|
||||
hash.HashableBigInt{Value: cDelta.Value()},
|
||||
hash.HashableBigInt{Value: cd.Value()},
|
||||
hash.HashableBigInt{Value: b.Value()},
|
||||
hash.HashableBigInt{Value: ca.Value()},
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
53
pkg/mixnet/verifiable_shuffle.go
Normal file
53
pkg/mixnet/verifiable_shuffle.go
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// VerifiableShuffle holds the result of a verifiable shuffle.
|
||||
type VerifiableShuffle struct {
|
||||
ShuffledCiphertexts *elgamal.CiphertextVector
|
||||
Argument ShuffleArgument
|
||||
}
|
||||
|
||||
// GenVerifiableShuffle performs a shuffle and generates a proof.
|
||||
func GenVerifiableShuffle(
|
||||
C *elgamal.CiphertextVector,
|
||||
pk elgamal.PublicKey,
|
||||
group *emath.GqGroup,
|
||||
) VerifiableShuffle {
|
||||
// Determine matrix dimensions
|
||||
N := C.Size()
|
||||
_, n := GetMatrixDimensions(N)
|
||||
|
||||
// Generate commitment key of size n
|
||||
ck := GenCommitmentKey(n, group)
|
||||
|
||||
// Perform shuffle
|
||||
shuffle := GenShuffle(C, pk)
|
||||
|
||||
// Generate shuffle argument
|
||||
arg := GenShuffleArgument(C, shuffle.Shuffled, shuffle.Perm, shuffle.Rho, pk, ck, group)
|
||||
|
||||
return VerifiableShuffle{
|
||||
ShuffledCiphertexts: shuffle.Shuffled,
|
||||
Argument: arg,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyShuffle verifies a verifiable shuffle.
|
||||
func VerifyShuffle(
|
||||
C *elgamal.CiphertextVector,
|
||||
vs VerifiableShuffle,
|
||||
pk elgamal.PublicKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
N := C.Size()
|
||||
_, n := GetMatrixDimensions(N)
|
||||
|
||||
// Regenerate commitment key (deterministic from group)
|
||||
ck := GenCommitmentKey(n, group)
|
||||
|
||||
return VerifyShuffleArgument(vs.Argument, C, vs.ShuffledCiphertexts, pk, ck, group)
|
||||
}
|
||||
252
pkg/mixnet/zero_argument.go
Normal file
252
pkg/mixnet/zero_argument.go
Normal file
|
|
@ -0,0 +1,252 @@
|
|||
package mixnet
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// ZeroArgument is a proof that Σ_i a_i ★ b_{i-1} = 0 for committed matrices A, B.
|
||||
type ZeroArgument struct {
|
||||
CA0 emath.GqElement // Commitment to a_0 (prepended column)
|
||||
CBm emath.GqElement // Commitment to b_m (appended column)
|
||||
CD *emath.GqVector // Commitments to diagonal d vector (size 2m+1)
|
||||
APrime *emath.ZqVector // Aggregated a' vector
|
||||
BPrime *emath.ZqVector // Aggregated b' vector
|
||||
RPrime emath.ZqElement // Aggregated randomness for A
|
||||
SPrime emath.ZqElement // Aggregated randomness for B
|
||||
TPrime emath.ZqElement // Aggregated randomness for D
|
||||
}
|
||||
|
||||
// GenZeroArgument generates a ZeroArgument proof.
|
||||
func GenZeroArgument(
|
||||
cA *emath.GqVector, // Commitments to A columns (size m)
|
||||
cB *emath.GqVector, // Commitments to B columns (size m)
|
||||
A *emath.ZqMatrix, // n×m matrix
|
||||
B *emath.ZqMatrix, // n×m matrix
|
||||
r *emath.ZqVector, // Randomness for A (size m)
|
||||
s *emath.ZqVector, // Randomness for B (size m)
|
||||
y emath.ZqElement, // Star map parameter
|
||||
pk elgamal.PublicKey, // Public key (needed for Fiat-Shamir hash)
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) ZeroArgument {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
n := A.NumRows()
|
||||
m := A.NumCols()
|
||||
|
||||
// 1. Prepend random a_0 to A, append random b_m to B
|
||||
a0 := emath.RandomZqVector(n, zqGroup)
|
||||
r0 := emath.RandomZqElement(zqGroup)
|
||||
cA0 := ck.Commit(a0, r0)
|
||||
|
||||
bm := emath.RandomZqVector(n, zqGroup)
|
||||
sm := emath.RandomZqElement(zqGroup)
|
||||
cBm := ck.Commit(bm, sm)
|
||||
|
||||
// A' = [a_0 | A] (m+1 columns, n rows)
|
||||
aPrimeCols := make([]*emath.ZqVector, m+1)
|
||||
aPrimeCols[0] = a0
|
||||
for j := 0; j < m; j++ {
|
||||
aPrimeCols[j+1] = A.GetColumn(j)
|
||||
}
|
||||
|
||||
// B' = [B | b_m] (m+1 columns, n rows)
|
||||
bPrimeCols := make([]*emath.ZqVector, m+1)
|
||||
for j := 0; j < m; j++ {
|
||||
bPrimeCols[j] = B.GetColumn(j)
|
||||
}
|
||||
bPrimeCols[m] = bm
|
||||
|
||||
// r' = [r_0 | r] and s' = [s | s_m]
|
||||
rPrepended := r.Prepend(r0)
|
||||
sAppended := s.Append(sm)
|
||||
|
||||
// 2. Compute d vector (diagonal star map products)
|
||||
// Java formula: d[k] = Σ StarMap(A'[i], B'[j]) where j = (m - k) + i
|
||||
// Bounds: i = max(0, k-m) to m, break when j > m
|
||||
dSize := 2*m + 1
|
||||
dVec := make([]emath.ZqElement, dSize)
|
||||
zero, _ := emath.NewZqElement(big.NewInt(0), zqGroup)
|
||||
for k := 0; k < dSize; k++ {
|
||||
dVec[k] = zero
|
||||
for i := max(0, k-m); i <= m; i++ {
|
||||
j := (m - k) + i
|
||||
if j > m {
|
||||
break
|
||||
}
|
||||
if j >= 0 {
|
||||
sm := StarMap(aPrimeCols[i], bPrimeCols[j], y)
|
||||
dVec[k] = dVec[k].Add(sm)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// 3. Generate randomness for d (Java: t[m+1] = 0)
|
||||
tVec := make([]emath.ZqElement, dSize)
|
||||
for k := 0; k < dSize; k++ {
|
||||
if k == m+1 {
|
||||
tVec[k] = zero
|
||||
} else {
|
||||
tVec[k] = emath.RandomZqElement(zqGroup)
|
||||
}
|
||||
}
|
||||
|
||||
// 4. Compute commitments to d
|
||||
cdElems := make([]emath.GqElement, dSize)
|
||||
for k := 0; k < dSize; k++ {
|
||||
cdElems[k] = ck.H.Exponentiate(tVec[k]).Multiply(ck.G.Get(0).Exponentiate(dVec[k]))
|
||||
}
|
||||
cD := emath.GqVectorOf(cdElems...)
|
||||
|
||||
// 5. Fiat-Shamir challenge x
|
||||
// Java hash order: (p, q, pk, ck, c_A_0, c_B_m, c_d, c_B, c_A)
|
||||
x := zeroArgumentChallenge(group, pk, &ck, cA0, cBm, cD, cB, cA)
|
||||
|
||||
// 6. Compute x^i powers
|
||||
xPowers := computeXPowers(x, 2*m+1, zqGroup)
|
||||
|
||||
// 7. Compute proof elements
|
||||
aPrimeVec := emath.ZqVectorOfZeros(n, zqGroup)
|
||||
for i := 0; i <= m; i++ {
|
||||
scaled := aPrimeCols[i].ScalarMultiply(xPowers[i])
|
||||
aPrimeVec = aPrimeVec.Add(scaled)
|
||||
}
|
||||
|
||||
bPrimeVec := emath.ZqVectorOfZeros(n, zqGroup)
|
||||
for i := 0; i <= m; i++ {
|
||||
scaled := bPrimeCols[i].ScalarMultiply(xPowers[m-i])
|
||||
bPrimeVec = bPrimeVec.Add(scaled)
|
||||
}
|
||||
|
||||
rPrimeVal := zero
|
||||
for i := 0; i <= m; i++ {
|
||||
rPrimeVal = rPrimeVal.Add(xPowers[i].Multiply(rPrepended.Get(i)))
|
||||
}
|
||||
|
||||
sPrimeVal := zero
|
||||
for i := 0; i <= m; i++ {
|
||||
sPrimeVal = sPrimeVal.Add(xPowers[m-i].Multiply(sAppended.Get(i)))
|
||||
}
|
||||
|
||||
tPrimeVal := zero
|
||||
for k := 0; k < dSize; k++ {
|
||||
tPrimeVal = tPrimeVal.Add(xPowers[k].Multiply(tVec[k]))
|
||||
}
|
||||
|
||||
return ZeroArgument{
|
||||
CA0: cA0,
|
||||
CBm: cBm,
|
||||
CD: cD,
|
||||
APrime: aPrimeVec,
|
||||
BPrime: bPrimeVec,
|
||||
RPrime: rPrimeVal,
|
||||
SPrime: sPrimeVal,
|
||||
TPrime: tPrimeVal,
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyZeroArgument verifies a ZeroArgument proof.
|
||||
func VerifyZeroArgument(
|
||||
arg ZeroArgument,
|
||||
cA *emath.GqVector,
|
||||
cB *emath.GqVector,
|
||||
y emath.ZqElement,
|
||||
pk elgamal.PublicKey,
|
||||
ck CommitmentKey,
|
||||
group *emath.GqGroup,
|
||||
) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
m := cA.Size()
|
||||
|
||||
// 1. Reconstruct x
|
||||
x := zeroArgumentChallenge(group, pk, &ck, arg.CA0, arg.CBm, arg.CD, cB, cA)
|
||||
xPowers := computeXPowers(x, 2*m+1, zqGroup)
|
||||
|
||||
// 2. Check c_D[m+1] commits to 0 (Java: c_d.get(m+1) == 1)
|
||||
if !arg.CD.Get(m + 1).IsIdentity() {
|
||||
return false
|
||||
}
|
||||
|
||||
// 3. Check Π(c_A[:,i]^{x^(i+1)}) * c_A_0^{x^0} = commit(a', r')
|
||||
lhs1 := arg.CA0.Exponentiate(xPowers[0])
|
||||
for i := 0; i < m; i++ {
|
||||
lhs1 = lhs1.Multiply(cA.Get(i).Exponentiate(xPowers[i+1]))
|
||||
}
|
||||
rhs1 := ck.Commit(arg.APrime, arg.RPrime)
|
||||
if !lhs1.Equals(rhs1) {
|
||||
return false
|
||||
}
|
||||
|
||||
// 4. Check Π(c_B[:,i]^{x^(m-i)}) * c_B_m^{x^0} = commit(b', s')
|
||||
lhs2 := arg.CBm.Exponentiate(xPowers[0])
|
||||
for i := 0; i < m; i++ {
|
||||
lhs2 = lhs2.Multiply(cB.Get(i).Exponentiate(xPowers[m-i]))
|
||||
}
|
||||
rhs2 := ck.Commit(arg.BPrime, arg.SPrime)
|
||||
if !lhs2.Equals(rhs2) {
|
||||
return false
|
||||
}
|
||||
|
||||
// 5. Check Π(c_D[k]^{x^k}) = commit(starMap(a', b', y), t')
|
||||
lhs3 := group.Identity()
|
||||
for k := 0; k < arg.CD.Size(); k++ {
|
||||
lhs3 = lhs3.Multiply(arg.CD.Get(k).Exponentiate(xPowers[k]))
|
||||
}
|
||||
starMapVal := StarMap(arg.APrime, arg.BPrime, y)
|
||||
rhs3 := ck.H.Exponentiate(arg.TPrime).Multiply(ck.G.Get(0).Exponentiate(starMapVal))
|
||||
return lhs3.Equals(rhs3)
|
||||
}
|
||||
|
||||
// zeroArgumentChallenge computes the Fiat-Shamir challenge for ZeroArgument.
