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https://github.com/saymrwulf/betrusted-ed25519-verified.git
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mrwulf
1bbc70e5ce
Port of the dalek Montgomery stack against THIS fork's own extraction (gen sections byte-identical, proofs recompiled from scratch here): - Proofs/ScalarMulSpec.lean - mul_internal: 9 exact schoolbook columns - Proofs/ScalarMontSpec.lean - part1/part2 exact-division rounds (LFACTOR*L0 = -1 mod 2^52), head/tail telescopes, mont_bound, tail walk - Proofs/ScalarReduceSpec.lean - montgomery_reduce main walk: scDenote r * 2^260 = Z in ZMod ell + 52-bit output bounds - Proofs/ScalarFullMulSpec.lean - mul = double Montgomery round through RR = R^2 mod ell; R cancelled as a unit; post: [mul a b] = [a]*[b] - Proofs/ScalarMain.lean - scalarImplementation aggregate (ScBnd interfaces; canonical inputs discharge the Montgomery bound) sub_val_spec/add_val_spec posts strengthened with result-limb bounds. check-scalar.sh: 9 proof files, 10 kernel audits, all exactly [propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
73 lines
3.5 KiB
Markdown
73 lines
3.5 KiB
Markdown
# betrusted-ed25519-verified
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Formal verification of the ed25519 implementation in **betrusted-io/curve25519-dalek (Precursor/Xous fork, v4.1.2)**, 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 | `scalarImplementation` (add ✅ sub ✅ mul ✅) | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
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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**: [betrusted-io/curve25519-dalek](https://github.com/betrusted-io/curve25519-dalek), commit `16e087a`
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- **Pinned/patched source**: [saymrwulf/betrusted-curve25519-dalek-source](https://github.com/saymrwulf/betrusted-curve25519-dalek-source), commit `64ee8f0`
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- **Patches**: minimal Aeneas-compatibility only (documented in the source repo)
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- **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.
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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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