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mrwulf
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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.
83 lines
3.9 KiB
Markdown
83 lines
3.9 KiB
Markdown
# dalek-ed25519-verified
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Formal verification of the ed25519 implementation in **dalek-cryptography/curve25519-dalek (upstream, v5.0.0-rc.1)**, built as a
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coherent proof pyramid in Lean 4 via the Charon/Aeneas transpilation pipeline:
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```
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┌──────────────────────────────┐
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│ Signature (EdDSA verify) │ accepted ⇒ [8][S]B = [8]R + [8][k]A
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├──────────────────────────────┤
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│ Scalar arithmetic mod ℓ │ Scalar52 ops correct mod ℓ
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├──────────────────────────────┤
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│ Group law (twisted Edwards) │ point ops = complete addition law
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├──────────────────────────────┤
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│ Field 𝔽_p, p = 2²⁵⁵ − 19 │ FieldElement51 ops correct mod p
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└──────────────────────────────┘
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```
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Every layer states its theorems about the **actual Aeneas-transpiled Rust
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code** (never about a hand-written re-model), and every claim in the status
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table below is backed by a compiled proof plus an axiom audit of the named
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certificate. Files that do not compile under `verification/check.sh` are not
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in this repository.
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## Layer status
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| Layer | Certificate | Status | Axioms of certificate |
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|-------|-------------|--------|-----------------------|
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| Field 𝔽_p | `fieldImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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| Group law (Edwards) | `edwardsImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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| Scalar mod ℓ | `scalarImplementation` (add ✅ sub ✅ mul ✅) | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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| Signature (EdDSA) | `verifyEquation` (planned) | ⏳ planned | — |
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Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started.
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This table is updated only when `verification/check.sh` passes for the layer.
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## Source
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- **Upstream**: [dalek-cryptography/curve25519-dalek](https://github.com/dalek-cryptography/curve25519-dalek), commit `4cf8db2`
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- **Pinned/patched source**: [saymrwulf/curve25519-dalek-source](https://github.com/saymrwulf/curve25519-dalek-source), commit `135ed70`
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- **Patches**: minimal Aeneas-compatibility only (documented in the source repo)
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- Verified backend: `backend/serial/u64` (`FieldElement51`, `Scalar52`). SIMD/AVX backends are out of scope (marked opaque).
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## Toolchain (pinned)
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| Component | Version |
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|-----------|---------|
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| Aeneas | `bf13c42e` |
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| Charon | `9dd7f23c` |
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| Lean | `v4.30.0-rc2` |
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| OCaml | `5.3.0` |
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## Reproducing
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```bash
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source ~/aeneas-toolchain/env.sh
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cd verification
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./extract.sh # Rust → LLBC → Lean (regenerates gen/)
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./check.sh # compiles EVERY shipped file + axiom-audits EVERY certificate
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```
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The scalar layer has its own pair of buttons:
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```bash
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./extract-scalar.sh # regenerates gen/CurveScalar (Scalar52 limb arithmetic)
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./check-scalar.sh # compiles the scalar gen + all scalar proofs (add, sub,
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# Montgomery mul) and kernel-audits 10 certificates,
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# including the scalarImplementation aggregate
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```
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## Trusted base
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See [TRUSTED-BASE.md](TRUSTED-BASE.md) for the complete list of assumptions
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(Lean kernel, mathlib, Charon/Aeneas semantics, external-function models,
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and — in the signature layer only — an opaque SHA-512 model).
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## Provenance
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Proof engineering in this repository builds on the verification methodology
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and proof architecture of
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[PlanetMacro/ed25519-verificationtest](https://github.com/PlanetMacro/ed25519-verificationtest)
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(the reference solution). All proofs here are checked against **this fork's
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own extracted code**; nothing is claimed that the check script does not compile.
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