fips205-slhdsa-verified

Machine-checked verification campaign for the SLH-DSA (FIPS 205) verify path, extracted from a pure-Rust implementation into Lean 4 via Charon/Aeneas — the same pipeline, discipline, and honesty rules as the four ed25519 campaigns (dalek/anza/risc0/betrusted-ed25519-verified).

STATUS: eleven certificates over the extracted verify model (external review round 2 applied)

verification/check.sh is green (exit 0): the model compiles, the proofs compile, and the axiom audit passes. The audit now runs inside Lean (verification/Proofs/Audit.lean): it reads each certificate's cone from the kernel via collectAxioms and asserts SET EQUALITY against that certificate's expected boundary — so an added axiom and a silently dropped oracle dependency both fail, with no text parsing to misparse (external review round 2, 2026-07-24, replaced the earlier #print axioms text parser, which could fail open on an empty or truncated report).

What is actually established — eleven Lean theorems about the Aeneas-generated model of the monomorphic verify_mono compatibility verify path (an additive, #![allow(dead_code)] re-expression of the deployed generic verifier, using named hash oracles because Charon/Aeneas cannot translate the deployed Hashers function-pointer struct):

• Ten loop-fidelity theorems (chain 5, WOTS+ 8, XMSS 10, hypertree 12, FORS-inner/outer 17, and the input-prep helpers to_int/to_byte/checksum/ base_2b-outer, Alg 2/3/4). Each equates one generated Aeneas loop with an explicit hand-written recursive fold — a local control-flow correspondence, not an Algorithm-level mathematical specification.
• The apex, fips205.slh_verify_128s_accepts_iff — the extracted verify_mono::slh_verify_128s returns ok true iff the recomputed hypertree root byte-equals pk.pk_root. This is an acceptance characterization: there is no acceptance path other than root equality over the extracted recomputation. Its #print axioms cone is exactly [propext, Classical.choice, Quot.sound] + the five SHA-2 oracles.

What is NOT (yet) established — do not overclaim:

• The apex proof does not compose the ten loop theorems. It is a structural factorization of the extracted verifier around its final equality check; it references none of the ten (it would remain provable if one were deleted). The ten are independent local-fidelity lemmas, not links in the apex's proof chain.
• Not "every loop": base_2b's inner accumulation loop (helpers.base_2b_loop0_loop0) is threaded opaquely and has no certificate — and it determines the FORS indices / WOTS digits, so a defect there could change the recomputed root while all eleven theorems still hold.
• Not the deployed public verifier: the proved subject is the private verify_mono facade; the bridge to upstream's generic pk.verify() is the finite in-snapshot differential test, not a machine-checked refinement.
• Not closed-form FIPS 205 correctness: the folds are transliterations of the extracted loops (the hash primitives stay opaque); nothing here relates the recomputed root to a mathematical SLH-DSA specification.

This is a real intermediate verification layer, not an end-to-end formal verification of the deployed verifier. After de-plumbing rounds 1+2 the model carries no plumbing axioms on the verify path — its external surface is exactly the five SHA-2 oracles (plus off-path zeroize impls). The trust base and residual assumptions are stated in TRUSTED-BASE.md.

• fips205.chain_free_loop_eq (Algorithm 5, WOTS+ chaining): the extracted chain_free loop equals the explicit s-fold hash chain, with the hash address set to i, i+1, …, i+s−1 in turn. This rules out — machine-checked, for the monomorphic SHA2-128s verify_mono path — an off-by-one loop bound, a wrong address field, and wrong threading. Its #print axioms cone is exactly [propext, Classical.choice, Quot.sound, verify_mono.oracle.f] — the three kernel axioms plus the one hash oracle it touches, and nothing else (no transpiler plumbing; the u32 range machinery was discharged with real definitions). check.sh Phase 3 (the in-Lean exact-cone audit) fails the build if any certificate's cone differs from its expected set — an extra axiom or a dropped oracle both break it.

• fips205.wots_loop1_eq (Algorithm 8, WOTS+ pk recomputation — the chain loop): the extracted wots_pk_from_sig_free_loop1 equals the fold that, at each index i in [0, LEN), sets the chain address to i and runs chain_free on sig[i] starting at digit msg[i] for W−1−msg[i] steps, writing tmp[i]. This is the layer above chain: it consumes chain_free and pins that the LEN chains run with the right start indices, step counts, and slots. Cone: kernel three + verify_mono.oracle.f.

