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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 06a7c1e603 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 15:07:59 +02:00
verification Double-scalar-mul proof campaign, bricks 1-3: table, digit step, loop 2026-07-04 15:07:59 +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

README.md

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 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: 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).