mirror of https://github.com/saymrwulf/dalek-ed25519-verified.git synced 2026-09-03 20:13:48 +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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mrwulf 4071d68457 Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop Three new proof files over the CurveField extraction, composing the proven group-law layer (no new axioms, no associativity assumed — computational layering over the abstract `edAdd`): - `Proofs/DsmTableSpec.lean` — `NafLookupTable5::from(&A)`: the 8 entries are valid `ProjectiveNielsPoint` caches of valid on-curve points denoting the odd multiples A, 3A, ..., 15A as the `edOdd` double-and-add recursion. 7 explicit loop peels over edwards_as_projective_niels_spec / add_projniels_law / compl_as_extended_law, seeded by edwards_double_law. `select`: both masserts (x odd, x < 16) DISCHARGED — panic-freedom is proven, not assumed; post enumerates all 8 digit cases. - `Proofs/DsmStepSpec.lean` — `proj_double_law` (the projective doubling denotes `edAdd P P`; same Z^2-scaled linear_combination discipline as the extended-coordinate law), `compl_as_projective_law` ((X:Z),(Y:T) to (XT:YZ:ZT) preserves the point), `naf_select_entry` (digit-indexed lookup returns THE entry: NafEntryOf r A ((x-1)/2)), and `dsm_step_p_law` / `dsm_step_b_law`: the three-way NAF digit step denotes `edDigit` — add the d-th odd multiple, add its negation, or pass through. - `Proofs/DsmLoopSpec.lean` — the 256-iteration Straus loop by GENUINE induction on the counter (one symbolic body walk, no unrolling): `dsm_loop_spec` — from the identity, the loop returns a valid on-curve point denoting `dsmFold ... edId 256`, the abstract double-and-add fold of both digit arrays over the table points. Digit and table hypotheses are exactly what the NAF spec and naf_table_spec provide (layering). check.sh wired: PROOFS + AUDIT_IMPORTS + 7 new CERTS (naf_table_spec, naf_select_spec, proj_double_law, compl_as_projective_law, dsm_step_p_law, dsm_step_b_law, dsm_loop_spec), each `#print axioms`-audited to exactly [propext, Classical.choice, Quot.sound]. Full check.sh green. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-04 15:30:18 +02:00
verification	Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop	2026-07-04 15:30:18 +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 proven, scalarImplementation aggregate	2026-07-03 21:06:15 +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` (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: 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 + all scalar proofs (add, sub,
                      # Montgomery mul) and kernel-audits 10 certificates,
                      # including 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).