• fips205.xmss_loop_eq (Algorithm 10, XMSS pk-from-sig — the authentication-path Merkle loop): the extracted xmss_pk_from_sig_free_loop equals the fold that, at step k, sets the tree height to k+1, tests bit k of the leaf index, and on an even bit halves the tree index and hashes H(node ∥ auth[k]), on an odd bit sets the tree index to (i−1)/2 and hashes H(auth[k] ∥ node). This pins the Merkle sibling ORDER (the even/odd rule), the tree-height/tree-index address schedule, and the auth-path indexing — the heart of Merkle-path verification. Cone: kernel three + verify_mono.oracle.h (the first certificate where H enters; F does not — the loop runs above the WOTS+ computation).

• fips205.ht_loop_eq (Algorithm 12, hypertree verification — the layer walk): the extracted ht_verify_free_loop equals the fold that, at layer j, splits the tree index (idx_leaf = idx_tree mod 2^h' by mask+cast, then idx_tree >>= h'), sets the layer address to j and the tree address to the shifted index, and recomputes the node through xmss_pk_from_sig on the j-th XMSS signature. This pins the layer schedule of hypertree verification; the final node = pk_root comparison sits one bind above, in ht_verify_free, and belongs to the apex composition. Cone: kernel three + verify_mono.oracle.{f, h, t_l} — the full WOTS+/XMSS machinery referenced through the fold, and nothing else.

Foundations behind this (2026-07-22/23): the Aeneas-compat patch (additive monomorphic verify module through a named oracle boundary; charon + aeneas exit 0); the u32 range-loop de-plumbing (faithful Step defs vs pinned rustc, axiom-clean); the 8-site source de-plumbing (snapshot commit 6f6a9d6: try_from/is_err/unwrap on pre-masked values → plain casts, the WOTS+ checksum iter().take() + &u32 Sub → an index loop — each site a local rewrite whose equivalence is argued in the commit and checked, for SHA2-128s, by the differential test; the obsoleted transpiler axioms were deleted from the external files); fidelity pinned by that differential test in the snapshot (valid / corrupted / wrong-message), re-run green after every source patch.

• fips205.fors_inner_loop_eq + fips205.fors_outer_loop_eq (Algorithm 17, FORS pk-from-sig): a nested loop, split into two theorems. The inner one pins the auth-path Merkle fold for a single FORS tree (bit source indices[i] >> j, H in the even/odd sibling order) — cone kernel-3 + oracle.h. The outer one pins the K-tree fold: for each tree compute the leaf with F at index (i<<a)+indices[i], run the inner Merkle loop, write root[i] — cone kernel-3 + oracle.{f, h}. Split into two files under the memory discipline; the outer step lemma closes by peeling its 16-bind body with bind_congr (a bare rfl there whnf-times- out over the nested inner loop).

• input-prep (fips205.to_int_loop_eq, to_byte_loop_eq, wots_csum_loop_eq, base2b_outer_loop_eq — Algorithms 2/3/4 + the WOTS+ checksum): the byte→integer, integer→byte, checksum, and digit-decomposition loops that prepare the verifier's inputs. All four cones are exactly [propext, Classical.choice, Quot.sound] — pure kernel-3, no hash oracle (byte/bit arithmetic touches no hash). base_2b's inner while loop is threaded opaquely, as every layer treats its sub-loops. These proofs became possible after de-plumbing round 2 (snapshot bea1051) rewrote to_int's iter().take() and base_2b's iter_mut() as index loops, removing the last Take/IterMut iterator adapters; the obsoleted Take axiom was then deleted.

The apex (slh_verify_128s_accepts_iff, above) sits at the top of this layer: the extracted verify_mono::slh_verify_128s accepts iff the recomputed hypertree root byte-equals the pinned public-key root. What remains genuinely unproven is stated in "What is NOT (yet) established" above — most sharply the opaque base_2b inner loop (no certificate) and the bridge from this private verify_mono facade to the deployed generic verifier (a finite differential test, not a machine-checked refinement). Each certificate is audited to the same boundary.

Subject

• Upstream: integritychain/fips205 — pure-Rust FIPS 205 (final standard, 2024-08-13), zero unsafe, no_std, const-generic parameterization, modules mirroring the FIPS 205 algorithm structure.
• Pinned at upstream commit 30bac08580aa61f653e5436d1bbacb5ffac446c4 (2025-09-01), snapshotted with full history at saymrwulf/fips205-source. The verbatim-import base commit's only deviation from upstream is the removal of CI workflows (documented in that commit); the Aeneas-compat and de-plumbing patches then landed as transparent, individually-justified commits on top — never upstream. The current snapshot head is 797b4ef (the round-2 reproducibility commit — committed Cargo.lock + pinned rust-toolchain.toml — on top of de-plumbing round 2, bea1051); the model in this repo is extracted from it, and verification/extract.sh refuses any other commit. No affiliation with, and no changes proposed to, the upstream project.
• Parameter set: SLH-DSA-SHA2-128s first (the small-signature profile deployed in the firmware/code-signing lane). The architecture generalizes; each further parameter set is a separate claim (rigor invariant R2).

