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mrwulf
7e0bac08c6
Nine parallel readers audited every doc against measured ground truth; every finding was re-verified against the file before any edit, and the sweep fixed by PROPERTY, not by flag — wording the readers caught in one repo was hunted in all siblings (the two-button README sentence existed in all four forks, not the three flagged; likewise the cone-overclaim in TRUSTED-BASE item 1). This repo: see the diff. Records were not rewritten; clarifications are dated. Doc-only except where noted in the estate summary; every gated doc change was followed by a green button run. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
126 lines
7 KiB
Markdown
126 lines
7 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 ⇔ decompress(R) = [k](−A)+[s]B
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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 compile under neither `verification/check.sh` nor
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`verification/check-scalar.sh` are not in this repository — each shipped
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proof source belongs to exactly one button's manifest, and the seam gate
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fails the build otherwise.
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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) | `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) |
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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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## The signature apex (phases 1 and 2)
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The apex certificate `CurveFieldProofs.verify_accepts_iff` is the literal EdDSA
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acceptance criterion, proven about the extracted verifier:
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> For a signature that parses, the verifier returns `Ok(())` **iff** the
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> recomputed compressed point `compress([s]·B − [k]·A)` equals the signature's
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> `R`, byte-for-byte — where `k` is whatever scalar the opaque SHA-512 oracle
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> produces from `(R, A, msg)`.
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The recomputation runs entirely through the **proven** model: the vendored `ed25519-dalek` verify glue is extracted as `gen/CurveSig`, whose
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hand-maintained externals import `gen/CurveField` — every curve and scalar call
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resolves by fully-qualified name to a **proven** definition. Only SHA-512 (a
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single monomorphic `sha512_hash3(R, A, m)` oracle — this fork's sha2-0.10 stack
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makes the incremental-hasher types untranslatable) and the wire-format types
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stay opaque.
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`check.sh` has a dedicated audit phase (Phase 3b) that fails the build unless
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each apex-tier certificate's axiom cone is **exactly**
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`[propext, Classical.choice, Quot.sound]` + `{ed25519.Signature, verifying.sha512_hash3, ed25519.Signature.to_bytes, signature.error.Error, signature.error.Error.new}`
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— i.e. the three Lean foundations plus the documented SHA-512/wire-format
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boundary. Zero curve, scalar, or backend axioms. The companion certificate
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`verify_loop_full` (the 32-byte comparison loop computes array equality)
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carries the standard three axioms only.
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**Phase 2 (complete): the point-level lift.** Phase 3b enforces the SAME
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axiom boundary on three further tiers that lift the byte equation to points:
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| Tier | Certificate | Statement |
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|------|-------------|-----------|
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| half-lift | `verify_accepts_iff_point` | accepted ⇔ R = the **canonical encoding** of `[k]·(−A) + [s]·B` (compress semantics + `as_bytes` canonicity + hash-to-scalar, recompute chain inverted) |
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| point equation | `verify_accepts_iff_point_eq` | for any valid on-curve `Q` canonically encoded by R: accepted ⇔ `Q = [k]·(−A) + [s]·B` **as points** (encoding-injectivity: d non-square + parity root-selection) |
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| full lift | `verify_accepts_iff_decompress` | R **decompresses** to a valid on-curve `Pt`, and accepted ⇔ `Pt = [k]·(−A) + [s]·B` — the constructive capstone |
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The full lift runs through the extracted `CompressedEdwardsY::decompress`
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itself, proven end-to-end: `from_bytes` parses the y-residue exactly below
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bit 255 (`from_bytes_spec`), `sqrt_ratio_i` returns the even square root of
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`(y²−1)/(dy²+1)` (`sqrt_ratio_i_sq_spec`, Fermat-exponent square root), and
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the sign bit selects the x-parity (`decompress_of_canonical`, standard three
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axioms). Byte comparison ↔ encoding equality ↔ point equality ↔
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decompressed-point equality: every link is machine-checked over the
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extracted code, and `check.sh` fails the build if any of the four tiers'
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cones deviates from the boundary above.
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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 `cee0e17` (adds the decompress step_2 negate-then-assign patch)
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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 + audits everything the MAIN manifest owns (scalar layer: its own button below)
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```
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The gen model is ONE merged universe (`gen/CurveField`: field + curve +
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scalar + the verify path's reachable code), regenerated in full by
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`extract.sh`. The scalar layer keeps its own check button:
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```bash
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./check-scalar.sh # compiles the merged gen + all scalar proofs (add, sub,
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# Montgomery mul, byte-parsing) and kernel-audits the
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# scalar certificates, incl. the scalarImplementation
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# aggregate
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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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