mirror of https://github.com/saymrwulf/anza-ed25519-verified.git synced 2026-09-03 20:13:46 +00:00

mrwulf 8440b53bdc Add scalar-layer foundation (Scalar52 arithmetic mod ℓ)

Transpile the Scalar52 limb backend (backend::serial::u64::scalar
add/sub/mul/square/montgomery_*) from Rust to Lean via Charon/Aeneas,
scoped at the function level to the iterator-free arithmetic core.

  - verification/extract-scalar.sh: function-level Charon/Aeneas extraction
  - verification/gen/CurveScalar/{Types,Funs}.lean: transpiled model (28 defs)
  - verification/gen/CurveScalar/{TypesExternal,FunsExternal}.lean: hand-written
    external models (subtle.Choice + 2 subtle fns; namespace = curve25519)
  - verification/Proofs/ScalarDenote.lean: semantic foundation — Scalar52
    denotation into ℤ/ℓℤ, limb-bound invariant, and L_val (the transpiled
    constants::L denotes exactly the group order ℓ, kernel-checked)
  - verification/check-scalar.sh: guarded compile of the four gen modules
    plus the denotation foundation

check-scalar.sh passes: gen compiles; denotation + L = ℓ proven.
add/sub/mul remain in progress.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

2026-07-02 21:19:58 +02:00

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anza-ed25519-verified

Formal verification of the ed25519 implementation in anza-xyz/cryptography (Solana, solana-ed25519 crate), 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`	🔨 foundation	denotation + L=ℓ proven; add/sub/mul in progress
Signature (EdDSA)	`verifyEquation`	⏳ in progress	—

Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started. This table is updated only when verification/check.sh passes for the layer.

Source

Upstream: anza-xyz/cryptography, commit 0a54cca
Pinned/patched source: saymrwulf/anza-cryptography-source, commit 77043ab
Patches: minimal Aeneas-compatibility only (documented in the source repo)
Closest relative of the reference solution (same crate layout as solana-ed25519).

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

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).

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