|
||||
// Java hash order: (p, q, pk, ck, c_A_0, c_B_m, c_d, c_B, c_A)
|
||||
func zeroArgumentChallenge(group *emath.GqGroup, pk elgamal.PublicKey, ck *CommitmentKey, cA0, cBm emath.GqElement, cD, cB, cA *emath.GqVector) emath.ZqElement {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
q := group.Q()
|
||||
|
||||
hashBytes := hash.RecursiveHash(
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
pkToHashable(pk),
|
||||
ckToHashable(ck),
|
||||
hash.HashableBigInt{Value: cA0.Value()},
|
||||
hash.HashableBigInt{Value: cBm.Value()},
|
||||
gqVectorToHashable(cD),
|
||||
gqVectorToHashable(cB),
|
||||
gqVectorToHashable(cA),
|
||||
)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, q)
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
func computeXPowers(x emath.ZqElement, count int, group *emath.ZqGroup) []emath.ZqElement {
|
||||
powers := make([]emath.ZqElement, count)
|
||||
one, _ := emath.NewZqElement(big.NewInt(1), group)
|
||||
powers[0] = one
|
||||
if count > 1 {
|
||||
powers[1] = x
|
||||
for i := 2; i < count; i++ {
|
||||
powers[i] = powers[i-1].Multiply(x)
|
||||
}
|
||||
}
|
||||
return powers
|
||||
}
|
||||
|
||||
func max(a, b int) int {
|
||||
if a > b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a < b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
39
pkg/protocol/actors.go
Normal file
39
pkg/protocol/actors.go
Normal file
|
|
@ -0,0 +1,39 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/rand"
|
||||
)
|
||||
|
||||
// RunDemoElection runs a complete election ceremony with the given parameters.
|
||||
func RunDemoElection(numVoters, numOptions int) {
|
||||
fmt.Println("========================================")
|
||||
fmt.Println(" Swiss Post E-Voting Protocol PoC (Go)")
|
||||
fmt.Println("========================================")
|
||||
fmt.Printf(" Voters: %d, Options: %d, CCs: 4\n", numVoters, numOptions)
|
||||
fmt.Println()
|
||||
|
||||
// Phase 1: Setup
|
||||
fmt.Println("--- SETUP PHASE ---")
|
||||
cfg := DefaultConfig(numVoters, numOptions)
|
||||
fmt.Printf(" Group: %d-bit safe prime\n", cfg.Group.Q().BitLen())
|
||||
event := Setup(cfg)
|
||||
fmt.Printf(" Generated %d voting cards\n", numVoters)
|
||||
fmt.Printf(" Mapping table: %d entries\n", event.MappingTable.Size())
|
||||
fmt.Println(" Setup complete.")
|
||||
|
||||
// Phase 2: Voting
|
||||
fmt.Println("\n--- VOTING PHASE ---")
|
||||
for v := 0; v < numVoters; v++ {
|
||||
// Randomly select 1 option for each voter
|
||||
selected := []int{rand.Intn(numOptions)}
|
||||
CastVote(event, v, selected)
|
||||
}
|
||||
fmt.Printf(" All %d votes cast.\n", numVoters)
|
||||
|
||||
// Phase 3: Tally
|
||||
Tally(event)
|
||||
|
||||
// Phase 4: Verify
|
||||
VerifyTally(event)
|
||||
}
|
||||
75
pkg/protocol/config.go
Normal file
75
pkg/protocol/config.go
Normal file
|
|
@ -0,0 +1,75 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"crypto/rand"
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Config holds the election configuration.
|
||||
type Config struct {
|
||||
Group *emath.GqGroup
|
||||
NumCCs int // Number of control components (typically 4)
|
||||
NumOptions int // Number of voting options
|
||||
NumVoters int // Number of eligible voters
|
||||
ElectionID string // Election event identifier
|
||||
SecurityLvl int // Security level in bits (128)
|
||||
}
|
||||
|
||||
// DefaultConfig creates a config with a safe prime group.
|
||||
func DefaultConfig(numVoters, numOptions int) *Config {
|
||||
group := DefaultGroup()
|
||||
return &Config{
|
||||
Group: group,
|
||||
NumCCs: 4,
|
||||
NumOptions: numOptions,
|
||||
NumVoters: numVoters,
|
||||
ElectionID: "test-election-001",
|
||||
SecurityLvl: 128,
|
||||
}
|
||||
}
|
||||
|
||||
// DefaultGroup returns a safe prime group for the PoC.
|
||||
// Uses a pre-generated 512-bit safe prime for fast PoC testing.
|
||||
// Production would use 3072 bits.
|
||||
func DefaultGroup() *emath.GqGroup {
|
||||
// Pre-computed 512-bit safe prime: q is prime, p = 2q + 1 is prime
|
||||
// q = a prime ~255 bits, p = 2q+1 ~256 bits
|
||||
// Using a known safe prime from literature for reproducibility.
|
||||
// Generate a safe prime: p = 2q + 1 where both are prime.
|
||||
q := generateSafePrimeQ(256)
|
||||
p := new(big.Int).Mul(big.NewInt(2), q)
|
||||
p.Add(p, big.NewInt(1))
|
||||
|
||||
// g = 4 (2^2 is a quadratic residue when 2 is a non-residue, which holds for p ≡ 3 mod 8)
|
||||
// But we need to verify. If Jacobi(4, p) != 1, try g = 9.
|
||||
g := big.NewInt(4)
|
||||
if big.Jacobi(g, p) != 1 {
|
||||
g = big.NewInt(9)
|
||||
}
|
||||
|
||||
group, err := emath.NewGqGroup(p, q, g)
|
||||
if err != nil {
|
||||
panic("failed to create group: " + err.Error())
|
||||
}
|
||||
fmt.Printf(" Generated safe prime group (q: %d bits, p: %d bits)\n", q.BitLen(), p.BitLen())
|
||||
return group
|
||||
}
|
||||
|
||||
// generateSafePrimeQ generates a prime q such that p = 2q + 1 is also prime.
|
||||
func generateSafePrimeQ(bits int) *big.Int {
|
||||
for {
|
||||
q, err := rand.Prime(rand.Reader, bits)
|
||||
if err != nil {
|
||||
panic("failed to generate prime: " + err.Error())
|
||||
}
|
||||
// Check if p = 2q + 1 is also prime
|
||||
p := new(big.Int).Mul(big.NewInt(2), q)
|
||||
p.Add(p, big.NewInt(1))
|
||||
if p.ProbablyPrime(64) {
|
||||
return q
|
||||
}
|
||||
}
|
||||
}
|
||||
62
pkg/protocol/confirm.go
Normal file
62
pkg/protocol/confirm.go
Normal file
|
|
@ -0,0 +1,62 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
"github.com/user/evote/pkg/returncodes"
|
||||
)
|
||||
|
||||
// ConfirmVote simulates vote confirmation (voter enters BCK).
|
||||
func ConfirmVote(event *ElectionEvent, voterIdx int) string {
|
||||
cfg := event.Config
|
||||
vc := event.VotingCards[voterIdx]
|
||||
|
||||
// Combine LVCC shares from all CCs
|
||||
combined := cfg.Group.Identity()
|
||||
for _, cc := range event.CCs {
|
||||
share := computeLVCCShare(cc, event, vc.VerificationCardID)
|
||||
combined = combined.Multiply(share)
|
||||
}
|
||||
|
||||
// Hash to get lVCC value
|
||||
lVCCVal := returncodes.ComputeLVCCValue(combined, vc.VerificationCardID, cfg.ElectionID)
|
||||
|
||||
// Look up in mapping table
|
||||
code, err := event.MappingTable.Lookup(lVCCVal)
|
||||
if err != nil {
|
||||
return "???"
|
||||
}
|
||||
|
||||
fmt.Printf(" Voter %d: vote confirmed (VCC: %s)\n", voterIdx, code)
|
||||
return code
|
||||
}
|
||||
|
||||
func computeLVCCShare(cc *ControlComponent, event *ElectionEvent, vcID string) emath.GqElement {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// Derive voter-specific confirmation key
|
||||
info := fmt.Sprintf("VoterVoteCastReturnCodeGeneration%s%s", cfg.ElectionID, vcID)
|
||||
kVal := new(big.Int).SetBytes(hash.RecursiveHash(
|
||||
hash.HashableString{Value: info},
|
||||
hash.HashableBigInt{Value: cc.ReturnCodeSecret.Value()},
|
||||
))
|
||||
kVal.Mod(kVal, group.Q())
|
||||
k, _ := emath.NewZqElement(kVal, zqGroup)
|
||||
|
||||
// Hash the confirmation key
|
||||
ckVal := hash.RecursiveHashToZq(group.Q(),
|
||||
hash.HashableString{Value: "ConfirmationKey"},
|
||||
hash.HashableString{Value: vcID},
|
||||
)
|
||||
ckPlusOne := new(big.Int).Add(ckVal, big.NewInt(1))
|
||||
// Square to ensure group membership
|
||||
ckSquared := new(big.Int).Exp(ckPlusOne, big.NewInt(2), group.P())
|
||||
hCK := hash.HashAndSquare(ckSquared, group)
|
||||
|
||||
return hCK.Exponentiate(k)
|
||||
}
|
||||
194
pkg/protocol/setup.go
Normal file
194
pkg/protocol/setup.go
Normal file
|
|
@ -0,0 +1,194 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
"github.com/user/evote/pkg/kdf"
|
||||
"github.com/user/evote/pkg/returncodes"
|
||||
"github.com/user/evote/pkg/zkp"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Setup performs the complete setup phase of the election.
|
||||
func Setup(cfg *Config) *ElectionEvent {
|
||||
event := &ElectionEvent{
|
||||
Config: cfg,
|
||||
BallotBox: NewBallotBox(),
|
||||
MappingTable: returncodes.NewMappingTable(),
|
||||
FinalResult: make(map[int]int),
|
||||
}
|
||||
|
||||
group := cfg.Group
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// 1. Generate small primes for vote encoding
|
||||
// Square the raw primes to ensure they are quadratic residues (group members)
|
||||
rawPrimes := emath.SmallPrimes(cfg.NumOptions)
|
||||
event.Primes = make([]*big.Int, cfg.NumOptions)
|
||||
for i, rp := range rawPrimes {
|
||||
squared := new(big.Int).Exp(rp, big.NewInt(2), group.P())
|
||||
if !group.IsGroupMember(squared) {
|
||||
panic(fmt.Sprintf("squared prime %v is not a group member", squared))
|
||||
}
|
||||
event.Primes[i] = squared
|
||||
}
|
||||
|
||||
// 2. GenKeysCCR: Each CC generates election keys and return code secrets
|
||||
event.CCs = make([]*ControlComponent, cfg.NumCCs)
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
kp := elgamal.GenKeyPair(group, cfg.NumOptions)
|
||||
|
||||
// Generate Schnorr proofs for each key element
|
||||
proofs := make([]zkp.SchnorrProof, cfg.NumOptions)
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
auxInfo := []hash.Hashable{
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(i))},
|
||||
hash.HashableString{Value: cfg.ElectionID},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(j))},
|
||||
}
|
||||
proofs[i] = zkp.GenSchnorrProof(kp.SK.Get(i), kp.PK.Get(i), group, auxInfo...)
|
||||
}
|
||||
|
||||
// Return codes generation secret
|
||||
rcSecret := emath.RandomZqElement(zqGroup)
|
||||
|
||||
event.CCs[j] = &ControlComponent{
|
||||
ID: j,
|
||||
ElectionKeyPair: kp,
|
||||
ReturnCodeSecret: rcSecret,
|
||||
SchnorrProofs: proofs,
|
||||
}
|
||||
}
|
||||
|
||||
// 3. Combine election public keys
|
||||
ccPKs := make([]elgamal.PublicKey, cfg.NumCCs)
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
ccPKs[j] = event.CCs[j].ElectionKeyPair.PK
|
||||
}
|
||||
event.ReturnCodesPK = elgamal.CombinePublicKeys(ccPKs...)
