mirror of
https://github.com/saymrwulf/anza-ed25519-verified.git
synced 2026-09-04 20:24:06 +00:00
mrwulf
25b73f1778
- README: pyramid-diagram apex row upgraded to the proven full lift (accepted <=> decompress(R) = [k](-A)+[s]B), status table names all four button-enforced tiers, apex section gains the phase-2 tier table (half-lift / point equation / full lift) + the decompress-chain summary; source pin updated to the pushed patch commit. - TRUSTED-BASE item 5: rewritten from the single byte-apex certificate to the FOUR enforced tiers (decompress_of_canonical noted as standard-three-only). - gen/CurveField/FunsExternal.lean: stale root-namespace edwards.decompress.step_1/step_2 axioms removed (dead weight left behind by un-opaquing; outside every cone, but they forced fully-qualified unfolds - see control FAILURES.md). - check.sh Phase 3b success echo aligned to "apex + full-lift" (echo only; the enforcing greps covered all four tiers already). Validated by the pass-4 sweep: 9/9 buttons green (this repo's check.sh + check-scalar.sh among them), logs retained in the pass workspace. Full record: formal-verification-control/COHERENCE-PASS-4.md. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
132 lines
7.2 KiB
Markdown
132 lines
7.2 KiB
Markdown
# anza-ed25519-verified
|
||
|
||
Formal verification of the ed25519 implementation in **anza-xyz/cryptography (Solana, solana-ed25519 crate)**, built as a
|
||
coherent proof pyramid in Lean 4 via the Charon/Aeneas transpilation pipeline:
|
||
|
||
```
|
||
┌──────────────────────────────┐
|
||
│ Signature (EdDSA verify) │ accepted ⇔ decompress(R) = [k](−A)+[s]B
|
||
├──────────────────────────────┤
|
||
│ 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 |
|
||
|-------|-------------|--------|-----------------------|
|
||
| Field 𝔽_p | `fieldImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
|
||
| Group law (Edwards) | `edwardsImplementation` | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
|
||
| Scalar mod ℓ | `scalarImplementation` (add ✅ sub ✅ mul ✅) | ✅ proven | `[propext, Classical.choice, Quot.sound]` |
|
||
| Signature (EdDSA) | `verify_accepts_iff` … `verify_accepts_iff_decompress` (4 tiers) | ✅ proven (phases 1+2) | standard three + the button-enforced SHA-512/wire-format boundary — see [The signature apex](#the-signature-apex-phases-1-and-2) |
|
||
|
||
Status legend: ✅ proven & axiom-audited · ⏳ in progress · ❌ not started.
|
||
This table is updated only when `verification/check.sh` passes for the layer.
|
||
|
||
## The signature apex (phases 1 and 2)
|
||
|
||
The apex certificate `CurveFieldProofs.verify_accepts_iff` is the literal EdDSA
|
||
acceptance criterion, proven about the extracted verifier:
|
||
|
||
> For a signature that parses, the verifier returns `Ok(())` **iff** the
|
||
> recomputed compressed point `compress([s]·B − [k]·A)` equals the signature's
|
||
> `R`, byte-for-byte — where `k` is whatever scalar the opaque SHA-512 oracle
|
||
> produces from `(R, A, msg)`.
|
||
|
||
The recomputation runs entirely through the **proven** model: anza's verify code lives in the **same crate** as the curve (`src/ed_sigs`), so
|
||
the whole verify path joins the one merged `gen/CurveField` extraction directly —
|
||
no glue layer, no name-welding. The `Error` enum and the parse/filter helpers are
|
||
real extracted code; only the SHA-512 oracle (`sha512_hash3`) and the foreign
|
||
`ed25519::Signature` type with its two byte accessors stay opaque — the tightest
|
||
boundary of the four sibling repos.
