2026-07-02 11:10:26 +00:00
|
|
|
|
# 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 |
|
|
|
|
|
|
|-------|-------------|--------|-----------------------|
|
2026-07-02 12:17:44 +00:00
|
|
|
|
| Field 𝔽_p | `fieldImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
|
2026-07-02 12:50:42 +00:00
|
|
|
|
| Group law (Edwards) | `edwardsImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
|
scalar layer: prove Scalar52::sub borrow + conditional-add-L carry chains
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>
2026-07-03 14:26:24 +00:00
|
|
|
|
| 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 |
|
2026-07-03 10:54:26 +00:00
|
|
|
|
| Signature (EdDSA) | `verifyEquation` (planned) | ⏳ planned | — |
|
2026-07-02 11:10:26 +00:00
|
|
|
|
|
|
|
|
|
|
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](https://github.com/dalek-cryptography/curve25519-dalek), commit `4cf8db2`
|
|
|
|
|
|
- **Pinned/patched source**: [saymrwulf/curve25519-dalek-source](https://github.com/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
|
|
|
|
|
|
|
|
|
|
|
|
```bash
|
|
|
|
|
|
source ~/aeneas-toolchain/env.sh
|
|
|
|
|
|
cd verification
|
|
|
|
|
|
./extract.sh # Rust → LLBC → Lean (regenerates gen/)
|
|
|
|
|
|
./check.sh # compiles EVERY shipped file + axiom-audits EVERY certificate
|
|
|
|
|
|
```
|
|
|
|
|
|
|
2026-07-02 21:58:29 +00:00
|
|
|
|
The scalar layer has its own pair of buttons:
|
|
|
|
|
|
|
|
|
|
|
|
```bash
|
|
|
|
|
|
./extract-scalar.sh # regenerates gen/CurveScalar (Scalar52 limb arithmetic)
|
|
|
|
|
|
./check-scalar.sh # compiles the scalar gen + the proven scalar foundation
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
|
2026-07-02 11:10:26 +00:00
|
|
|
|
## Trusted base
|
|
|
|
|
|
|
|
|
|
|
|
See [TRUSTED-BASE.md](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](https://github.com/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.
|