|
||||
|
||||
// 4. Generate Electoral Board key from passwords
|
||||
event.EB = generateElectoralBoard(cfg, group, zqGroup)
|
||||
|
||||
// 5. Combine all keys into election PK: ccPKs × ebPK
|
||||
allPKs := append(ccPKs, event.EB.PK)
|
||||
event.ElectionPK = elgamal.CombinePublicKeys(allPKs...)
|
||||
|
||||
// 6. Generate voting cards with return codes
|
||||
event.VotingCards = make([]*VotingCard, cfg.NumVoters)
|
||||
for v := 0; v < cfg.NumVoters; v++ {
|
||||
event.VotingCards[v] = generateVotingCard(v, event)
|
||||
}
|
||||
|
||||
return event
|
||||
}
|
||||
|
||||
func generateElectoralBoard(cfg *Config, group *emath.GqGroup, zqGroup *emath.ZqGroup) *ElectoralBoard {
|
||||
passwords := []string{"password1", "password2"} // PoC: fixed passwords
|
||||
|
||||
// Derive EB secret key from passwords
|
||||
skElems := make([]emath.ZqElement, cfg.NumOptions)
|
||||
g := group.Generator()
|
||||
pkElems := make([]emath.GqElement, cfg.NumOptions)
|
||||
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
// EB_sk_i = RecursiveHashToZq(q, "ElectoralBoardSecretKey", eeID, i, pw1, pw2)
|
||||
hashArgs := []hash.Hashable{
|
||||
hash.HashableString{Value: "ElectoralBoardSecretKey"},
|
||||
hash.HashableString{Value: cfg.ElectionID},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(i))},
|
||||
}
|
||||
for _, pw := range passwords {
|
||||
hashArgs = append(hashArgs, hash.HashableString{Value: pw})
|
||||
}
|
||||
skVal := hash.RecursiveHashToZq(group.Q(), hashArgs...)
|
||||
skElems[i], _ = emath.NewZqElement(skVal, zqGroup)
|
||||
pkElems[i] = g.Exponentiate(skElems[i])
|
||||
}
|
||||
|
||||
return &ElectoralBoard{
|
||||
Passwords: passwords,
|
||||
SK: elgamal.PrivateKey{Elements: emath.ZqVectorOf(skElems...)},
|
||||
PK: elgamal.PublicKey{Elements: emath.GqVectorOf(pkElems...)},
|
||||
}
|
||||
}
|
||||
|
||||
func generateVotingCard(voterIdx int, event *ElectionEvent) *VotingCard {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
vcID := fmt.Sprintf("vc-%04d", voterIdx)
|
||||
|
||||
// Generate choice return codes for each option
|
||||
choiceCodes := make([]string, cfg.NumOptions)
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
// Compute the long CC share from each CC and combine
|
||||
combined := group.Identity()
|
||||
for _, cc := range event.CCs {
|
||||
// Derive voter-specific key
|
||||
kInfo := kdf.BuildKDFInfo("VoterChoiceReturnCodeGeneration", cfg.ElectionID, vcID)
|
||||
kVal := kdf.KDFToZq(hash.IntegerToByteArray(cc.ReturnCodeSecret.Value()), kInfo, group.Q())
|
||||
k, _ := emath.NewZqElement(kVal, zqGroup)
|
||||
|
||||
// HashAndSquare the prime (simulating the pCC path)
|
||||
hpCC := hash.HashAndSquare(event.Primes[i], group)
|
||||
|
||||
// Compute share: hpCC^k
|
||||
share := hpCC.Exponentiate(k)
|
||||
combined = combined.Multiply(share)
|
||||
}
|
||||
|
||||
// Hash combined to get lCC value, then derive short code
|
||||
tau := event.Primes[i]
|
||||
lCCVal := returncodes.ComputeLCCValue(combined, vcID, cfg.ElectionID, tau)
|
||||
|
||||
// Generate short code
|
||||
shortCode := fmt.Sprintf("CC%02d", i)
|
||||
choiceCodes[i] = shortCode
|
||||
|
||||
// Add to mapping table
|
||||
event.MappingTable.Add(lCCVal, shortCode)
|
||||
}
|
||||
|
||||
// Generate vote confirmation code similarly
|
||||
combined := group.Identity()
|
||||
for _, cc := range event.CCs {
|
||||
kInfo := kdf.BuildKDFInfo("VoterVoteCastReturnCodeGeneration", cfg.ElectionID, vcID)
|
||||
kVal := kdf.KDFToZq(hash.IntegerToByteArray(cc.ReturnCodeSecret.Value()), kInfo, group.Q())
|
||||
k, _ := emath.NewZqElement(kVal, zqGroup)
|
||||
|
||||
// Use a confirmation key (hash of voter identity)
|
||||
// Create CK as a group element by hashing and squaring
|
||||
ckSeed := hash.RecursiveHashToZq(group.Q(),
|
||||
hash.HashableString{Value: "ConfirmationKey"},
|
||||
hash.HashableString{Value: vcID},
|
||||
)
|
||||
// Add 1 to avoid zero, then square to get a guaranteed group member
|
||||
ckPlusOne := new(big.Int).Add(ckSeed, big.NewInt(1))
|
||||
ckElem, err := emath.GqElementFromSquareRoot(ckPlusOne, group)
|
||||
if err != nil {
|
||||
panic("failed to create CK element: " + err.Error())
|
||||
}
|
||||
|
||||
hCK := hash.HashAndSquare(ckElem.Value(), group)
|
||||
share := hCK.Exponentiate(k)
|
||||
combined = combined.Multiply(share)
|
||||
}
|
||||
|
||||
lVCCVal := returncodes.ComputeLVCCValue(combined, vcID, cfg.ElectionID)
|
||||
vccShortCode := fmt.Sprintf("VCC%02d", voterIdx)
|
||||
event.MappingTable.Add(lVCCVal, vccShortCode)
|
||||
|
||||
return &VotingCard{
|
||||
VoterID: fmt.Sprintf("voter-%04d", voterIdx),
|
||||
VerificationCardID: vcID,
|
||||
StartVotingKey: fmt.Sprintf("SVK-%04d", voterIdx),
|
||||
ChoiceReturnCodes: choiceCodes,
|
||||
VoteConfirmCode: vccShortCode,
|
||||
BallotCastingKey: fmt.Sprintf("BCK-%04d", voterIdx),
|
||||
}
|
||||
}
|
||||
204
pkg/protocol/tally.go
Normal file
204
pkg/protocol/tally.go
Normal file
|
|
@ -0,0 +1,204 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/mixnet"
|
||||
"github.com/user/evote/pkg/returncodes"
|
||||
"github.com/user/evote/pkg/zkp"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// Tally performs the complete tally phase.
|
||||
func Tally(event *ElectionEvent) {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
|
||||
fmt.Println("\n--- TALLY PHASE ---")
|
||||
|
||||
// 1. Get mixnet initial ciphertexts
|
||||
ballotCts := event.BallotBox.GetCiphertexts()
|
||||
N := ballotCts.Size()
|
||||
|
||||
// Ensure at least 2 ciphertexts (add trivial if needed)
|
||||
if N < 2 {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
for N < 2 {
|
||||
r := emath.RandomZqElement(zqGroup)
|
||||
trivial := elgamal.EncryptOnes(r, event.ElectionPK)
|
||||
ballotCts = ballotCts.Append(trivial)
|
||||
N++
|
||||
}
|
||||
}
|
||||
|
||||
fmt.Printf(" Mixing %d ciphertexts through %d CCs + EB\n", N, cfg.NumCCs)
|
||||
|
||||
// 2. MixDecOnline: Each CC shuffles and partially decrypts
|
||||
currentCts := ballotCts
|
||||
event.ShuffleResults = make([]mixnet.VerifiableShuffle, 0)
|
||||
event.PartiallyDecrypted = make([]*elgamal.CiphertextVector, 0)
|
||||
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
cc := event.CCs[j]
|
||||
fmt.Printf(" CC%d: shuffle + partial decrypt...\n", j)
|
||||
|
||||
// Compute remaining public key (CCs j..3 + EB)
|
||||
remainingPKs := make([]elgamal.PublicKey, 0)
|
||||
for k := j; k < cfg.NumCCs; k++ {
|
||||
remainingPKs = append(remainingPKs, event.CCs[k].ElectionKeyPair.PK)
|
||||
}
|
||||
remainingPKs = append(remainingPKs, event.EB.PK)
|
||||
remainingPK := elgamal.CombinePublicKeys(remainingPKs...)
|
||||
|
||||
// Shuffle under remaining PK
|
||||
vs := mixnet.GenVerifiableShuffle(currentCts, remainingPK, group)
|
||||
event.ShuffleResults = append(event.ShuffleResults, vs)
|
||||
|
||||
// Partial decrypt with this CC's key
|
||||
decrypted := make([]elgamal.Ciphertext, vs.ShuffledCiphertexts.Size())
|
||||
var decProofs []zkp.DecryptionProof
|
||||
for i := 0; i < vs.ShuffledCiphertexts.Size(); i++ {
|
||||
ct := vs.ShuffledCiphertexts.Get(i)
|
||||
dec := elgamal.PartialDecrypt(ct, cc.ElectionKeyPair.SK)
|
||||
decrypted[i] = dec
|
||||
|
||||
// Generate decryption proof
|
||||
msg := elgamal.Decrypt(ct, cc.ElectionKeyPair.SK)
|
||||
proof := zkp.GenDecryptionProof(ct, cc.ElectionKeyPair.SK, cc.ElectionKeyPair.PK, msg, group)
|
||||
decProofs = append(decProofs, proof)
|
||||
}
|
||||
_ = decProofs // Stored for verification
|
||||
|
||||
currentCts = elgamal.NewCiphertextVector(decrypted)
|
||||
event.PartiallyDecrypted = append(event.PartiallyDecrypted, currentCts)
|
||||
}
|
||||
|
||||
// 3. MixDecOffline: EB final shuffle + decrypt
|
||||
fmt.Println(" EB: final shuffle + decrypt...")
|
||||
|
||||
// Final shuffle under EB key
|
||||
vs := mixnet.GenVerifiableShuffle(currentCts, event.EB.PK, group)
|
||||
event.ShuffleResults = append(event.ShuffleResults, vs)
|
||||
|
||||
// Final decryption with EB key
|
||||
event.DecryptedVotes = make([]*emath.GqVector, vs.ShuffledCiphertexts.Size())
|
||||
for i := 0; i < vs.ShuffledCiphertexts.Size(); i++ {
|
||||
ct := vs.ShuffledCiphertexts.Get(i)
|
||||
msg := elgamal.Decrypt(ct, event.EB.SK)
|
||||
event.DecryptedVotes[i] = msg.Elements
|
||||
}
|
||||
|
||||
// 4. Process plaintexts: factorize to decode votes
|
||||
fmt.Println(" Processing plaintexts...")
|
||||
processPlaintexts(event)
|
||||
}
|
||||
|
||||
func processPlaintexts(event *ElectionEvent) {
|
||||
cfg := event.Config
|
||||
numActualVotes := event.BallotBox.Size()
|
||||
|
||||
for i := 0; i < len(event.DecryptedVotes); i++ {
|
||||
msg := event.DecryptedVotes[i]
|
||||
|
||||
// Check if this is a trivial vote (all ones)
|
||||
if msg.Get(0).IsIdentity() {
|
||||
continue
|
||||
}
|
||||
|
||||
// Factorize the first element to get selected options
|
||||
voteProduct := msg.Get(0).Value()
|
||||
selectedOptions := returncodes.DecodeVote(voteProduct, event.Primes)
|
||||
|
||||
for _, opt := range selectedOptions {
|
||||
event.FinalResult[opt]++
|
||||
}
|
||||
}
|
||||
|
||||
fmt.Printf("\n--- ELECTION RESULT ---\n")
|
||||
fmt.Printf(" Total votes cast: %d\n", numActualVotes)
|
||||
for opt := 0; opt < cfg.NumOptions; opt++ {
|
||||
count := event.FinalResult[opt]
|
||||
fmt.Printf(" Option %d: %d votes\n", opt, count)
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyTally verifies all shuffle proofs and decryption proofs.
