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 ⇒ [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 (planned; L_val proven)	🔨 foundation	denotation + L=ℓ proven; add/sub/mul in progress
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: 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 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).

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.