Formally verified ed25519 (betrusted-io curve25519-dalek fork v4.1.2, Precursor/Xous): field + complete Edwards addition law proven in Lean 4 via Charon/Aeneas; axiom-audited certificates
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mrwulf b408df3765 Merge scalar into CurveField: one type universe, serial-only backend
Replicates dalek's gen merge: extract.sh co-extracts the Scalar52 backend
and scalar::from_bytes_mod_order[_wide] into the CurveField model, pins
RUSTFLAGS --cfg curve25519_dalek_backend="serial" (SIMD dispatch compiles
out; get_selected_backend becomes a real definition), and upgrades
unwrap_u8 to the documented Choice-model definition. ScalarDenote repoints
by one import line; both buttons green over the merged gen.

Prepares the verify-glue integration (CurveSig) on this fork.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 22:20:26 +02:00
verification Merge scalar into CurveField: one type universe, serial-only backend 2026-07-04 22:20:26 +02:00
.gitignore skeleton: proof-pyramid layout, honest status table, trusted-base doc 2026-07-02 13:10:26 +02:00
README.md Scalar layer complete: Montgomery reduction + full mul ported, scalarImplementation aggregate 2026-07-03 21:46:57 +02:00
TRUSTED-BASE.md skeleton: proof-pyramid layout, honest status table, trusted-base doc 2026-07-02 13:10:26 +02:00

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      │   Scalar52 ops correct mod 
        ├──────────────────────────────┤
        │  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 scalarImplementation (add sub mul ) proven [propext, Classical.choice, Quot.sound]
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).