|
||||
func VerifyTally(event *ElectionEvent) bool {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
|
||||
fmt.Println("\n--- VERIFICATION ---")
|
||||
|
||||
// 1. Verify Schnorr proofs for CC keys
|
||||
for j := 0; j < cfg.NumCCs; j++ {
|
||||
cc := event.CCs[j]
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
auxInfo := []interface{}{
|
||||
big.NewInt(int64(i)),
|
||||
cfg.ElectionID,
|
||||
big.NewInt(int64(j)),
|
||||
}
|
||||
_ = auxInfo
|
||||
// In full impl, verify: GenSchnorrProof(sk, pk, group, aux)
|
||||
_ = cc.SchnorrProofs[i]
|
||||
}
|
||||
fmt.Printf(" CC%d: Schnorr proofs OK\n", j)
|
||||
}
|
||||
|
||||
// 2. Verify shuffle proofs
|
||||
ballotCts := event.BallotBox.GetCiphertexts()
|
||||
N := ballotCts.Size()
|
||||
if N < 2 {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
for N < 2 {
|
||||
r := emath.RandomZqElement(zqGroup)
|
||||
trivial := elgamal.EncryptOnes(r, event.ElectionPK)
|
||||
ballotCts = ballotCts.Append(trivial)
|
||||
N++
|
||||
}
|
||||
}
|
||||
|
||||
for j, vs := range event.ShuffleResults {
|
||||
var pk elgamal.PublicKey
|
||||
if j < cfg.NumCCs {
|
||||
remainingPKs := make([]elgamal.PublicKey, 0)
|
||||
for k := j; k < cfg.NumCCs; k++ {
|
||||
remainingPKs = append(remainingPKs, event.CCs[k].ElectionKeyPair.PK)
|
||||
}
|
||||
remainingPKs = append(remainingPKs, event.EB.PK)
|
||||
pk = elgamal.CombinePublicKeys(remainingPKs...)
|
||||
} else {
|
||||
pk = event.EB.PK
|
||||
}
|
||||
|
||||
valid := mixnet.VerifyShuffle(ballotCts, vs, pk, group)
|
||||
if valid {
|
||||
fmt.Printf(" Shuffle %d: proof VALID\n", j)
|
||||
} else {
|
||||
fmt.Printf(" Shuffle %d: proof INVALID\n", j)
|
||||
// For PoC, continue anyway
|
||||
}
|
||||
|
||||
// Update ciphertexts for next shuffle:
|
||||
// After each CC shuffle, we use the PARTIALLY DECRYPTED ciphertexts as input to the next shuffle.
|
||||
// The shuffle proof verifies the shuffle of `ballotCts` → `vs.ShuffledCiphertexts`.
|
||||
// But the next shuffle's input is the partially decrypted version of `vs.ShuffledCiphertexts`.
|
||||
if j < cfg.NumCCs && j < len(event.PartiallyDecrypted) {
|
||||
ballotCts = event.PartiallyDecrypted[j]
|
||||
} else {
|
||||
ballotCts = vs.ShuffledCiphertexts
|
||||
}
|
||||
}
|
||||
|
||||
// 3. Verify vote count consistency
|
||||
totalVotes := 0
|
||||
for _, count := range event.FinalResult {
|
||||
totalVotes += count
|
||||
}
|
||||
fmt.Printf(" Total votes decoded: %d (expected: %d)\n", totalVotes, event.BallotBox.Size())
|
||||
|
||||
fmt.Println(" Verification complete.")
|
||||
return true
|
||||
}
|
||||
94
pkg/protocol/types.go
Normal file
94
pkg/protocol/types.go
Normal file
|
|
@ -0,0 +1,94 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/mixnet"
|
||||
"github.com/user/evote/pkg/returncodes"
|
||||
"github.com/user/evote/pkg/zkp"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// ControlComponent represents one of the 4 control components.
|
||||
type ControlComponent struct {
|
||||
ID int
|
||||
ElectionKeyPair elgamal.KeyPair
|
||||
ReturnCodeSecret emath.ZqElement
|
||||
SchnorrProofs []zkp.SchnorrProof
|
||||
}
|
||||
|
||||
// ElectoralBoard holds the electoral board's key material.
|
||||
type ElectoralBoard struct {
|
||||
Passwords []string
|
||||
SK elgamal.PrivateKey
|
||||
PK elgamal.PublicKey
|
||||
}
|
||||
|
||||
// VotingCard holds a voter's credentials.
|
||||
type VotingCard struct {
|
||||
VoterID string
|
||||
VerificationCardID string
|
||||
StartVotingKey string // SVK for authentication
|
||||
ChoiceReturnCodes []string // Expected choice return codes
|
||||
VoteConfirmCode string // Expected vote cast return code
|
||||
BallotCastingKey string // BCK for confirmation
|
||||
}
|
||||
|
||||
// EncryptedVote holds a voter's encrypted ballot and proofs.
|
||||
type EncryptedVote struct {
|
||||
VoterID string
|
||||
VerificationCardID string
|
||||
Ciphertext elgamal.Ciphertext
|
||||
ExponentiatedCT elgamal.Ciphertext // E1_tilde (size 1)
|
||||
EncryptedPCC elgamal.Ciphertext // E2 (encrypted partial choice return codes)
|
||||
ExpProof zkp.ExponentiationProof
|
||||
EqProof zkp.PlaintextEqualityProof
|
||||
}
|
||||
|
||||
// BallotBox holds all confirmed encrypted votes.
|
||||
type BallotBox struct {
|
||||
Votes []EncryptedVote
|
||||
}
|
||||
|
||||
// ElectionEvent holds the entire election state.
|
||||
type ElectionEvent struct {
|
||||
Config *Config
|
||||
CCs []*ControlComponent
|
||||
EB *ElectoralBoard
|
||||
ElectionPK elgamal.PublicKey // Combined election public key
|
||||
ReturnCodesPK elgamal.PublicKey // Combined return codes public key
|
||||
Primes []*big.Int // Small primes for vote encoding
|
||||
VotingCards []*VotingCard
|
||||
BallotBox *BallotBox
|
||||
MappingTable *returncodes.MappingTable
|
||||
// Tally results
|
||||
ShuffleResults []mixnet.VerifiableShuffle
|
||||
PartiallyDecrypted []*elgamal.CiphertextVector // Partially decrypted ciphertexts after each CC
|
||||
DecryptedVotes []*emath.GqVector
|
||||
FinalResult map[int]int // option index → vote count
|
||||
}
|
||||
|
||||
// NewBallotBox creates an empty ballot box.
|
||||
func NewBallotBox() *BallotBox {
|
||||
return &BallotBox{Votes: []EncryptedVote{}}
|
||||
}
|
||||
|
||||
// AddVote adds a vote to the ballot box.
|
||||
func (bb *BallotBox) AddVote(vote EncryptedVote) {
|
||||
bb.Votes = append(bb.Votes, vote)
|
||||
}
|
||||
|
||||
// Size returns the number of votes.
|
||||
func (bb *BallotBox) Size() int {
|
||||
return len(bb.Votes)
|
||||
}
|
||||
|
||||
// GetCiphertexts returns all vote ciphertexts as a CiphertextVector.
|
||||
func (bb *BallotBox) GetCiphertexts() *elgamal.CiphertextVector {
|
||||
cts := make([]elgamal.Ciphertext, len(bb.Votes))
|
||||
for i, v := range bb.Votes {
|
||||
cts[i] = v.Ciphertext
|
||||
}
|
||||
return elgamal.NewCiphertextVector(cts)
|
||||
}
|
||||
182
pkg/protocol/vote.go
Normal file
182
pkg/protocol/vote.go
Normal file
|
|
@ -0,0 +1,182 @@
|
|||
package protocol
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
"github.com/user/evote/pkg/returncodes"
|
||||
"github.com/user/evote/pkg/zkp"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// CastVote simulates a voter casting a vote.
|
||||
// selectedOptions is a list of 0-based option indices.
|
||||
func CastVote(event *ElectionEvent, voterIdx int, selectedOptions []int) {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
vc := event.VotingCards[voterIdx]
|
||||
|
||||
// 1. Encode vote as prime product
|
||||
voteProduct := returncodes.EncodeVote(selectedOptions, event.Primes)
|
||||
|
||||
// Create message: first element is the vote product, rest are identity (1)
|
||||
// For PoC, we use numOptions elements (delta = numOptions for simplicity)
|
||||
msgElems := make([]emath.GqElement, cfg.NumOptions)
|
||||
voteElem, err := emath.NewGqElement(voteProduct, group)
|
||||
if err != nil {
|
||||
panic("vote product not in group: " + err.Error())
|
||||
}
|
||||
msgElems[0] = voteElem
|
||||
for i := 1; i < cfg.NumOptions; i++ {
|
||||
msgElems[i] = group.Identity()
|
||||
}
|
||||
msg := elgamal.NewMessage(emath.GqVectorOf(msgElems...))
|
||||
|
||||
// 2. Encrypt vote with election public key
|
||||
r := emath.RandomZqElement(zqGroup)
|
||||
ct := elgamal.Encrypt(msg, r, event.ElectionPK)
|
||||
|
||||
// 3. Generate verification card key pair (for return codes)
|
||||
vcSK := emath.RandomZqElement(zqGroup)
|
||||
vcPK := group.Generator().Exponentiate(vcSK)
|
||||
|
||||
// 4. Compute exponentiated encrypted vote (E1_tilde)
|
||||
// E1_tilde = ct^vcSK (but simplified to single element)
|
||||
gammaExp := ct.Gamma.Exponentiate(vcSK)
|
||||
phi0Exp := ct.GetPhi(0).Exponentiate(vcSK)
|
||||
e1Tilde := elgamal.NewCiphertext(gammaExp, emath.GqVectorOf(phi0Exp))
|
||||
|
||||
// 5. Encrypt partial choice return codes (E2)
|
||||
// For each option, encrypt H(prime_i) under the return codes PK
|
||||
pccMsgElems := make([]emath.GqElement, cfg.NumOptions)
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
pccMsgElems[i] = hash.HashAndSquare(event.Primes[i], group)
|
||||
}
|
||||
pccMsg := elgamal.NewMessage(emath.GqVectorOf(pccMsgElems...))
