mirror of https://github.com/saymrwulf/dalek-ed25519-verified.git synced 2026-09-04 20:24:12 +00:00

Formally verified ed25519 (upstream curve25519-dalek v5): field + complete Edwards addition law proven in Lean 4 via Charon/Aeneas; axiom-audited certificates

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saymrwulf 1766544daf scalar layer: Scalar52::sub FULLY proven mod l (sub_val_spec) sub_val_spec closes the top-level two-clause value spec: denote(Scalar52.sub a b) = denote(a) - denote(b) in ZMod l for limb-bounded inputs with canonical subtrahend (scVal b < l). Axiom-clean [propext, Classical.choice, Quot.sound]; no sorry. The assembly documented-as-remaining last session is now done. Key resolutions: - Applied the WP "spec_bind" rule manually instead of "step", and reduced the resulting "let (difference,borrow) := (dw,w)" Prod-let with an explicit "show" — this was the destructuring friction that blocked the earlier attempt (step's arity heuristics mis-typed the pair result). - Inlined the subtle "Choice::from" identity (no step-spec, like csel_step). - PERFORMANCE: kept "scLimbs" as opaque atoms in the gamma5=1 derivation instead of "unfold ... at *" — the unfold exploded omega with 2^52..2^260 coefficients and blew past 600s; atomic form proves in ~1 min (METHOD 4, same kernel-cost discipline as the field layer). - The 2^260 borrow-wrap and the +l conditional-add cancel in ZMod l: beta5=0 direct; beta5=1 forces top carry gamma5=1 from scVal b < l, closed by linear_combination over the two telescopes (sub_telescope, add_telescope). check-scalar.sh: sub_val_spec in the manifest + Phase-3 audit (4/4 clean); proof-phase caps raised to 600s/8192MB for the assembly; full button green. exponentiation.threshold raised to 300 for the 2^260 literal. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-03 17:27:23 +02:00
verification	scalar layer: Scalar52::sub FULLY proven mod l (sub_val_spec)	2026-07-03 17:27:23 +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: Scalar52::sub FULLY proven mod l (sub_val_spec)	2026-07-03 17:27:23 +02:00
TRUSTED-BASE.md	skeleton: proof-pyramid layout, honest status table, trusted-base doc	2026-07-02 13:10:26 +02:00

README.md

dalek-ed25519-verified

Formal verification of the ed25519 implementation in dalek-cryptography/curve25519-dalek (upstream, v5.0.0-rc.1), 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; `sub_val_spec` ✅, `L_val`, loop specs proven)	🔨 sub done · add/mul next	denotation + L=ℓ + FULL sub (⟦sub a b⟧=⟦a⟧−⟦b⟧ in ZMod ℓ) proven; add & Montgomery mul next
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: dalek-cryptography/curve25519-dalek, commit 4cf8db2
Pinned/patched source: saymrwulf/curve25519-dalek-source, commit 135ed70
Patches: minimal Aeneas-compatibility only (documented in the source repo)
Verified backend: backend/serial/u64 (FieldElement51, Scalar52). SIMD/AVX backends are out of scope (marked opaque).

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).