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https://github.com/saymrwulf/fips205-slhdsa-verified.git
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mrwulf
e3f68b2473
Two theorems, split into two files (METHOD-4 discipline — each proof a clean
unit). NB: an early single-file/bare-rfl attempt appeared to "OOM at the clamp",
but that memory pressure was a SYMPTOM of the runaway whnf diagnosed below, not
a real memory need — the fixed proofs compile in seconds at the default caps.
fips205.fors_inner_loop_eq (Proofs/ForsInnerSpec.lean): the extracted inner
Merkle auth-path loop for ONE FORS tree (fors_pk_from_sig_free_loop0_loop0)
equals the explicit auth-path fold — at level j set tree height j+1, test bit j
of THIS tree's leaf index indices[i], hash the current node with auth.tree[j] in
the bit order (even: node||auth[j]; odd: auth[j]||node), halving the tree index.
Structurally the XMSS auth-path loop, but the bit source is indices[i]>>j and the
loop returns the (adrs,node) pair. Cone: kernel-3 + verify_mono.oracle.h.
fips205.fors_outer_loop_eq (Proofs/ForsOuterSpec.lean): the extracted outer
per-tree loop (fors_pk_from_sig_free_loop0) equals the explicit K-tree fold — for
each tree i, compute the leaf with F at tree index (i<<a)+indices[i], run the
inner Merkle loop over the A levels, write the result to root[i]. Consumes the
inner loop as an opaque sub-call. Cone: kernel-3 + verify_mono.oracle.{f,h}
(F per leaf; H transitively through the inner loop).
Fidelity review at authorship (three-way, both loops): extracted bodies (gen
Funs.lean 893-933 inner, 954-985 outer) == Rust verify_mono.rs
fors_pk_from_sig_free (verbatim from upstream fors.rs, hash calls -> oracle) ==
FIPS 205 Algorithm 17, incl. the even/odd sibling order and the (i<<a)+indices[i]
leaf index.
Proof: the branched-Merkle recipe (XMSS) for the inner loop (by_cases on the
index bit, pair-bind matcher made concrete via bind_congr+rintro then full simp);
the HT straight-line recipe for the outer loop, adapted (bind_congr-peeled step
lemma + bind_congr x16 induction, both threading the inner-loop sub-call opaquely). loop_unfold_bind / u32_succ
/ fwd_succ / hnext reused verbatim from ChainSpec.
check.sh: PROOFS += ForsInnerSpec, ForsOuterSpec; CERTS += the two fors certs;
audit imports both; check.sh settings unchanged (400s/4096MB). ForsOuterSpec
compiles in 4.4s / 2.4GB after the fix below. check.sh green over ALL SIX
certificates with the axiom audit. README status -> FIVE certificates.
DIAGNOSIS NOTE (honesty): ForsOuterSpec's fors_outer_step first closed with a
bare `rfl`, which whnf'd the whole 16-bind body INCLUDING the inner-loop `loop`
term and hit a DETERMINISTIC 4M-heartbeat timeout (never actually passed — an
earlier "green" reading was a misread wrapper exit code; the real error was
hidden by check.sh piping per-file output to /dev/null). Fix: peel the 16 binds
with bind_congr so the closing rfl only sees the small loop-tail, and close the
post-pair-rintro tail with a full simp (the pair `let` won't iota via simp only).
This is the HtSpec straight-line recipe adapted for a body that nests a loop.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
193 lines
9.1 KiB
Text
193 lines
9.1 KiB
Text
/- Proofs/ForsOuterSpec.lean — FORS outer per-tree loop (Algorithm 17).
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THEOREM fors_outer_loop_eq: the extracted outer loop
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(fors_pk_from_sig_free_loop0) equals the explicit K-tree fold — for each
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tree i, compute the leaf with F at tree index (i << a) + indices[i], run
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the inner Merkle loop over the A levels, and write the result to root[i].
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Straight-line body (like HtSpec) that consumes the inner loop
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(fors_pk_from_sig_free_loop0_loop0) as an opaque sub-call — its own
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fidelity is fors_inner_loop_eq in ForsInnerSpec. Cone: kernel three +
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verify_mono.oracle.{f, h} (F for each leaf; H reached transitively through
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the referenced inner loop).
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Split from the inner loop (ForsInnerSpec) so each file stays under the
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memory ceiling (METHOD-4 file split). Reuses u32_succ / fwd_succ / hnext /
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loop_unfold_bind from ChainSpec.
