betrusted-ed25519-verified

Formal verification of the ed25519 implementation in betrusted-io/curve25519-dalek (Precursor/Xous fork, v4.1.2), 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 (a single monomorphic sha512_hash3(R, A, m) oracle — this fork's sha2-0.10 stack makes the incremental-hasher types untranslatable) 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, verifying.sha512_hash3, 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: betrusted-io/curve25519-dalek, commit 16e087a
• Pinned/patched source: saymrwulf/betrusted-curve25519-dalek-source, commit 64ee8f0
• Patches: minimal Aeneas-compatibility only (documented in the source repo)
• Scope caveat: this verifies the fork's pure-Rust serial/u64 path. The Engine25519 hardware-accelerator path on Precursor is different code and is NOT covered by these proofs.

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).

Provenance

Proof engineering in this repository builds on the verification methodology and proof architecture of PlanetMacro/ed25519-verificationtest (the reference solution). All proofs here are checked against this fork's own extracted code; nothing is claimed that the check script does not compile.