saymrwulf
ff1eea473d
New in Proofs/ScalarSubSpec.lean (all axiom-clean [propext, Classical.choice, Quot.sound], no sorry, no native_decide): - nat_and_mask52 / nat_shift52 / nat_shift63 : 52/63-bit ops -> %,/ - sub_step_arith : isolated per-limb borrow accounting (tiny ℕ context, correction-on-the-left so no truncated subtraction) — the METHOD-4 discipline that keeps 2^260-scale coefficients out of any one certificate - sub_loop_spec : the FULL 5-limb borrow chain of Scalar52::sub, unrolled via loop_step/range_next_*; wrapping_sub, 52-bit mask store, borrow-out bit. This is the loop unroll that blocked the earlier attempt. - csel_step : step-spec for the subtle conditional_select (faithful model) - cond_add_l_zero_spec / cond_add_l_one_spec : BOTH cases of conditional add-of-L, full carry chains; the condition-1 case steps the addend as a clean value so the index_mut write-back matches sub_loop's pattern - sub_telescope / add_telescope : the 2^52i-weighted value telescopes to 2^260, discharged by omega (no kernel-capacity blowup) check-scalar.sh: ScalarSubSpec added to the compile manifest; Phase-3 axiom audit extended to sub_loop_spec + cond_add_l_one_spec (3/3 clean). Full button green. Honest boundary: top-level sub_val_spec (⟦sub a b⟧ = ⟦a⟧-⟦b⟧ in ZMod ℓ) is documented as remaining — every lemma it needs is proven; what's left is the Aeneas binding-arity for destructuring sub_loop_spec's pair-valued multi-existential postcondition inside the do-block, a mechanical not a mathematical gap. No sorry shipped (Invariants H1/H4). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
3.9 KiB
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; L_val, sub_loop_spec, cond_add_l_*_spec proven) |
🔨 foundation+sub | denotation + L=ℓ + sub borrow/carry chains proven; sub value-assembly & mul in progress |
| 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).
Provenance
Proof engineering in this repository builds on the verification methodology and proof architecture of PlanetMacro/ed25519-verificationtest (the reference solution). All proofs here are checked against this fork's own extracted code; nothing is claimed that the check script does not compile.