Scope

Verify path only. The extraction cone, mirroring FIPS 205's own algorithm tree:

slh_verify -> slh_verify_internal
  -> fors_pk_from_sig
  -> ht_verify -> xmss_pk_from_sig -> wots_pk_from_sig -> chain

Key generation and signing are out of scope (trusted base), exactly as ed25519 signing was. The five verify-path hash oracles (h_msg, f, h, t_l, t_len — SHA-2 instantiations; prf/prf_msg are sign-side only and never enter the cone) are opaque external models with written justifications. They are the only things beyond Lean's three kernel axioms that any certificate cone contains: each cone is exactly the kernel three plus the specific oracles that certificate's computation reaches (e.g. chain reaches F, so oracle.f is inside its cone; the input-prep helpers reach no hash, so their cones are kernel-3 alone). That the cones contain nothing else — no transpiler plumbing, no hidden axiom — is what the audit enforces (honesty invariant H4); their semantics are the standing SHA-2 oracle boundary documented in TRUSTED-BASE.md.

Gate-0 record (2026-07-22)

Per TARGETS.md ("re-verify before use"), the subject was probed before this repository was created:

• Charon: clean (charon cargo --preset=aeneas, roots at the verify cone, sha2/sha3/zeroize/rand_core opaque, features slh_dsa_sha2_128s) — LLBC produced, exit 0.
• Aeneas: translated the entire const-generic verify cone to Lean definitions (wots.chain … slh.slh_verify_internal all generated), with exactly one obstruction class (3 unique errors): the crate::hashers::Hashers struct of plain function pointers cannot be translated.
• Phase 1 — DONE (2026-07-22): the Aeneas-compat patch landed in fips205-source (snapshot 2d89ee3): an additive monomorphic SHA2-128s verify module (src/verify_mono.rs) whose hash suite is reached through named free functions in verify_mono::oracle (marked opaque at the Charon boundary) — the sha512_*-shim pattern. Two further compat refinements: the message-digest input M' passes as a single &[u8] (nested &[&[u8]] is untranslatable), and one let-else became the is_err/unwrap idiom. verification/extract.sh now re-derives the model from the mono root; charon + aeneas both exit 0, and verification/check.sh compiles the result. At this compat-patch commit the only change to pre-existing code was two lines wiring the new module; the generic paths and all twelve parameter sets stayed untouched. (The later de-plumbing commits — rounds 1 and 2 — then made further local edits to helpers.rs/wots.rs, each documented and differential-tested; see the snapshot history at head 797b4ef.)

What is claimed (the button is green)

Each certificate is a statement about the extracted functions (H3), compiled by verification/check.sh with the in-Lean exact-cone audit (H1): chain semantics, WOTS+ pk recomputation, XMSS path recomputation, hypertree acceptance, FORS pk recomputation, the input-prep helpers, and the apex — verify_mono::slh_verify_128s accepts iff the recomputed hypertree root equals the pinned public-key root. The precise scope and non-claims are in the STATUS section above.

The allowed axiom set, stated precisely: unlike the ed25519 field and scalar layers (whose cones are exactly [propext, Classical.choice, Quot.sound]), the hash oracles permeate every SLH-DSA layer — chain already calls F. Each certificate's cone is therefore the three kernel axioms plus exactly the named oracles its computation reaches (and nothing else). The transpiler-plumbing axioms that once sat in FunsExternal.lean were discharged (de-plumbing rounds 1+2) before any certificate shipped; the audit fails the button if anything outside a certificate's expected boundary — plumbing, an extra oracle, or a dropped one — appears in its cone.

Discipline

Every Lean compile in this repository runs under verification/lean-guard (memory-capped, machine-wide serialized). Extraction is reproducible: the full pin set (source commit, Charon/Aeneas commits + toolchain channel, Lean and OCaml versions) is in verification/PROVENANCE.json; verification/extract.sh refuses to run against a wrong-commit or dirty source tree, and re-running it reproduces the aeneas-generated model byte-identically (verified 2026-07-24). The axiom audit runs inside Lean (verification/Proofs/Audit.lean): exact per-certificate cone equality, fail-closed, adversarially exercised by verification/check-selftest.sh. What cannot be proven is named in TRUSTED-BASE.md, not hidden (H5).