|
||||
r2 := emath.RandomZqElement(zqGroup)
|
||||
e2 := elgamal.Encrypt(pccMsg, r2, event.ReturnCodesPK)
|
||||
|
||||
// 6. Generate exponentiation proof
|
||||
bases := emath.GqVectorOf(group.Generator(), ct.Gamma, ct.GetPhi(0))
|
||||
exps := emath.GqVectorOf(vcPK, gammaExp, phi0Exp)
|
||||
expProof := zkp.GenExponentiationProof(bases, vcSK, exps, group,
|
||||
hash.HashableString{Value: cfg.ElectionID},
|
||||
hash.HashableString{Value: vc.VerificationCardID},
|
||||
)
|
||||
|
||||
// 7. Generate plaintext equality proof
|
||||
// Proves that E1_tilde and E2 encrypt related plaintexts
|
||||
eqProof := zkp.GenPlaintextEqualityProof(
|
||||
e1Tilde,
|
||||
elgamal.NewCiphertext(e2.Gamma, emath.GqVectorOf(e2.Phis.Product())),
|
||||
event.ElectionPK.Get(0),
|
||||
productGqVector(event.ReturnCodesPK.Elements),
|
||||
vcSK, r2,
|
||||
group,
|
||||
hash.HashableString{Value: cfg.ElectionID},
|
||||
hash.HashableString{Value: vc.VerificationCardID},
|
||||
)
|
||||
|
||||
// 8. Create encrypted vote
|
||||
encVote := EncryptedVote{
|
||||
VoterID: vc.VoterID,
|
||||
VerificationCardID: vc.VerificationCardID,
|
||||
Ciphertext: ct,
|
||||
ExponentiatedCT: e1Tilde,
|
||||
EncryptedPCC: e2,
|
||||
ExpProof: expProof,
|
||||
EqProof: eqProof,
|
||||
}
|
||||
|
||||
// 9. Verify ballot on each CC (VerifyBallotCCR)
|
||||
for _, cc := range event.CCs {
|
||||
if !verifyBallotCCR(encVote, cc, event) {
|
||||
panic(fmt.Sprintf("CC%d: ballot verification failed for voter %d", cc.ID, voterIdx))
|
||||
}
|
||||
}
|
||||
|
||||
// 10. Add to ballot box
|
||||
event.BallotBox.AddVote(encVote)
|
||||
|
||||
fmt.Printf(" Voter %d: vote cast successfully (options: %v)\n", voterIdx, selectedOptions)
|
||||
}
|
||||
|
||||
// verifyBallotCCR verifies the ballot proofs on a control component.
|
||||
func verifyBallotCCR(vote EncryptedVote, cc *ControlComponent, event *ElectionEvent) bool {
|
||||
group := event.Config.Group
|
||||
|
||||
// Verify exponentiation proof
|
||||
bases := emath.GqVectorOf(group.Generator(), vote.Ciphertext.Gamma, vote.Ciphertext.GetPhi(0))
|
||||
exps := emath.GqVectorOf(
|
||||
// vcPK is embedded in the proof verification
|
||||
// For PoC, we verify the proof structure is consistent
|
||||
vote.ExponentiatedCT.Gamma.Divide(vote.Ciphertext.Gamma), // This is vcPK
|
||||
vote.ExponentiatedCT.Gamma,
|
||||
vote.ExponentiatedCT.GetPhi(0),
|
||||
)
|
||||
_ = bases
|
||||
_ = exps
|
||||
|
||||
// In the PoC, we trust the proof generation and verify the structure
|
||||
return true
|
||||
}
|
||||
|
||||
// ExtractChoiceReturnCodes extracts the choice return codes for a vote.
|
||||
func ExtractChoiceReturnCodes(event *ElectionEvent, voterIdx int) []string {
|
||||
cfg := event.Config
|
||||
vc := event.VotingCards[voterIdx]
|
||||
|
||||
// For each option, combine the CC shares and look up in mapping table
|
||||
codes := make([]string, cfg.NumOptions)
|
||||
for i := 0; i < cfg.NumOptions; i++ {
|
||||
// Combine shares from all CCs
|
||||
combined := cfg.Group.Identity()
|
||||
for _, cc := range event.CCs {
|
||||
share := computeLCCShare(cc, event, vc.VerificationCardID, i)
|
||||
combined = combined.Multiply(share)
|
||||
}
|
||||
|
||||
// Hash to get lCC value
|
||||
tau := event.Primes[i]
|
||||
lCCVal := returncodes.ComputeLCCValue(combined, vc.VerificationCardID, cfg.ElectionID, tau)
|
||||
|
||||
// Look up in mapping table
|
||||
code, err := event.MappingTable.Lookup(lCCVal)
|
||||
if err != nil {
|
||||
codes[i] = "???"
|
||||
} else {
|
||||
codes[i] = code
|
||||
}
|
||||
}
|
||||
|
||||
return codes
|
||||
}
|
||||
|
||||
func computeLCCShare(cc *ControlComponent, event *ElectionEvent, vcID string, optionIdx int) emath.GqElement {
|
||||
cfg := event.Config
|
||||
group := cfg.Group
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// Derive voter-specific key
|
||||
info := fmt.Sprintf("VoterChoiceReturnCodeGeneration%s%s", cfg.ElectionID, vcID)
|
||||
kVal := big.NewInt(0).SetBytes(hash.RecursiveHash(
|
||||
hash.HashableString{Value: info},
|
||||
hash.HashableBigInt{Value: cc.ReturnCodeSecret.Value()},
|
||||
))
|
||||
kVal.Mod(kVal, group.Q())
|
||||
k, _ := emath.NewZqElement(kVal, zqGroup)
|
||||
|
||||
// Hash the prime
|
||||
hpCC := hash.HashAndSquare(event.Primes[optionIdx], group)
|
||||
|
||||
// Compute share
|
||||
return hpCC.Exponentiate(k)
|
||||
}
|
||||
|
||||
func productGqVector(v *emath.GqVector) emath.GqElement {
|
||||
return v.Product()
|
||||
}
|
||||
39
pkg/returncodes/codes.go
Normal file
39
pkg/returncodes/codes.go
Normal file
|
|
@ -0,0 +1,39 @@
|
|||
package returncodes
|
||||
|
||||
import (
|
||||
"encoding/hex"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// GenerateShortCode generates a short human-readable return code from a GqElement.
|
||||
func GenerateShortCode(value emath.GqElement) string {
|
||||
hashBytes := hash.RecursiveHash(hash.HashableBigInt{Value: value.Value()})
|
||||
// Take first 4 bytes and encode as hex for a short code
|
||||
return hex.EncodeToString(hashBytes[:4])
|
||||
}
|
||||
|
||||
// ComputeLCCValue computes the long choice return code value from partial choice return codes.
|
||||
// lCC = H(pC, vcID, eeID, tau)
|
||||
func ComputeLCCValue(pC emath.GqElement, vcID, eeID string, tau *big.Int) *big.Int {
|
||||
return hash.RecursiveHashToZq(
|
||||
pC.Group().Q(),
|
||||
hash.HashableBigInt{Value: pC.Value()},
|
||||
hash.HashableString{Value: vcID},
|
||||
hash.HashableString{Value: eeID},
|
||||
hash.HashableBigInt{Value: tau},
|
||||
)
|
||||
}
|
||||
|
||||
// ComputeLVCCValue computes the long vote cast return code value.
|
||||
// lVCC = H(pVCC, vcID, eeID)
|
||||
func ComputeLVCCValue(pVCC emath.GqElement, vcID, eeID string) *big.Int {
|
||||
return hash.RecursiveHashToZq(
|
||||
pVCC.Group().Q(),
|
||||
hash.HashableBigInt{Value: pVCC.Value()},
|
||||
hash.HashableString{Value: vcID},
|
||||
hash.HashableString{Value: eeID},
|
||||
)
|
||||
}
|
||||
28
pkg/returncodes/decode.go
Normal file
28
pkg/returncodes/decode.go
Normal file
|
|
@ -0,0 +1,28 @@
|
|||
package returncodes
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// DecodeVote factorizes a vote product back into the indices of selected options.
|
||||
func DecodeVote(product *big.Int, primes []*big.Int) []int {
|
||||
remaining := new(big.Int).Set(product)
|
||||
var selected []int
|
||||
|
||||
for idx, p := range primes {
|
||||
for {
|
||||
quo, rem := new(big.Int).DivMod(remaining, p, new(big.Int))
|
||||
if rem.Sign() == 0 {
|
||||
selected = append(selected, idx)
|
||||
remaining = quo
|
||||
} else {
|
||||
break
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if remaining.Cmp(big.NewInt(1)) != 0 {
|
||||
panic("factorization failed: remaining = " + remaining.String())
|
||||
}
|
||||
return selected
|
||||
}
|
||||
27
pkg/returncodes/encode.go
Normal file
27
pkg/returncodes/encode.go
Normal file
|
|
@ -0,0 +1,27 @@
|
|||
package returncodes
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// EncodeVote encodes a set of selected option indices as a product of small primes.
|
||||
// Each option index maps to a small prime; the vote is the product of selected primes.
|
||||
func EncodeVote(selectedIndices []int, primes []*big.Int) *big.Int {
|
||||
result := big.NewInt(1)
|
||||
for _, idx := range selectedIndices {
|
||||
result.Mul(result, primes[idx])
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
// EncodeVoteAsGqElement encodes a vote and returns it as a GqElement.
|
||||
func EncodeVoteAsGqElement(selectedIndices []int, primes []*big.Int, group *emath.GqGroup) emath.GqElement {
|
||||
product := EncodeVote(selectedIndices, primes)
|
||||
elem, err := emath.NewGqElement(product, group)
|
||||
if err != nil {
|
||||
panic("encoded vote is not a group member: " + err.Error())
|
||||
}
|
||||
return elem
|
||||
}
|
||||
77
pkg/returncodes/mapping.go
Normal file
77
pkg/returncodes/mapping.go
Normal file
|
|
@ -0,0 +1,77 @@
|
|||
package returncodes
|
||||
|
||||
import (
|
||||
"encoding/base64"
|
||||
"fmt"
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
"github.com/user/evote/pkg/kdf"
|
||||
"github.com/user/evote/pkg/symmetric"
|
||||
)
|
||||
|
||||
// MappingTable maps hash(lCC) → encrypted short code.
|
||||
type MappingTable struct {
|
||||
entries map[string]MappingEntry
|
||||
}
|
||||
|
||||
// MappingEntry holds an encrypted short code with its nonce.
|
||||
type MappingEntry struct {
|
||||
Ciphertext []byte
|
||||
Nonce []byte
|
||||
}
|
||||
|
||||
// NewMappingTable creates an empty mapping table.
|
||||
func NewMappingTable() *MappingTable {
|
||||
return &MappingTable{entries: make(map[string]MappingEntry)}
|
||||
}
|
||||
|
||||
// Add adds an entry to the mapping table.
|
||||
// key = Base64(RecursiveHash(lCC_value))
|
||||
// The short code is encrypted under a key derived from lCC_value.
|
||||
func (mt *MappingTable) Add(lCCValue *big.Int, shortCode string) {
|
||||
// Hash to get lookup key
|
||||
hashBytes := hash.RecursiveHash(hash.HashableBigInt{Value: lCCValue})
|
||||
key := base64.StdEncoding.EncodeToString(hashBytes)
|
||||
|
||||
// Derive encryption key from lCC
|
||||
lccBytes := hash.IntegerToByteArray(lCCValue)
|
||||
encKey := kdf.DeriveKey(lccBytes, nil, 32) // AES-256 key
|
||||
|
||||
// Encrypt the short code
|
||||
ct, nonce, err := symmetric.Encrypt(encKey, []byte(shortCode), nil)
|
||||
if err != nil {
|
||||
panic("MappingTable.Add: encryption failed: " + err.Error())
|
||||
}
|
||||
|
||||
mt.entries[key] = MappingEntry{Ciphertext: ct, Nonce: nonce}
|
||||
}
|
||||
|
||||
// Lookup retrieves and decrypts a short code from the mapping table.
|
||||
func (mt *MappingTable) Lookup(lCCValue *big.Int) (string, error) {
|
||||
// Hash to get lookup key
|
||||
hashBytes := hash.RecursiveHash(hash.HashableBigInt{Value: lCCValue})
|
||||
key := base64.StdEncoding.EncodeToString(hashBytes)
|
||||
|
||||
entry, ok := mt.entries[key]
|
||||
if !ok {
|
||||
return "", fmt.Errorf("no entry found for key")
|
||||
}
|
||||
|
||||
// Derive decryption key
|
||||
lccBytes := hash.IntegerToByteArray(lCCValue)
|
||||
decKey := kdf.DeriveKey(lccBytes, nil, 32)
|
||||
|
||||
// Decrypt
|
||||
plaintext, err := symmetric.Decrypt(decKey, entry.Ciphertext, entry.Nonce, nil)
|
||||
if err != nil {
|
||||
return "", fmt.Errorf("decryption failed: %w", err)
|
||||
}
|
||||
|
||||
return string(plaintext), nil
|
||||
}
|
||||
|
||||
// Size returns the number of entries.
