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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 e07f51c7f7 Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited) The load-bearing brick of the point-level apex equation: FieldElement51::to_bytes always succeeds and its 32 output bytes denote EXACTLY the represented residue - bytesVal s = feVal a mod p. Since the canonical residue determines the bytes, this is simultaneously canonicity ("output is the canonical encoding") and the injectivity compress needs ("equal residues iff equal bytes"). - Proofs/ToBytesMath.lean: the context-free ℕ mathematics (METHOD 4) - the 5-rung carry telescope (div_rung/q_telescope), the q-trick facts (q = (h+19)/2^255 is a bit, fires iff h >= p), q_mod_p (adding 19q and discarding bit 255 subtracts pq exactly), carry_pack (the masked-limb assembly mod 2^255), five per-limb byte-chunk splits, and bytes_pack (the 32-byte little-endian reassembly, closed by one zify + linear_combination over the five splits). - Proofs/ToBytesSpec.lean: the symbolic execution - at ~150 machine ops the longest walk in the repo, loop-free: weak reduce (reduce_spec), the q pass, the fold + carry pass, 32 byte extractions (the four limb-boundary bytes turn disjoint ORs into additions via Nat.two_pow_add_eq_or_of_lt), and the trailing top-bit debug-assert DISCHARGED (b31 = f4/2^44 < 2^7), not assumed. - check.sh: ToBytesMath/ToBytesSpec in PROOFS, to_bytes_spec in CERTS (exact standard-three audit) - full button green fresh. Walk lessons (for the control repo, next push): rw index-equations into their consumers instead of subst (subst eliminates the wrong side or dies on dependent do-motives); never rw [Nat.mod_eq_of_lt (by omega)] (metavariable goal reaches omega) - state the bound with show. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-05 13:10:43 +02:00
verification	Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited)	2026-07-05 13:10:43 +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