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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2026-08-07 14:00:54 +00:00
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`src/fields/fp.rs`. The rule is **no bridge axioms**: nothing is claimed
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proven that is in fact assumed. Proven today: sub/neg, the adc/sbb/mac
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helpers, the constants, primality, and the denotation layer;
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add/mul/montgomery_reduce/square/invert are **in progress** (drafted in
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`Proofs/drafts/`, blocked on kernel proof-checking memory — see Layer status
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below). No curve extraction exists yet. (A previous attempt at this target
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axiomatized exactly the statements this repository refuses to assume; it
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exists to do them properly or not claim them.)
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2026-07-02 11:10:26 +00:00
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## Layer status
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2026-07-02 18:16:07 +00:00
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> **Construction status (2026-07-02).** The field FOUNDATION is proven and
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> compiles (`verification/check.sh` is green): **PPallas** (Lucas/Pratt
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> primality certificate for the 255-bit Pallas modulus), **Denote** (the
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> Montgomery denotation ⟪a⟫ = feVal a·R⁻¹ and the `Canon` invariant),
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> **HelperSpecs** (exact ℕ specs for the `adc`/`sbb`/`mac` u64 primitives,
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> proven against the transpiled code), **SubNegSpec** (`sub`/`neg`), and
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> **ConstSpecs** (R, R², INV, zero, one). Every one is stated about the REAL
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> Aeneas-extracted code with **no bridge axioms**.
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>
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> **In progress:** `add`, `mul`, `montgomery_reduce`, `square`, `invert`, and
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> the aggregate `fieldImplementation` certificate. These are drafted in
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> `verification/Proofs/drafts/` and the Montgomery accounting is proven
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> standalone, but the full theorems currently overflow the Lean **kernel's
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> proof-checking memory**: omega certificates with 2²⁵⁶/2⁵¹²-scale
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> coefficients (unavoidable in 4×64 Montgomery arithmetic) are too large for
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> the kernel, whereas the ed25519 5×51 field (2⁵¹-scale, ×19 folding) stays
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> small. The fix — reformulating every arithmetic step via `linear_combination`
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> and isolating each big-coefficient step into a context-free lemma (the
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> `montgomery_rows_conclusion` accounting lemma already does this and compiles)
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> — is mechanical but not yet complete. Tracked honestly here rather than
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> shipped behind an axiom.
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2026-07-02 15:23:44 +00:00
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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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