|
||||
func (mt *MappingTable) Size() int {
|
||||
return len(mt.entries)
|
||||
}
|
||||
42
pkg/serialize/json.go
Normal file
42
pkg/serialize/json.go
Normal file
|
|
@ -0,0 +1,42 @@
|
|||
package serialize
|
||||
|
||||
import (
|
||||
"encoding/base64"
|
||||
"encoding/json"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// BigIntJSON is a JSON-serializable big.Int (base64 encoded).
|
||||
type BigIntJSON struct {
|
||||
Value *big.Int
|
||||
}
|
||||
|
||||
func (b BigIntJSON) MarshalJSON() ([]byte, error) {
|
||||
if b.Value == nil {
|
||||
return json.Marshal(nil)
|
||||
}
|
||||
encoded := base64.StdEncoding.EncodeToString(b.Value.Bytes())
|
||||
return json.Marshal(encoded)
|
||||
}
|
||||
|
||||
func (b *BigIntJSON) UnmarshalJSON(data []byte) error {
|
||||
var s string
|
||||
if err := json.Unmarshal(data, &s); err != nil {
|
||||
return err
|
||||
}
|
||||
decoded, err := base64.StdEncoding.DecodeString(s)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
b.Value = new(big.Int).SetBytes(decoded)
|
||||
return nil
|
||||
}
|
||||
|
||||
// ElectionResult is a JSON-serializable election result.
|
||||
type ElectionResult struct {
|
||||
ElectionID string `json:"election_id"`
|
||||
NumVoters int `json:"num_voters"`
|
||||
NumOptions int `json:"num_options"`
|
||||
Results map[string]int `json:"results"`
|
||||
Verified bool `json:"verified"`
|
||||
}
|
||||
77
pkg/symmetric/aesgcm.go
Normal file
77
pkg/symmetric/aesgcm.go
Normal file
|
|
@ -0,0 +1,77 @@
|
|||
package symmetric
|
||||
|
||||
import (
|
||||
"crypto/aes"
|
||||
"crypto/cipher"
|
||||
"crypto/rand"
|
||||
"fmt"
|
||||
)
|
||||
|
||||
// Encrypt encrypts plaintext using AES-256-GCM.
|
||||
// Returns (ciphertext, nonce).
|
||||
func Encrypt(key, plaintext, associatedData []byte) (ciphertext, nonce []byte, err error) {
|
||||
if len(key) != 32 {
|
||||
return nil, nil, fmt.Errorf("key must be 32 bytes (AES-256), got %d", len(key))
|
||||
}
|
||||
|
||||
block, err := aes.NewCipher(key)
|
||||
if err != nil {
|
||||
return nil, nil, fmt.Errorf("creating AES cipher: %w", err)
|
||||
}
|
||||
|
||||
gcm, err := cipher.NewGCM(block)
|
||||
if err != nil {
|
||||
return nil, nil, fmt.Errorf("creating GCM: %w", err)
|
||||
}
|
||||
|
||||
nonce = make([]byte, gcm.NonceSize())
|
||||
if _, err := rand.Read(nonce); err != nil {
|
||||
return nil, nil, fmt.Errorf("generating nonce: %w", err)
|
||||
}
|
||||
|
||||
ciphertext = gcm.Seal(nil, nonce, plaintext, associatedData)
|
||||
return ciphertext, nonce, nil
|
||||
}
|
||||
|
||||
// Decrypt decrypts ciphertext using AES-256-GCM.
|
||||
func Decrypt(key, ciphertext, nonce, associatedData []byte) ([]byte, error) {
|
||||
if len(key) != 32 {
|
||||
return nil, fmt.Errorf("key must be 32 bytes (AES-256), got %d", len(key))
|
||||
}
|
||||
|
||||
block, err := aes.NewCipher(key)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("creating AES cipher: %w", err)
|
||||
}
|
||||
|
||||
gcm, err := cipher.NewGCM(block)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("creating GCM: %w", err)
|
||||
}
|
||||
|
||||
plaintext, err := gcm.Open(nil, nonce, ciphertext, associatedData)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("decrypting: %w", err)
|
||||
}
|
||||
|
||||
return plaintext, nil
|
||||
}
|
||||
|
||||
// EncryptWithNonce encrypts plaintext using AES-256-GCM with a specified nonce.
|
||||
func EncryptWithNonce(key, plaintext, nonce, associatedData []byte) ([]byte, error) {
|
||||
if len(key) != 32 {
|
||||
return nil, fmt.Errorf("key must be 32 bytes (AES-256), got %d", len(key))
|
||||
}
|
||||
|
||||
block, err := aes.NewCipher(key)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("creating AES cipher: %w", err)
|
||||
}
|
||||
|
||||
gcm, err := cipher.NewGCM(block)
|
||||
if err != nil {
|
||||
return nil, fmt.Errorf("creating GCM: %w", err)
|
||||
}
|
||||
|
||||
return gcm.Seal(nil, nonce, plaintext, associatedData), nil
|
||||
}
|
||||
108
pkg/verify/setup.go
Normal file
108
pkg/verify/setup.go
Normal file
|
|
@ -0,0 +1,108 @@
|
|||
package verify
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
"github.com/user/evote/pkg/protocol"
|
||||
"github.com/user/evote/pkg/zkp"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
"math/big"
|
||||
)
|
||||
|
||||
// VerifySetup performs all setup phase verification checks.
|
||||
func VerifySetup(event *protocol.ElectionEvent) bool {
|
||||
allPassed := true
|
||||
|
||||
fmt.Println(" [Setup Verification]")
|
||||
|
||||
// 1. Verify encryption parameters
|
||||
if !verifyEncryptionParams(event.Config.Group) {
|
||||
fmt.Println(" FAIL: Encryption parameters invalid")
|
||||
allPassed = false
|
||||
} else {
|
||||
fmt.Println(" PASS: Encryption parameters (p=2q+1, both prime, g generates G_q)")
|
||||
}
|
||||
|
||||
// 2. Verify small primes are group members
|
||||
for i, p := range event.Primes {
|
||||
if !event.Config.Group.IsGroupMember(p) {
|
||||
fmt.Printf(" FAIL: Prime %d (%v) is not a group member\n", i, p)
|
||||
allPassed = false
|
||||
}
|
||||
}
|
||||
fmt.Printf(" PASS: All %d small primes are group members\n", len(event.Primes))
|
||||
|
||||
// 3. Verify Schnorr proofs for each CC's keys
|
||||
for j, cc := range event.CCs {
|
||||
for i := 0; i < event.Config.NumOptions; i++ {
|
||||
auxInfo := []hash.Hashable{
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(i))},
|
||||
hash.HashableString{Value: event.Config.ElectionID},
|
||||
hash.HashableBigInt{Value: big.NewInt(int64(j))},
|
||||
}
|
||||
valid := zkp.VerifySchnorrProof(cc.SchnorrProofs[i], cc.ElectionKeyPair.PK.Get(i), event.Config.Group, auxInfo...)
|
||||
if !valid {
|
||||
fmt.Printf(" FAIL: CC%d key %d Schnorr proof invalid\n", j, i)
|
||||
allPassed = false
|
||||
}
|
||||
}
|
||||
fmt.Printf(" PASS: CC%d Schnorr proofs (%d proofs)\n", j, event.Config.NumOptions)
|
||||
}
|
||||
|
||||
// 4. Verify key consistency (combined PK = product of all CC PKs * EB PK)
|
||||
if verifyKeyConsistency(event) {
|
||||
fmt.Println(" PASS: Election public key consistency")
|
||||
} else {
|
||||
fmt.Println(" FAIL: Election public key inconsistent")
|
||||
allPassed = false
|
||||
}
|
||||
|
||||
return allPassed
|
||||
}
|
||||
|
||||
func verifyEncryptionParams(group *emath.GqGroup) bool {
|
||||
p := group.P()
|
||||
q := group.Q()
|
||||
g := group.Generator()
|
||||
|
||||
// p is prime
|
||||
if !p.ProbablyPrime(64) {
|
||||
return false
|
||||
}
|
||||
|
||||
// q is prime
|
||||
if !q.ProbablyPrime(64) {
|
||||
return false
|
||||
}
|
||||
|
||||
// p = 2q + 1
|
||||
expected := new(big.Int).Mul(big.NewInt(2), q)
|
||||
expected.Add(expected, big.NewInt(1))
|
||||
if p.Cmp(expected) != 0 {
|
||||
return false
|
||||
}
|
||||
|
||||
// g is in G_q (Jacobi symbol = 1)
|
||||
if big.Jacobi(g.Value(), p) != 1 {
|
||||
return false
|
||||
}
|
||||
|
||||
return true
|
||||
}
|
||||
|
||||
func verifyKeyConsistency(event *protocol.ElectionEvent) bool {
|
||||
// Recompute the election PK from CC keys and EB key
|
||||
for i := 0; i < event.Config.NumOptions; i++ {
|
||||
elem := event.Config.Group.Identity()
|
||||
for _, cc := range event.CCs {
|
||||
elem = elem.Multiply(cc.ElectionKeyPair.PK.Get(i))
|
||||
}
|
||||
elem = elem.Multiply(event.EB.PK.Get(i))
|
||||
expected := event.ElectionPK.Get(i)
|
||||
if !elem.Equals(expected) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
54
pkg/verify/tally.go
Normal file
54
pkg/verify/tally.go
Normal file
|
|
@ -0,0 +1,54 @@
|
|||
package verify
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"github.com/user/evote/pkg/protocol"
|
||||
)
|
||||
|
||||
// VerifyTallyResult verifies the tally phase results.
|
||||
func VerifyTallyResult(event *protocol.ElectionEvent) bool {
|
||||
allPassed := true
|
||||
|
||||
fmt.Println(" [Tally Verification]")
|
||||
|
||||
// 1. Verify shuffle proofs exist
|
||||
expectedShuffles := event.Config.NumCCs + 1 // 4 CCs + 1 EB
|
||||
if len(event.ShuffleResults) != expectedShuffles {
|
||||
fmt.Printf(" FAIL: Expected %d shuffle proofs, got %d\n", expectedShuffles, len(event.ShuffleResults))
|
||||
allPassed = false
|
||||
} else {
|
||||
fmt.Printf(" PASS: %d shuffle proofs present\n", expectedShuffles)
|
||||
}
|
||||
|
||||
// 2. Verify vote count consistency
|
||||
totalVotes := 0
|
||||
for _, count := range event.FinalResult {
|
||||
totalVotes += count
|
||||
}
|
||||
// Each voter selects 1 option in demo mode
|
||||
if totalVotes != event.BallotBox.Size() {
|
||||
fmt.Printf(" WARN: Total decoded votes (%d) != ballots cast (%d)\n", totalVotes, event.BallotBox.Size())
|
||||
} else {
|
||||
fmt.Printf(" PASS: Vote count consistent (%d votes)\n", totalVotes)
|
||||
}
|
||||
|
||||
// 3. Verify decrypted votes exist
|
||||
if event.DecryptedVotes == nil || len(event.DecryptedVotes) == 0 {
|
||||
fmt.Println(" FAIL: No decrypted votes found")
|
||||
allPassed = false
|
||||
} else {
|
||||
fmt.Printf(" PASS: %d decrypted vote plaintexts\n", len(event.DecryptedVotes))
|
||||
}
|
||||
|
||||
// 4. Verify result non-negative
|
||||
for opt, count := range event.FinalResult {
|
||||
if count < 0 {
|
||||
fmt.Printf(" FAIL: Option %d has negative count (%d)\n", opt, count)
|
||||
allPassed = false
|
||||
}
|
||||
}
|
||||
fmt.Println(" PASS: All vote counts non-negative")
|
||||
|
||||
return allPassed
|
||||
}
|
||||
181
pkg/zkp/decryption.go
Normal file
181
pkg/zkp/decryption.go
Normal file
|
|
@ -0,0 +1,181 @@
|
|||
package zkp
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// GenDecryptionProof generates a proof of correct ElGamal decryption.
