Formally verified ed25519 (anza-xyz solana-ed25519): field + complete Edwards addition law proven in Lean 4 via Charon/Aeneas; axiom-audited certificates
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mrwulf 3a89c3c5be verification: lifted phases run under the buttons shell options, enforced in lift-guard
A lift is evidence about the shipping gate only if it executes the way the
shipping gate executes. Every button here runs `set -euo pipefail`. Eighteen
lift sites prefixed their driver with `set -uo pipefail` and no -e — four per
fork (selftest-harness, selftest-scalar-statements, selftest-statements twice)
and both accumulator lifts — while sixteen other sites got it right. The estate
did it both ways, which is what made this a defect and not a convention.

Without -e a failing command does not abort: execution continues and the driver
returns the LAST command status. A lifted phase can therefore reach a verdict
the shipping phase would never reach while the self-test reports the gate
"works". selftest_statements.sh:27 claims the tested logic IS the shipping
logic; in this respect it was not.

NO VERDICT CHANGED. Every self-test that passed before passes now, at the same
timings, so -e was not masking a false green at these commits. The defect was
fidelity and the claim is no larger than that.

The durable part is not the 18 edits. lift-guard.sh already inspects every
driver, so it now REFUSES any lift whose driver does not enable errexit and
prints the drivers actual shell options. Negative-tested four ways: no -e
rejects, `set -euo` passes, bare `set -e` passes, no set line at all rejects.
Byte-identical across the four forks. The nineteenth lift someone writes fails
closed rather than silently testing a more permissive shell.

Certified by the round-15 sweep: 50/50 GREEN, six repositories, both buttons
and every self-test, exit 0.

Registered and NOT fixed here: ltl-accumulator-verified has no lift-guard.sh
at all and calls it zero times, so its two lifts remain unguarded — the one
place this class can still recur silently.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-08-04 12:58:28 +02:00
verification verification: lifted phases run under the buttons shell options, enforced in lift-guard 2026-08-04 12:58:28 +02:00
.gitignore Round-7 F1: make model/template correspondence SEMANTIC, and fail closed 2026-08-02 02:24:15 +02:00
README.md Coherence pass 4 (the closing pass): 4-tier apex documentation + hygiene 2026-07-06 04:01:17 +02:00
TRUSTED-BASE.md P2-c: classify and pin the extraction boundary 2026-07-31 17:53:31 +02:00

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      │   Scalar52 ops correct mod 
        ├──────────────────────────────┤
        │  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 scalarImplementation (add sub mul ) proven [propext, Classical.choice, Quot.sound]
Signature (EdDSA) verify_accepts_iffverify_accepts_iff_decompress (4 tiers) proven (phases 1+2) standard three + the button-enforced SHA-512/wire-format boundary — see The signature apex

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 < 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 (y²1)/(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, commit 0a54cca
  • Pinned/patched source: 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

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:

./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 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).