mrwulf
5faaa3226a
Phase B - montgomery_reduce (Proofs/ScalarMontSpec.lean + Proofs/ScalarReduceSpec.lean): - mont_key: LFACTOR*L0 + 1 = 214835089243030*2^52 (the -1 inverse identity, norm_num) - mont_cancel: (s + ((s*LFACTOR) % 2^52)*L0) % 2^52 = 0 via Nat.ModEq - every part1 shift is an EXACT division, nothing discarded - part1_spec / part2_spec: per-round helpers (carry*2^52 = sum + p*L0; exact split) - mont_head_telescope (E0-E4) and mont_tail_telescope (E5-E8): linear_combination certificates with weights 2^52k; mont_bound: X' < 2*ell from Z < 2^260*ell - montgomery_reduce_spec: post `scDenote r * 2^260 = Z` in ZMod ell + 52-bit bounds. METHOD-4 split at the round-4/5 boundary: the 74-step monolith is elaboration-pathological; each half compiles in ~25s/3GB. - The single death-spiral line: an omega for the nonce-sum bound with ~110 hypotheses in context never returns; extracted to nonce_sum_bound (5 hypotheses, instant). Bisected with fail-probes; documented in control-repo FAILURES.md. Phase C - mul (Proofs/ScalarFullMulSpec.lean): - RR_limbs/RR_scVal/RR_lt; RR_denote: RR = 2^520 - K*ell kernel-checked, so ⟦RR⟧ = R^2; R_isUnit: 2^260 unit of ZMod ell (coprime oddness witness) - mul_spec: mul_internal -> montgomery_reduce -> mul_internal(*, RR) -> montgomery_reduce composed; column values folded by `ring`; R cancelled via IsUnit.mul_right_cancel. Hypothesis scVal a * scVal b < 2^260*ell (honest Montgomery bound; canonical inputs satisfy it). Aggregate (Proofs/ScalarMain.lean): scalar_add/sub/mul_correct on ScBnd interfaces + canonical_mul_bound + scalarImplementation bundling all three. sub_val_spec/add_val_spec posts strengthened with result-limb 52-bit bounds (the montgomery tail feeds sub's output back into mul_internal). check-scalar.sh: 9 proof files, 10 kernel audits (was 6), all exactly [propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
3.9 KiB
dalek-ed25519-verified
Formal verification of the ed25519 implementation in dalek-cryptography/curve25519-dalek (upstream, v5.0.0-rc.1), built as a coherent proof pyramid in Lean 4 via the Charon/Aeneas transpilation pipeline:
┌──────────────────────────────┐
│ Signature (EdDSA verify) │ accepted ⇒ [8][S]B = [8]R + [8][k]A
├──────────────────────────────┤
│ Scalar arithmetic mod ℓ │ Scalar52 ops correct mod ℓ
├──────────────────────────────┤
│ Group law (twisted Edwards) │ point ops = complete addition law
├──────────────────────────────┤
│ Field 𝔽_p, p = 2²⁵⁵ − 19 │ FieldElement51 ops correct mod p
└──────────────────────────────┘
Every layer states its theorems about the actual Aeneas-transpiled Rust
code (never about a hand-written re-model), and every claim in the status
table below is backed by a compiled proof plus an axiom audit of the named
certificate. Files that do not compile under verification/check.sh are not
in this repository.
Layer status
| Layer | Certificate | Status | Axioms of certificate |
|---|---|---|---|
| Field 𝔽_p | fieldImplementation |
✅ proven | [propext, Classical.choice, Quot.sound] |
| Group law (Edwards) | edwardsImplementation |
✅ proven | [propext, Classical.choice, Quot.sound] |
| Scalar mod ℓ | scalarImplementation (add ✅ sub ✅ mul ✅) |
✅ proven | [propext, Classical.choice, Quot.sound] |
| Signature (EdDSA) | verifyEquation (planned) |
⏳ planned | — |
Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started.
This table is updated only when verification/check.sh passes for the layer.
Source
- Upstream: dalek-cryptography/curve25519-dalek, commit
4cf8db2 - Pinned/patched source: saymrwulf/curve25519-dalek-source, commit
135ed70 - Patches: minimal Aeneas-compatibility only (documented in the source repo)
- Verified backend:
backend/serial/u64(FieldElement51,Scalar52). SIMD/AVX backends are out of scope (marked opaque).
Toolchain (pinned)
| Component | Version |
|---|---|
| Aeneas | bf13c42e |
| Charon | 9dd7f23c |
| Lean | v4.30.0-rc2 |
| OCaml | 5.3.0 |
Reproducing
source ~/aeneas-toolchain/env.sh
cd verification
./extract.sh # Rust → LLBC → Lean (regenerates gen/)
./check.sh # compiles EVERY shipped file + axiom-audits EVERY certificate
The scalar layer has its own pair of buttons:
./extract-scalar.sh # regenerates gen/CurveScalar (Scalar52 limb arithmetic)
./check-scalar.sh # compiles the scalar gen + all scalar proofs (add, sub,
# Montgomery mul) and kernel-audits 10 certificates,
# including the scalarImplementation aggregate
Trusted base
See TRUSTED-BASE.md for the complete list of assumptions (Lean kernel, mathlib, Charon/Aeneas semantics, external-function models, and — in the signature layer only — an opaque SHA-512 model).
Provenance
Proof engineering in this repository builds on the verification methodology and proof architecture of PlanetMacro/ed25519-verificationtest (the reference solution). All proofs here are checked against this fork's own extracted code; nothing is claimed that the check script does not compile.