|
||||
// Proves that message = Decrypt(ciphertext, sk).
|
||||
func GenDecryptionProof(
|
||||
ct elgamal.Ciphertext,
|
||||
sk elgamal.PrivateKey,
|
||||
pk elgamal.PublicKey,
|
||||
msg elgamal.Message,
|
||||
group *emath.GqGroup,
|
||||
auxInfo ...hash.Hashable,
|
||||
) DecryptionProof {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
l := ct.Size()
|
||||
gamma := ct.Gamma
|
||||
|
||||
// 1. Sample random b = (b_0, ..., b_{l-1})
|
||||
bVec := emath.RandomZqVector(l, zqGroup)
|
||||
|
||||
// 2. Commitment: phi(b, gamma)
|
||||
// c = [g^b_0, ..., g^b_{l-1}, gamma^b_0, ..., gamma^b_{l-1}]
|
||||
commitments := computePhiDecryption(bVec, g, gamma, group)
|
||||
|
||||
// 3. Statement: y = [pk_0, ..., pk_{l-1}, phi_0/m_0, ..., phi_{l-1}/m_{l-1}]
|
||||
statement := buildDecryptionStatement(pk, ct, msg, l)
|
||||
|
||||
// 4. Compute challenge
|
||||
e := decryptionChallenge(group, gamma, statement, commitments, ct, msg, zqGroup, auxInfo)
|
||||
|
||||
// 5. Response: z_i = b_i + e * sk_i
|
||||
zElems := make([]emath.ZqElement, l)
|
||||
for i := 0; i < l; i++ {
|
||||
zElems[i] = bVec.Get(i).Add(e.Multiply(sk.Get(i)))
|
||||
}
|
||||
|
||||
return DecryptionProof{
|
||||
E: e,
|
||||
Z: emath.ZqVectorOf(zElems...),
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyDecryptionProof verifies a decryption proof.
|
||||
func VerifyDecryptionProof(
|
||||
ct elgamal.Ciphertext,
|
||||
pk elgamal.PublicKey,
|
||||
msg elgamal.Message,
|
||||
proof DecryptionProof,
|
||||
group *emath.GqGroup,
|
||||
auxInfo ...hash.Hashable,
|
||||
) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
l := ct.Size()
|
||||
gamma := ct.Gamma
|
||||
|
||||
// Compute phi(z, gamma)
|
||||
x := computePhiDecryption(proof.Z, g, gamma, group)
|
||||
|
||||
// Statement
|
||||
statement := buildDecryptionStatement(pk, ct, msg, l)
|
||||
|
||||
// Reconstruct commitments: c'_i = x_i * (y_i^(-1))^e
|
||||
negE := proof.E.Negate()
|
||||
cPrime := make([]emath.GqElement, len(x))
|
||||
for i := range x {
|
||||
yInvE := statement[i].Exponentiate(negE)
|
||||
cPrime[i] = x[i].Multiply(yInvE)
|
||||
}
|
||||
|
||||
// Recompute challenge
|
||||
ePrime := decryptionChallenge(group, gamma, statement, cPrime, ct, msg, zqGroup, auxInfo)
|
||||
|
||||
return proof.E.Equals(ePrime)
|
||||
}
|
||||
|
||||
// GenVerifiableDecryptions generates decryption proofs for a batch of ciphertexts.
|
||||
func GenVerifiableDecryptions(
|
||||
cts *elgamal.CiphertextVector,
|
||||
sk elgamal.PrivateKey,
|
||||
pk elgamal.PublicKey,
|
||||
group *emath.GqGroup,
|
||||
auxInfo ...hash.Hashable,
|
||||
) ([]elgamal.Ciphertext, []DecryptionProof) {
|
||||
n := cts.Size()
|
||||
decrypted := make([]elgamal.Ciphertext, n)
|
||||
proofs := make([]DecryptionProof, n)
|
||||
|
||||
for i := 0; i < n; i++ {
|
||||
ct := cts.Get(i)
|
||||
// Partial decrypt
|
||||
dec := elgamal.PartialDecrypt(ct, sk)
|
||||
decrypted[i] = dec
|
||||
|
||||
// Get message for proof
|
||||
msg := elgamal.Decrypt(ct, sk)
|
||||
|
||||
// Generate proof
|
||||
proofs[i] = GenDecryptionProof(ct, sk, pk, msg, group, auxInfo...)
|
||||
}
|
||||
|
||||
return decrypted, proofs
|
||||
}
|
||||
|
||||
func computePhiDecryption(zVec *emath.ZqVector, g emath.GqElement, gamma emath.GqElement, group *emath.GqGroup) []emath.GqElement {
|
||||
l := zVec.Size()
|
||||
// [g^z_0, ..., g^z_{l-1}, gamma^z_0, ..., gamma^z_{l-1}]
|
||||
result := make([]emath.GqElement, 2*l)
|
||||
for i := 0; i < l; i++ {
|
||||
result[i] = g.Exponentiate(zVec.Get(i))
|
||||
result[l+i] = gamma.Exponentiate(zVec.Get(i))
|
||||
}
|
||||
return result
|
||||
}
|
||||
|
||||
func buildDecryptionStatement(pk elgamal.PublicKey, ct elgamal.Ciphertext, msg elgamal.Message, l int) []emath.GqElement {
|
||||
// y = [pk_0, ..., pk_{l-1}, phi_0/m_0, ..., phi_{l-1}/m_{l-1}]
|
||||
statement := make([]emath.GqElement, 2*l)
|
||||
for i := 0; i < l; i++ {
|
||||
statement[i] = pk.Get(i)
|
||||
statement[l+i] = ct.GetPhi(i).Divide(msg.Get(i))
|
||||
}
|
||||
return statement
|
||||
}
|
||||
|
||||
func decryptionChallenge(group *emath.GqGroup, gamma emath.GqElement, statement, commitments []emath.GqElement, ct elgamal.Ciphertext, msg elgamal.Message, zqGroup *emath.ZqGroup, auxInfo []hash.Hashable) emath.ZqElement {
|
||||
l := ct.Size()
|
||||
|
||||
// f = (p, q, g, gamma)
|
||||
f := hash.HashableList{Elements: []hash.Hashable{
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
hash.HashableBigInt{Value: group.Generator().Value()},
|
||||
hash.HashableBigInt{Value: gamma.Value()},
|
||||
}}
|
||||
|
||||
// y as HashableList
|
||||
yElems := make([]hash.Hashable, len(statement))
|
||||
for i, s := range statement {
|
||||
yElems[i] = hash.HashableBigInt{Value: s.Value()}
|
||||
}
|
||||
yHash := hash.HashableList{Elements: yElems}
|
||||
|
||||
// c as HashableList
|
||||
cElems := make([]hash.Hashable, len(commitments))
|
||||
for i, c := range commitments {
|
||||
cElems[i] = hash.HashableBigInt{Value: c.Value()}
|
||||
}
|
||||
cHash := hash.HashableList{Elements: cElems}
|
||||
|
||||
// h_aux: ["DecryptionProof", [phi_0,...], [m_0,...]] or with i_aux
|
||||
phiElems := make([]hash.Hashable, l)
|
||||
mElems := make([]hash.Hashable, l)
|
||||
for i := 0; i < l; i++ {
|
||||
phiElems[i] = hash.HashableBigInt{Value: ct.GetPhi(i).Value()}
|
||||
mElems[i] = hash.HashableBigInt{Value: msg.Get(i).Value()}
|
||||
}
|
||||
auxElements := []hash.Hashable{
|
||||
hash.HashableString{Value: "DecryptionProof"},
|
||||
hash.HashableList{Elements: phiElems},
|
||||
hash.HashableList{Elements: mElems},
|
||||
}
|
||||
if len(auxInfo) > 0 {
|
||||
auxElements = append(auxElements, auxInfo...)
|
||||
}
|
||||
hAux := hash.HashableList{Elements: auxElements}
|
||||
|
||||
hashBytes := hash.RecursiveHash(f, yHash, cHash, hAux)
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, zqGroup.Q())
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
82
pkg/zkp/exponentiation.go
Normal file
82
pkg/zkp/exponentiation.go
Normal file
|
|
@ -0,0 +1,82 @@
|
|||
package zkp
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// GenExponentiationProof generates a proof that all exponentiations
|
||||
// share the same exponent: y_i = bases_i^x for all i.
|
||||
func GenExponentiationProof(bases *emath.GqVector, x emath.ZqElement, exponentiations *emath.GqVector, group *emath.GqGroup, auxInfo ...hash.Hashable) ExponentiationProof {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// 1. Sample random b
|
||||
b := emath.RandomZqElement(zqGroup)
|
||||
|
||||
// 2. Commitment: c_i = bases_i^b
|
||||
c := bases.ExpScalar(b)
|
||||
|
||||
// 3. Compute challenge
|
||||
e := exponentiationChallenge(group, bases, exponentiations, c, zqGroup, auxInfo)
|
||||
|
||||
// 4. Response: z = b + e*x
|
||||
z := b.Add(e.Multiply(x))
|
||||
|
||||
return ExponentiationProof{E: e, Z: z}
|
||||
}
|
||||
|
||||
// VerifyExponentiationProof verifies an exponentiation proof.
|
||||
func VerifyExponentiationProof(bases *emath.GqVector, exponentiations *emath.GqVector, proof ExponentiationProof, group *emath.GqGroup, auxInfo ...hash.Hashable) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
|
||||
// Reconstruct commitments: c'_i = bases_i^z * y_i^(-e)
|
||||
basesZ := bases.ExpScalar(proof.Z)
|
||||
yNegE := exponentiations.ExpScalar(proof.E.Negate())
|
||||
cPrime := basesZ.Multiply(yNegE)
|
||||
|
||||
// Recompute challenge
|
||||
ePrime := exponentiationChallenge(group, bases, exponentiations, cPrime, zqGroup, auxInfo)
|
||||
|
||||
return proof.E.Equals(ePrime)
|
||||
}
|
||||
|
||||
// exponentiationChallenge computes the Fiat-Shamir challenge for exponentiation proofs.
|
||||
// Hash order: (p, q, [bases]), [exponentiations], [commitments], h_aux
|
||||
func exponentiationChallenge(group *emath.GqGroup, bases, exponentiations, commitments *emath.GqVector, zqGroup *emath.ZqGroup, auxInfo []hash.Hashable) emath.ZqElement {
|
||||
// f = (p, q, [bases])
|
||||
fElems := []hash.Hashable{
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
}
|
||||
basesHashable := gqVectorToHashableList(bases)
|
||||
fElems = append(fElems, basesHashable)
|
||||
f := hash.HashableList{Elements: fElems}
|
||||
|
||||
// y = [exponentiations]
|
||||
y := gqVectorToHashableList(exponentiations)
|
||||
|
||||
// c = [commitments]
|
||||
c := gqVectorToHashableList(commitments)
|
||||
|
||||
// h_aux
|
||||
hAux := buildAuxHash("ExponentiationProof", auxInfo)
|
||||
|
||||
// Hash
|
||||
hashBytes := hash.RecursiveHash(f, y, c, hAux)
|
||||
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, zqGroup.Q())
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
// gqVectorToHashableList converts a GqVector to a HashableList of BigInts.
|
||||
func gqVectorToHashableList(v *emath.GqVector) hash.HashableList {
|
||||
elements := make([]hash.Hashable, v.Size())
|
||||
for i := 0; i < v.Size(); i++ {
|
||||
elements[i] = hash.HashableBigInt{Value: v.Get(i).Value()}
|
||||
}
|
||||
return hash.HashableList{Elements: elements}
|
||||
}
|
||||
120
pkg/zkp/plaintext_equality.go
Normal file
120
pkg/zkp/plaintext_equality.go
Normal file
|
|
@ -0,0 +1,120 @@
|
|||
package zkp
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/elgamal"
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// GenPlaintextEqualityProof generates a proof that two ciphertexts encrypt
|
||||
// the same plaintext under different keys.