|
||
|
||
> **Which verifier is verified?** The certificate is about
|
||
> `VerificationKey::verify_sha512`, which is semantically identical (documented,
|
||
> pure refactor) to `VerificationKey::verify_dalek` — the dalek-style
|
||
> canonical-`R` byte-comparison path, **including** this crate's legacy filters
|
||
> (all-zero key, excluded-`R` list) and the strict `s < ℓ` check. The crate's
|
||
> *default* `verify()` uses the HEEA-accelerated Zebra/ZIP-215 path, which is a
|
||
> different acceptance criterion and is **not** covered by this certificate.
|
||
|
||
`check.sh` has a dedicated audit phase (Phase 3b) that fails the build unless
|
||
each apex-tier certificate's axiom cone is **exactly**
|
||
|
||
`[propext, Classical.choice, Quot.sound]` + `{ed25519.Signature, ed_sigs.sha512_hash3, ed25519.Signature.r_bytes, ed25519.Signature.s_bytes}`
|
||
|
||
— i.e. the three Lean foundations plus the documented SHA-512/wire-format
|
||
boundary. Zero curve, scalar, or backend axioms. The companion certificate
|
||
`verify_loop_full` (the 32-byte comparison loop computes array equality)
|
||
carries the standard three axioms only.
|
||
|
||
**Phase 2 (complete): the point-level lift.** Phase 3b enforces the SAME
|
||
axiom boundary on three further tiers that lift the byte equation to points:
|
||
|
||
| Tier | Certificate | Statement |
|
||
|------|-------------|-----------|
|
||
| half-lift | `verify_accepts_iff_point` | accepted ⇔ R = the **canonical encoding** of `[k]·minus_A + [s]·B` (compress semantics + `as_bytes` canonicity + hash-to-scalar, recompute chain inverted) |
|
||
| point equation | `verify_accepts_iff_point_eq` | for any valid on-curve `Q` canonically encoded by R: accepted ⇔ `Q = [k]·minus_A + [s]·B` **as points** (encoding-injectivity: d non-square + parity root-selection) |
|
||
| full lift | `verify_accepts_iff_decompress` | R **decompresses** to a valid on-curve `Pt`, and accepted ⇔ `Pt = [k]·minus_A + [s]·B` — the constructive capstone |
|
||
|
||
The full lift runs through the extracted `CompressedEdwardsY::decompress`
|
||
itself, proven end-to-end: `from_bytes` parses the y-residue exactly below
|
||
bit 255 (`from_bytes_spec`), `sqrt_ratio_i` returns the even square root of
|
||
`(y²−1)/(dy²+1)` (`sqrt_ratio_i_sq_spec`, Fermat-exponent square root), and
|
||
the sign bit selects the x-parity (`decompress_of_canonical`, standard three
|
||
axioms). Byte comparison ↔ encoding equality ↔ point equality ↔
|
||
decompressed-point equality: every link is machine-checked over the
|
||
extracted code, and `check.sh` fails the build if any of the four tiers'
|
||
cones deviates from the boundary above.
|
||
|
||
|
||
## Source
|
||
|
||
- **Upstream**: [anza-xyz/cryptography](https://github.com/anza-xyz/cryptography), commit `0a54cca`
|
||
- **Pinned/patched source**: [saymrwulf/anza-cryptography-source](https://github.com/saymrwulf/anza-cryptography-source), commit `5f8e70e` (adds the decompress step_2 negate-then-assign patch)
|
||
- **Patches**: minimal Aeneas-compatibility only (documented in the source repo)
|
||
- Closest relative of the reference solution (same crate layout as solana-ed25519).
|
||
|
||
## 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
|
||
```
|
||
|
||
The gen model is ONE merged universe (`gen/CurveField`: field + curve +
|
||
scalar + the verify path's reachable code), regenerated in full by
|
||
`extract.sh`. The scalar layer keeps its own check button:
|
||
|
||
```bash
|
||
./check-scalar.sh # compiles the merged gen + all scalar proofs (add, sub,
|
||
# Montgomery mul, byte-parsing) and kernel-audits the
|
||
# scalar certificates, incl. the scalarImplementation
|
||
# aggregate
|
||
```
|
||
|
||
|
||
## 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).
|