2026-07-02 11:10:26 +00:00
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# pasta-pallas-verified
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Formal verification of Pallas (Pasta curve cycle, Zcash Halo 2) arithmetic in
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**zcash/pasta_curves**, built as a coherent proof pyramid in Lean 4 via the
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Charon/Aeneas transpilation pipeline:
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```
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┌────────────────────────────────────┐
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│ Scalar multiplication │ [n]P correct over the group
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├────────────────────────────────────┤
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│ Group law (short Weierstrass) │ point ops = curve group law
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├────────────────────────────────────┤
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│ Field 𝔽_p (Montgomery form) │ 4×64-limb Fp ops correct mod p
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└────────────────────────────────────┘
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p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
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```
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Every theorem is stated about the **actual Aeneas-transpiled Rust code** from
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`src/fields/fp.rs` / `src/curves.rs`. There are **no bridge axioms**: the
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correctness of add/sub/neg/mul/square/montgomery_reduce/invert is *proven*,
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not assumed. (A previous attempt at this target axiomatized exactly those
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statements; this repository exists to do it properly.)
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## Layer status
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2026-07-02 15:23:44 +00:00
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> **Construction note (2026-07-02):** the field layer is mid-build. PROVEN and
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> compiled: PPallas (primality), Denote (Montgomery denotation), HelperSpecs
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> (adc/sbb/mac), SubNegSpec (sub/neg). DRAFTED, awaiting compilation:
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> AddSpec, ConstSpecs, ReduceSpec (Montgomery reduction), MulSpec. Not yet
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> written: SquareSpec, InvertSpec, FieldMain (the certificate), check.sh.
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> This note is removed when `verification/check.sh` goes green end-to-end.
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2026-07-02 11:10:26 +00:00
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| Layer | Certificate | Status | Axioms of certificate |
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|-------|-------------|--------|-----------------------|
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| Field 𝔽_p (Montgomery) | `fieldImplementation` | ⏳ in progress | — |
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| Group law (Pallas) | `curveImplementation` | ⏳ in progress | — |
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| Scalar multiplication | `scalarMulCorrect` | ⏳ in progress | — |
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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**: [zcash/pasta_curves](https://github.com/zcash/pasta_curves), commit `fe08536`
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- **Pinned/patched source**: [saymrwulf/pasta_curves-source](https://github.com/saymrwulf/pasta_curves-source), commit `7f32788`
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- Representation: 4×64-bit limbs, Montgomery form (a·R mod p, R = 2²⁵⁶)
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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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## Trusted base
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See [TRUSTED-BASE.md](TRUSTED-BASE.md).
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