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-/
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import Proofs.ChainSpec
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open Aeneas Aeneas.Std Result ControlFlow
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open fips205
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set_option maxHeartbeats 4000000
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namespace fips205
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/-- Outer loop body on a non-empty range, resolved to the successor w. -/
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theorem hbody_fo {A K N : Std.Usize} (sig_fors : types.ForsSig A K N) (pk_seed : Slice Std.U8)
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(a32 : Std.U32) (indices : Array Std.U32 K) (start stop w : Std.U32)
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(adrs : types.Adrs) (root : Array (Array Std.U8 N) K)
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(hd : decide (start.val < stop.val) = true) (hwok : start + 1#u32 = ok w) :
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verify_mono.fors_pk_from_sig_free_loop0.body sig_fors pk_seed a32 indices
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{ start := start, «end» := stop } adrs root
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= (do
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let i1 ← lift (UScalar.cast .Usize start)
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let sk ← Array.index_usize sig_fors.private_key_value i1
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let adrs1 ← helpers.Adrs.set_tree_height adrs 0#u32
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let i2 ← start <<< a32
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let i3 ← lift (UScalar.cast .Usize start)
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let i4 ← Array.index_usize indices i3
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let i5 ← i2 + i4
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let adrs2 ← helpers.Adrs.set_tree_index adrs1 i5
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let s ← lift (Array.to_slice sk)
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let node_0 ← verify_mono.oracle.f N pk_seed adrs2 s
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let i6 ← lift (UScalar.cast .Usize start)
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let a ← Array.index_usize sig_fors.auth i6
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let auth ← types.Auth.Insts.CoreCloneClone.clone a
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let (adrs3, node_01) ←
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verify_mono.fors_pk_from_sig_free_loop0_loop0
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{ start := 0#u32, «end» := a32 } pk_seed adrs2 indices start node_0 auth
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let i7 ← lift (UScalar.cast .Usize start)
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let a1 ← Array.update root i7 node_01
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ok (cont (({ start := w, «end» := stop } : core.ops.range.Range Std.U32), adrs3, a1))) := by
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unfold verify_mono.fors_pk_from_sig_free_loop0.body
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rw [hnext hd hwok]
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simp
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/-- The outer per-tree fold: at tree i, F-leaf then the inner Merkle loop,
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writing root[i]. The inner loop is consumed as an opaque sub-call. -/
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noncomputable def forsOuterFold {A K N : Std.Usize} (sig_fors : types.ForsSig A K N)
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(pk_seed : Slice Std.U8) (a32 : Std.U32) (indices : Array Std.U32 K) :
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types.Adrs → Array (Array Std.U8 N) K → Std.U32 → Nat →
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Result (types.Adrs × Array (Array Std.U8 N) K)
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| adrs, root, _, 0 => ok (adrs, root)
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| adrs, root, i, (s+1) => do
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let i1 ← lift (UScalar.cast .Usize i)
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let sk ← Array.index_usize sig_fors.private_key_value i1
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let adrs1 ← helpers.Adrs.set_tree_height adrs 0#u32
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let i2 ← i <<< a32
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let i3 ← lift (UScalar.cast .Usize i)
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let i4 ← Array.index_usize indices i3
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let i5 ← i2 + i4
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let adrs2 ← helpers.Adrs.set_tree_index adrs1 i5
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let s0 ← lift (Array.to_slice sk)
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let node_0 ← verify_mono.oracle.f N pk_seed adrs2 s0
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let i6 ← lift (UScalar.cast .Usize i)
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let a ← Array.index_usize sig_fors.auth i6
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let auth ← types.Auth.Insts.CoreCloneClone.clone a
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let (adrs3, node_01) ←
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verify_mono.fors_pk_from_sig_free_loop0_loop0
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{ start := 0#u32, «end» := a32 } pk_seed adrs2 indices i node_0 auth
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let i7 ← lift (UScalar.cast .Usize i)
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let a1 ← Array.update root i7 node_01
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let w ← i + 1#u32
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forsOuterFold sig_fors pk_seed a32 indices adrs3 a1 w s
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/-- One outer loop step = one fold step (straight-line body). -/
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theorem fors_outer_step {A K N : Std.Usize} (sig_fors : types.ForsSig A K N) (pk_seed : Slice Std.U8)
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(a32 : Std.U32) (indices : Array Std.U32 K) (start stop : Std.U32)
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(adrs : types.Adrs) (root : Array (Array Std.U8 N) K)
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(hlt : start.val < stop.val) (hb : start.val + 1 < 2 ^ 32) :
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verify_mono.fors_pk_from_sig_free_loop0 { start := start, «end» := stop }
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sig_fors pk_seed a32 adrs indices root
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= (do
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let i1 ← lift (UScalar.cast .Usize start)
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let sk ← Array.index_usize sig_fors.private_key_value i1
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let adrs1 ← helpers.Adrs.set_tree_height adrs 0#u32
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let i2 ← start <<< a32
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let i3 ← lift (UScalar.cast .Usize start)
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let i4 ← Array.index_usize indices i3
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let i5 ← i2 + i4
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let adrs2 ← helpers.Adrs.set_tree_index adrs1 i5
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let s ← lift (Array.to_slice sk)
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let node_0 ← verify_mono.oracle.f N pk_seed adrs2 s
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let i6 ← lift (UScalar.cast .Usize start)
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let a ← Array.index_usize sig_fors.auth i6
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let auth ← types.Auth.Insts.CoreCloneClone.clone a
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let (adrs3, node_01) ←
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verify_mono.fors_pk_from_sig_free_loop0_loop0
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{ start := 0#u32, «end» := a32 } pk_seed adrs2 indices start node_0 auth
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let i7 ← lift (UScalar.cast .Usize start)
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let a1 ← Array.update root i7 node_01
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let w ← start + 1#u32
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verify_mono.fors_pk_from_sig_free_loop0 { start := w, «end» := stop }
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sig_fors pk_seed a32 adrs3 indices a1) := by
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obtain ⟨w, hwok, _⟩ := u32_succ hb
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have hd : decide (start.val < stop.val) = true := by simp [hlt]
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conv_lhs => rw [verify_mono.fors_pk_from_sig_free_loop0, loop_unfold_bind]
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dsimp only
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rw [hbody_fo sig_fors pk_seed a32 indices start stop w adrs root hd hwok]
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simp only [bind_assoc, bind_ok]
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conv_rhs => rw [show (start + 1#u32) = ok w from hwok]
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simp only [bind_tc_ok, bind_ok]
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-- Peel all 16 binds with bind_congr so the closing `rfl` only whnf's the
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-- small loop-tail, not the whole body threading the inner `loop` term
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-- (a bare `rfl` here blows the 4M-heartbeat whnf budget — the HtSpec body had
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-- no nested loop, so its rfl was cheap; the FORS outer body does).