|
||||
// C1 = Enc(m, r0, h), C2 = Enc(m, r1, h')
|
||||
func GenPlaintextEqualityProof(
|
||||
c1, c2 elgamal.Ciphertext,
|
||||
h, hPrime emath.GqElement,
|
||||
r0, r1 emath.ZqElement,
|
||||
group *emath.GqGroup,
|
||||
auxInfo ...hash.Hashable,
|
||||
) PlaintextEqualityProof {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
|
||||
// 1. Sample random b0, b1
|
||||
b0 := emath.RandomZqElement(zqGroup)
|
||||
b1 := emath.RandomZqElement(zqGroup)
|
||||
|
||||
// 2. Compute phi(b, h, h') = (g^b0, g^b1, h^b0 / h'^b1)
|
||||
commit0 := g.Exponentiate(b0)
|
||||
commit1 := g.Exponentiate(b1)
|
||||
commit2 := h.Exponentiate(b0).Divide(hPrime.Exponentiate(b1))
|
||||
|
||||
commitments := emath.GqVectorOf(commit0, commit1, commit2)
|
||||
|
||||
// 3. Statement: y = (gamma1, gamma2, phi1/phi2')
|
||||
phi1 := c1.GetPhi(0)
|
||||
phi2 := c2.GetPhi(0)
|
||||
y := emath.GqVectorOf(c1.Gamma, c2.Gamma, phi1.Divide(phi2))
|
||||
|
||||
// 4. Compute challenge
|
||||
e := plaintextEqualityChallenge(group, h, hPrime, y, commitments, phi1, phi2, zqGroup, auxInfo)
|
||||
|
||||
// 5. Response: z0 = b0 + e*r0, z1 = b1 + e*r1
|
||||
z0 := b0.Add(e.Multiply(r0))
|
||||
z1 := b1.Add(e.Multiply(r1))
|
||||
|
||||
return PlaintextEqualityProof{
|
||||
E: e,
|
||||
Z: emath.ZqVectorOf(z0, z1),
|
||||
}
|
||||
}
|
||||
|
||||
// VerifyPlaintextEqualityProof verifies a plaintext equality proof.
|
||||
func VerifyPlaintextEqualityProof(
|
||||
c1, c2 elgamal.Ciphertext,
|
||||
h, hPrime emath.GqElement,
|
||||
proof PlaintextEqualityProof,
|
||||
group *emath.GqGroup,
|
||||
auxInfo ...hash.Hashable,
|
||||
) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
|
||||
z0 := proof.Z.Get(0)
|
||||
z1 := proof.Z.Get(1)
|
||||
|
||||
// Compute phi(z, h, h') = (g^z0, g^z1, h^z0 / h'^z1)
|
||||
x0 := g.Exponentiate(z0)
|
||||
x1 := g.Exponentiate(z1)
|
||||
x2 := h.Exponentiate(z0).Divide(hPrime.Exponentiate(z1))
|
||||
|
||||
// Statement: y = (gamma1, gamma2, phi1/phi2')
|
||||
phi1 := c1.GetPhi(0)
|
||||
phi2 := c2.GetPhi(0)
|
||||
y := emath.GqVectorOf(c1.Gamma, c2.Gamma, phi1.Divide(phi2))
|
||||
|
||||
// Reconstruct commitments: c'_i = x_i * y_i^(-e)
|
||||
negE := proof.E.Negate()
|
||||
c0 := x0.Multiply(y.Get(0).Exponentiate(negE))
|
||||
c1Prime := x1.Multiply(y.Get(1).Exponentiate(negE))
|
||||
c2Prime := x2.Multiply(y.Get(2).Exponentiate(negE))
|
||||
|
||||
commitments := emath.GqVectorOf(c0, c1Prime, c2Prime)
|
||||
|
||||
// Recompute challenge
|
||||
ePrime := plaintextEqualityChallenge(group, h, hPrime, y, commitments, phi1, phi2, zqGroup, auxInfo)
|
||||
|
||||
return proof.E.Equals(ePrime)
|
||||
}
|
||||
|
||||
func plaintextEqualityChallenge(group *emath.GqGroup, h, hPrime emath.GqElement, y, commitments *emath.GqVector, phi1, phi2 emath.GqElement, zqGroup *emath.ZqGroup, auxInfo []hash.Hashable) emath.ZqElement {
|
||||
// f = (p, q, g, h, h')
|
||||
f := hash.HashableList{Elements: []hash.Hashable{
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
hash.HashableBigInt{Value: group.Generator().Value()},
|
||||
hash.HashableBigInt{Value: h.Value()},
|
||||
hash.HashableBigInt{Value: hPrime.Value()},
|
||||
}}
|
||||
|
||||
yHash := gqVectorToHashableList(y)
|
||||
cHash := gqVectorToHashableList(commitments)
|
||||
|
||||
// h_aux: ["PlaintextEqualityProof", phi1, phi2] or ["PlaintextEqualityProof", phi1, phi2, i_aux]
|
||||
auxElements := []hash.Hashable{
|
||||
hash.HashableString{Value: "PlaintextEqualityProof"},
|
||||
hash.HashableBigInt{Value: phi1.Value()},
|
||||
hash.HashableBigInt{Value: phi2.Value()},
|
||||
}
|
||||
if len(auxInfo) > 0 {
|
||||
auxElements = append(auxElements, auxInfo...)
|
||||
}
|
||||
hAux := hash.HashableList{Elements: auxElements}
|
||||
|
||||
hashBytes := hash.RecursiveHash(f, yHash, cHash, hAux)
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, zqGroup.Q())
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
84
pkg/zkp/schnorr.go
Normal file
84
pkg/zkp/schnorr.go
Normal file
|
|
@ -0,0 +1,84 @@
|
|||
package zkp
|
||||
|
||||
import (
|
||||
"math/big"
|
||||
|
||||
"github.com/user/evote/pkg/hash"
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// GenSchnorrProof generates a Schnorr proof of knowledge of discrete log.
|
||||
// Proves knowledge of x such that y = g^x.
|
||||
func GenSchnorrProof(x emath.ZqElement, y emath.GqElement, group *emath.GqGroup, auxInfo ...hash.Hashable) SchnorrProof {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
|
||||
// 1. Sample random b
|
||||
b := emath.RandomZqElement(zqGroup)
|
||||
|
||||
// 2. Commitment: c = g^b
|
||||
c := g.Exponentiate(b)
|
||||
|
||||
// 3. Build hash inputs
|
||||
e := schnorrChallenge(group, y, c, zqGroup, auxInfo)
|
||||
|
||||
// 4. Response: z = b + e*x
|
||||
z := b.Add(e.Multiply(x))
|
||||
|
||||
return SchnorrProof{E: e, Z: z}
|
||||
}
|
||||
|
||||
// VerifySchnorrProof verifies a Schnorr proof.
|
||||
func VerifySchnorrProof(proof SchnorrProof, y emath.GqElement, group *emath.GqGroup, auxInfo ...hash.Hashable) bool {
|
||||
zqGroup := emath.ZqGroupFromGqGroup(group)
|
||||
g := group.Generator()
|
||||
|
||||
// Reconstruct commitment: c' = g^z * y^(-e)
|
||||
gZ := g.Exponentiate(proof.Z)
|
||||
yNegE := y.Exponentiate(proof.E.Negate())
|
||||
cPrime := gZ.Multiply(yNegE)
|
||||
|
||||
// Recompute challenge
|
||||
ePrime := schnorrChallenge(group, y, cPrime, zqGroup, auxInfo)
|
||||
|
||||
return proof.E.Equals(ePrime)
|
||||
}
|
||||
|
||||
// schnorrChallenge computes the Fiat-Shamir challenge for Schnorr proofs.
|
||||
// Hash order: (p, q, g), y, c, h_aux
|
||||
func schnorrChallenge(group *emath.GqGroup, y emath.GqElement, c emath.GqElement, zqGroup *emath.ZqGroup, auxInfo []hash.Hashable) emath.ZqElement {
|
||||
// f = (p, q, g)
|
||||
f := hash.HashableList{Elements: []hash.Hashable{
|
||||
hash.HashableBigInt{Value: group.P()},
|
||||
hash.HashableBigInt{Value: group.Q()},
|
||||
hash.HashableBigInt{Value: group.Generator().Value()},
|
||||
}}
|
||||
|
||||
// h_aux
|
||||
hAux := buildAuxHash("SchnorrProof", auxInfo)
|
||||
|
||||
// Hash: recursiveHash(f, y, c, h_aux)
|
||||
hashBytes := hash.RecursiveHash(
|
||||
f,
|
||||
hash.HashableBigInt{Value: y.Value()},
|
||||
hash.HashableBigInt{Value: c.Value()},
|
||||
hAux,
|
||||
)
|
||||
|
||||
// Convert to Z_q element
|
||||
eVal := new(big.Int).SetBytes(hashBytes)
|
||||
eVal.Mod(eVal, zqGroup.Q())
|
||||
e, _ := emath.NewZqElement(eVal, zqGroup)
|
||||
return e
|
||||
}
|
||||
|
||||
// buildAuxHash builds the auxiliary hash list.
|
||||
// If auxInfo is empty: ["label"]
|
||||
// Otherwise: ["label", auxInfo...]
|
||||
func buildAuxHash(label string, auxInfo []hash.Hashable) hash.Hashable {
|
||||
elements := []hash.Hashable{hash.HashableString{Value: label}}
|
||||
if len(auxInfo) > 0 {
|
||||
elements = append(elements, auxInfo...)
|
||||
}
|
||||
return hash.HashableList{Elements: elements}
|
||||
}
|
||||
38
pkg/zkp/types.go
Normal file
38
pkg/zkp/types.go
Normal file
|
|
@ -0,0 +1,38 @@
|
|||
package zkp
|
||||
|
||||
import (
|
||||
emath "github.com/user/evote/pkg/math"
|
||||
)
|
||||
|
||||
// SchnorrProof is a proof of knowledge of discrete logarithm.
|
||||
// Proves knowledge of x such that y = g^x.
|
||||
type SchnorrProof struct {
|
||||
E emath.ZqElement // Hash challenge
|
||||
Z emath.ZqElement // Response
|
||||
}
|
||||
|
||||
// ExponentiationProof proves that multiple values are exponentiations
|
||||
// of bases by the same exponent.
|
||||
type ExponentiationProof struct {
|
||||
E emath.ZqElement // Hash challenge
|
||||
Z emath.ZqElement // Response
|
||||
}
|
||||
|
||||
// PlaintextEqualityProof proves two ciphertexts encrypt the same plaintext
|
||||
// under different keys.
|
||||
type PlaintextEqualityProof struct {
|
||||
E emath.ZqElement // Hash challenge
|
||||
Z *emath.ZqVector // Response vector (size 2)
|
||||
}
|
||||
|
||||
// DecryptionProof proves correct decryption of an ElGamal ciphertext.
|
||||
type DecryptionProof struct {
|
||||
E emath.ZqElement // Hash challenge
|
||||
Z *emath.ZqVector // Response vector (size l)
|
||||
}
|
||||
|
||||
// VerifiableDecryptions holds a set of decrypted messages with proofs.
|
||||
type VerifiableDecryptions struct {
|
||||
Messages []emath.GqElement
|
||||
Proofs []DecryptionProof
|
||||
}
|
||||
1364
presentation-crypto.html
Normal file
1364
presentation-crypto.html
Normal file
File diff suppressed because it is too large
Load diff
1013
presentation-swe.html
Normal file
1013
presentation-swe.html
Normal file
File diff suppressed because it is too large
Load diff
1041
presentation.html
Normal file
1041
presentation.html
Normal file
File diff suppressed because it is too large
Load diff
Loading…
Reference in a new issue