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 ⇔ decompress(R) = [k](−A)+[s]B
        ├──────────────────────────────┤
        │  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 … verify_accepts_iff_decompress (4 tiers)	✅ proven (phases 1+2)	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 (phases 1 and 2)

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 each apex-tier 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 (complete): the point-level lift. Phase 3b enforces the SAME axiom boundary on three further tiers that lift the byte equation to points:

Tier	Certificate	Statement
half-lift	verify_accepts_iff_point	accepted ⇔ R = the canonical encoding of [k]·(−A) + [s]·B (compress semantics + as_bytes canonicity + hash-to-scalar, recompute chain inverted)
point equation	verify_accepts_iff_point_eq	for any valid on-curve Q canonically encoded by R: accepted ⇔ Q = [k]·(−A) + [s]·B as points (encoding-injectivity: d non-square + parity root-selection)
full lift	verify_accepts_iff_decompress	R decompresses to a valid on-curve Pt, and accepted ⇔ Pt = [k]·(−A) + [s]·B — the constructive capstone

The full lift runs through the extracted CompressedEdwardsY::decompress itself, proven end-to-end: from_bytes parses the y-residue exactly below bit 255 (from_bytes_spec), sqrt_ratio_i returns the even square root of (y²−1)/(dy²+1) (sqrt_ratio_i_sq_spec, Fermat-exponent square root), and the sign bit selects the x-parity (decompress_of_canonical, standard three axioms). Byte comparison ↔ encoding equality ↔ point equality ↔ decompressed-point equality: every link is machine-checked over the extracted code, and check.sh fails the build if any of the four tiers' cones deviates from the boundary above.

Source

• Upstream: betrusted-io/curve25519-dalek, commit 16e087a
• Pinned/patched source: saymrwulf/betrusted-curve25519-dalek-source, commit cee0e17 (adds the decompress step_2 negate-then-assign patch)
• 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).