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apply bind_congr; intro i1
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apply bind_congr; intro sk
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apply bind_congr; intro adrs1
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apply bind_congr; intro i2
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apply bind_congr; intro i3
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apply bind_congr; intro i4
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apply bind_congr; intro i5
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apply bind_congr; intro adrs2
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apply bind_congr; intro s0
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apply bind_congr; intro node_0
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apply bind_congr; intro i6
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apply bind_congr; intro a
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apply bind_congr; intro auth
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apply bind_congr; rintro ⟨adrs3, node_01⟩
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-- the pair `let` blocks further bind_congr (won't iota via simp only); the
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-- remaining tail (i7, a1, loop recursion) is small, so a full simp closes it
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-- cheaply — no whnf over the body, so no heartbeat blowup
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simp [bind_assoc, bind_ok, verify_mono.fors_pk_from_sig_free_loop0]
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/-- **Algorithm 17 outer fidelity.** The extracted per-tree loop over
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[start, start+s) equals the explicit K-tree fold. -/
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theorem fors_outer_loop_eq {A K N : Std.Usize} (sig_fors : types.ForsSig A K N)
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(pk_seed : Slice Std.U8) (a32 : Std.U32) (indices : Array Std.U32 K) (s : Nat) :
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∀ (start : Std.U32) (adrs : types.Adrs) (root : Array (Array Std.U8 N) K),
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start.val + s < 2 ^ 32 →
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∀ (stop : Std.U32), stop.val = start.val + s →
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verify_mono.fors_pk_from_sig_free_loop0 { start := start, «end» := stop }
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sig_fors pk_seed a32 adrs indices root
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= forsOuterFold sig_fors pk_seed a32 indices adrs root start s := by
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induction s with
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| zero =>
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intro start adrs root _ stop hstop
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have hse : start = stop := by apply Std.UScalar.eq_of_val_eq; omega
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subst hse
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unfold verify_mono.fors_pk_from_sig_free_loop0 forsOuterFold
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rw [loop.eq_1]
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unfold verify_mono.fors_pk_from_sig_free_loop0.body core.iter.range.IteratorRange.next
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simp [core.cmp.impls.PartialOrdU32.lt]
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| succ k ih =>
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intro start adrs root hb stop hstop
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have hlt : start.val < stop.val := by omega
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have hb1 : start.val + 1 < 2 ^ 32 := by omega
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obtain ⟨w, hwok, hwv⟩ := u32_succ hb1
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rw [fors_outer_step sig_fors pk_seed a32 indices start stop adrs root hlt hb1]
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unfold forsOuterFold
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rw [hwok]
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simp only [bind_tc_ok, bind_ok]
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have hbound : w.val + k < 2 ^ 32 := by omega
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have hstop' : stop.val = w.val + k := by omega
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apply bind_congr; intro i1
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apply bind_congr; intro sk
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apply bind_congr; intro adrs1
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apply bind_congr; intro i2
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apply bind_congr; intro i3
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apply bind_congr; intro i4
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apply bind_congr; intro i5
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apply bind_congr; intro adrs2
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apply bind_congr; intro s0
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apply bind_congr; intro node_0
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apply bind_congr; intro i6
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apply bind_congr; intro a
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apply bind_congr; intro auth
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apply bind_congr; rintro ⟨adrs3, node_01⟩
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apply bind_congr; intro i7
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apply bind_congr; intro a1
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exact ih w adrs3 a1 hbound stop hstop'
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end fips205
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