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saymrwulf
7dff4157a2
Proofs/ScalarAddSpec.lean, axiom-clean, no sorry: - add_loop_spec: the 5-limb carry loop unrolled (same skeleton as the proven conditional-add-L chain, with b's limbs in place of L's constants); per-limb equations r_i + 2^52*g_(i+1) = a_i + b_i + g_i. - add_val_spec: denote(add a b) = denote a + denote b in ZMod l for limb-bounded canonical inputs. Composition: add_telescope lifts the carry equations to scLimbs sum + 2^260*g5 = scVal a + scVal b; canonicity (a,b < l < 2^253) forces g5 = 0; the trailing sub(sum, L) goes through sub_val_spec with subtrahend L — enabled by weakening sub_val_spec's hypothesis from scVal b < l to scVal b <= l (the gamma5=1 forcing argument only needs <=), since scVal L = l exactly. denote L = 0 in ZMod l closes it. check-scalar.sh: ScalarAddSpec in manifest + audit (5/5 clean), button green at the re-budgeted 300s/4096MB caps. With sub (previous commit): the scalar layer's + and - are both fully verified against dalek's own extraction. Remaining: x3 fork port, Montgomery mul/reduce (kernel frontier). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
81 lines
3.9 KiB
Markdown
81 lines
3.9 KiB
Markdown
# dalek-ed25519-verified
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Formal verification of the ed25519 implementation in **dalek-cryptography/curve25519-dalek (upstream, v5.0.0-rc.1)**, built as a
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coherent proof pyramid in Lean 4 via the Charon/Aeneas transpilation pipeline:
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```
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┌──────────────────────────────┐
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│ Signature (EdDSA verify) │ accepted ⇒ [8][S]B = [8]R + [8][k]A
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├──────────────────────────────┤
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│ Scalar arithmetic mod ℓ │ Scalar52 ops correct mod ℓ
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├──────────────────────────────┤
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│ Group law (twisted Edwards) │ point ops = complete addition law
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├──────────────────────────────┤
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│ Field 𝔽_p, p = 2²⁵⁵ − 19 │ FieldElement51 ops correct mod p
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└──────────────────────────────┘
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```
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Every layer states its theorems about the **actual Aeneas-transpiled Rust
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code** (never about a hand-written re-model), and every claim in the status
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table below is backed by a compiled proof plus an axiom audit of the named
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certificate. Files that do not compile under `verification/check.sh` are not
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in this repository.
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## Layer status
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| Layer | Certificate | Status | Axioms of certificate |
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|-------|-------------|--------|-----------------------|
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| Field 𝔽_p | `fieldImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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| Group law (Edwards) | `edwardsImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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| Scalar mod ℓ | `add_val_spec` ✅ `sub_val_spec` ✅ (`scalarImplementation` aggregate planned) | 🔨 add+sub done · mul next | ⟦add a b⟧=⟦a⟧+⟦b⟧ and ⟦sub a b⟧=⟦a⟧−⟦b⟧ in ZMod ℓ proven on dalek; ×3 port & Montgomery mul next |
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| Signature (EdDSA) | `verifyEquation` (planned) | ⏳ planned | — |
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Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started.
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This table is updated only when `verification/check.sh` passes for the layer.
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## Source
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- **Upstream**: [dalek-cryptography/curve25519-dalek](https://github.com/dalek-cryptography/curve25519-dalek), commit `4cf8db2`
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- **Pinned/patched source**: [saymrwulf/curve25519-dalek-source](https://github.com/saymrwulf/curve25519-dalek-source), commit `135ed70`
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- **Patches**: minimal Aeneas-compatibility only (documented in the source repo)
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- Verified backend: `backend/serial/u64` (`FieldElement51`, `Scalar52`). SIMD/AVX backends are out of scope (marked opaque).
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## Toolchain (pinned)
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| Component | Version |
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|-----------|---------|
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| Aeneas | `bf13c42e` |
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| Charon | `9dd7f23c` |
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| Lean | `v4.30.0-rc2` |
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| OCaml | `5.3.0` |
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## Reproducing
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```bash
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source ~/aeneas-toolchain/env.sh
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cd verification
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./extract.sh # Rust → LLBC → Lean (regenerates gen/)
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./check.sh # compiles EVERY shipped file + axiom-audits EVERY certificate
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```
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The scalar layer has its own pair of buttons:
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```bash
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./extract-scalar.sh # regenerates gen/CurveScalar (Scalar52 limb arithmetic)
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./check-scalar.sh # compiles the scalar gen + the proven scalar foundation
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```
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## Trusted base
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See [TRUSTED-BASE.md](TRUSTED-BASE.md) for the complete list of assumptions
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(Lean kernel, mathlib, Charon/Aeneas semantics, external-function models,
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and — in the signature layer only — an opaque SHA-512 model).
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## Provenance
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Proof engineering in this repository builds on the verification methodology
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and proof architecture of
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[PlanetMacro/ed25519-verificationtest](https://github.com/PlanetMacro/ed25519-verificationtest)
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(the reference solution). All proofs here are checked against **this fork's
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own extracted code**; nothing is claimed that the check script does not compile.
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