mirror of https://github.com/saymrwulf/dalek-ed25519-verified.git synced 2026-09-04 20:24:12 +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 32d3c05495 Phase 2, decompress part 2a: fe conditional-select + THE SQUARE-ROOT CORE (kernel-audited) - fe_cond_assign_spec: the per-limb constant-time selection on field elements (real extracted code: five index_mut rounds over the u64 select) keeps self iff the choice is 0 - the operation sqrt_ratio_i uses for both the root flip and the sign normalization. Walked with backfun-rewrite hygiene; the u64 model lemma restated locally (Proofs.Basic is a parallel root that clashes with ConstSpecs). - sqrt_core: THE ALGEBRAIC HEART - for square u/v (witness x, v nonzero) the candidate r = (uv^3)(uv^7)^((p-5)/8) satisfies vr^2 = +/-u. The v-part of the exponent collapses by Fermat (8*(2^253-5) = 2(p-1)); the residual x^((p-1)/2) is +/-1 by factoring its square. Exponent bookkeeping: (p-5)/8 = 2^252-3, (p-1)/2 = 2^254-10, all closed by norm_num after pow_mul merges. Both certificates exact standard three. Full button green fresh. Remaining: the sqrt_ratio_i walk composing these, from_bytes, decompress_of_canonical. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-05 21:16:05 +02:00
verification	Phase 2, decompress part 2a: fe conditional-select + THE SQUARE-ROOT CORE	2026-07-05 21:16:05 +02:00
.gitignore	skeleton: proof-pyramid layout, honest status table, trusted-base doc	2026-07-02 13:10:26 +02:00
README.md	Coherence pass 3: post-apex accuracy sweep, hygiene, guard ladder	2026-07-05 11:48:17 +02:00
TRUSTED-BASE.md	Coherence pass 3: post-apex accuracy sweep, hygiene, guard ladder	2026-07-05 11:48:17 +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 ⇔ compress([s]B−[k]A) = R
        ├──────────────────────────────┤
        │  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)	`verify_accepts_iff`	✅ proven (phase 1)	standard three + the button-enforced SHA-512/wire-format boundary — see The signature apex

Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started. This table is updated only when verification/check.sh passes for the layer.

The signature apex (phase 1)

The apex certificate CurveFieldProofs.verify_accepts_iff is the literal EdDSA acceptance criterion, proven about the extracted verifier:

For a signature that parses, the verifier returns Ok(()) iff the recomputed compressed point compress([s]·B − [k]·A) equals the signature's R, byte-for-byte — where k is whatever scalar the opaque SHA-512 oracle produces from (R, A, msg).

The recomputation runs entirely through the proven model: the vendored ed25519-dalek verify glue is extracted as gen/CurveSig, whose hand-maintained externals import gen/CurveField — every curve and scalar call resolves by fully-qualified name to a proven definition. Only SHA-512 (three stateful wrapper calls) and the wire-format types stay opaque.

check.sh has a dedicated audit phase (Phase 3b) that fails the build unless the apex certificate's axiom cone is exactly

[propext, Classical.choice, Quot.sound] + {ed25519.Signature, sha2.Sha512, verifying.sha512_new, verifying.sha512_update, verifying.sha512_finalize_bytes, ed25519.Signature.to_bytes, signature.error.Error, signature.error.Error.new}

— i.e. the three Lean foundations plus the documented SHA-512/wire-format boundary. Zero curve, scalar, or backend axioms. The companion certificate verify_loop_full (the 32-byte comparison loop computes array equality) carries the standard three axioms only.

Phase 2 (deferred, documented): lifting the byte-level equation to the point level ([s]B − [k]A = decompress R) additionally needs compress canonicity and a verified decompress; it is deliberately out of scope for this milestone, mirroring the layer-by-layer phase split used below the apex.

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 gen model is ONE merged universe (gen/CurveField: field + curve + scalar + the verify path's reachable code), regenerated in full by extract.sh. The scalar layer keeps its own check button:

./check-scalar.sh     # compiles the merged gen + all scalar proofs (add, sub,
                      # Montgomery mul, byte-parsing) and kernel-audits the
                      # scalar certificates, incl. 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).

README.md Unescape Escape