saymrwulf
5fade418de
Proofs/ScalarAddSpec.lean, axiom-clean, no sorry: - add_loop_spec: the 5-limb carry loop unrolled (same skeleton as the proven conditional-add-L chain, with b's limbs in place of L's constants); per-limb equations r_i + 2^52*g_(i+1) = a_i + b_i + g_i. - add_val_spec: denote(add a b) = denote a + denote b in ZMod l for limb-bounded canonical inputs. Composition: add_telescope lifts the carry equations to scLimbs sum + 2^260*g5 = scVal a + scVal b; canonicity (a,b < l < 2^253) forces g5 = 0; the trailing sub(sum, L) goes through sub_val_spec with subtrahend L — enabled by weakening sub_val_spec's hypothesis from scVal b < l to scVal b <= l (the gamma5=1 forcing argument only needs <=), since scVal L = l exactly. denote L = 0 in ZMod l closes it. check-scalar.sh: ScalarAddSpec in manifest + audit (5/5 clean), button green at the re-budgeted 300s/4096MB caps. With sub (previous commit): the scalar layer's + and - are both fully verified against dalek's own extraction. Remaining: x3 fork port, Montgomery mul/reduce (kernel frontier). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
3.5 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 | add_val_spec ✅ sub_val_spec ✅ (scalarImplementation aggregate planned) |
🔨 add+sub done · mul next | ⟦add a b⟧=⟦a⟧+⟦b⟧ and ⟦sub a b⟧=⟦a⟧−⟦b⟧ in ZMod ℓ proven on dalek; ×3 port & Montgomery mul next |
| 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 + the proven scalar foundation
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).