mirror of https://github.com/saymrwulf/dalek-ed25519-verified.git synced 2026-09-03 20:13:48 +00:00

Formally verified ed25519 (upstream curve25519-dalek v5): field + complete Edwards addition law proven in Lean 4 via Charon/Aeneas; axiom-audited certificates

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mrwulf a6b6e86865 Scalar layer complete: Montgomery reduction + full mul proven, scalarImplementation aggregate Phase B - montgomery_reduce (Proofs/ScalarMontSpec.lean + Proofs/ScalarReduceSpec.lean): - mont_key: LFACTORL0 + 1 = 2148350892430302^52 (the -1 inverse identity, norm_num) - mont_cancel: (s + ((sLFACTOR) % 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 (carry2^52 = sum + pL0; exact split) - mont_head_telescope (E0-E4) and mont_tail_telescope (E5-E8): linear_combination certificates with weights 2^52k; mont_bound: X' < 2ell from Z < 2^260ell - 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 - Kell 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.		2026-07-03 21:06:15 +02:00
verification	Scalar layer complete: Montgomery reduction + full mul proven, scalarImplementation aggregate	2026-07-03 21:06:15 +02:00
.gitignore	skeleton: proof-pyramid layout, honest status table, trusted-base doc	2026-07-02 13:10:26 +02:00
README.md	Scalar layer complete: Montgomery reduction + full mul proven, scalarImplementation aggregate	2026-07-03 21:06:15 +02:00
TRUSTED-BASE.md	skeleton: proof-pyramid layout, honest status table, trusted-base doc	2026-07-02 13:10:26 +02:00

README.md

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).