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mrwulf
d6e4d938de
drafts/ChainSpec.lean (NOT in Proofs/, NOT in check.sh — carries a
sorry, so nothing is claimed proven; H1/H2 hold):
- chainFoldN: the mathematical s-fold of the opaque hash F, threading
the hash-address (i, i+1, …, i+s-1) and index exactly as the extracted
loop body does. Equational spec (chain_free_loop = chainFoldN) — chosen
over a WP triple so it needs no assumption that the opaque oracle.f
succeeds (both sides fail together if it does).
- chain_free_loop_eq: induction on the step count via loop.eq_1.
BASE CASE PROVEN (empty range start..start reduces to ok tmp,
PartialOrdU32.lt start start = false). Step case is the one open
front: align the loop's monadic forward_checked with the fold's
start+1 (u32 add-spec from the no-overflow bound) and fold the loop
continuation back for the IH — the dalek loop-spec pattern, tractable.
De-plumbing (prior commit bde63f5) means this cone will carry only the
kernel three + oracle.f once closed. First real certificate incoming.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
67 lines
3 KiB
Text
67 lines
3 KiB
Text
/- drafts/ChainSpec.lean — WIP: Algorithm 5 (chain) fidelity.
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Goal: the extracted `chain_free` loop equals the explicit s-fold
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application of the (opaque) hash F, with hash-address set to
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i, i+1, …, i+s−1 in turn. Proving this rules out off-by-one loop
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bounds, a wrong address field, and wrong threading — the exact bug
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class the SLH-DSA verify path is exposed to. F stays opaque
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(verify_mono.oracle.f), so the certificate cone is the three kernel
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axioms + oracle.f only.
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-/
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import SlhVerify.Funs
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open Aeneas Aeneas.Std Result ControlFlow
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open fips205
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set_option maxHeartbeats 2000000
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namespace fips205
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/-- The mathematical chaining fold, threading the address exactly as the
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extracted body does: at each step set the hash address to the current
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index, hash, advance the index (monadically, matching the u32 range
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iterator's `forward_checked`). Recursion on the step count. -/
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noncomputable def chainFoldN {N : Std.Usize} (pk_seed : Slice Std.U8) :
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types.Adrs → Array Std.U8 N → Std.U32 → Nat → Result (Array Std.U8 N)
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| _, tmp, _, 0 => ok tmp
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| adrs, tmp, start, (k+1) => do
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let adrs1 ← helpers.Adrs.set_hash_address adrs start
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let s ← lift (Array.to_slice tmp)
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let tmp1 ← verify_mono.oracle.f N pk_seed adrs1 s
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let start1 ← start + 1#u32
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chainFoldN pk_seed adrs1 tmp1 start1 k
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/-- The loop over the range [start, start+s) equals the s-step fold. -/
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theorem chain_free_loop_eq {N : Std.Usize} (pk_seed : Slice Std.U8) (s : Nat) :
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∀ (start : Std.U32) (adrs : types.Adrs) (tmp : Array Std.U8 N),
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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.chain_free_loop { start := start, «end» := stop } pk_seed adrs tmp
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= chainFoldN pk_seed adrs tmp start s := by
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induction s with
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| zero =>
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intro start adrs tmp _ stop hstop
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-- empty range: start.val = stop.val, so start = stop and lt is false
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have hse : start = stop := by
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apply Std.UScalar.eq_of_val_eq; omega
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subst hse
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unfold verify_mono.chain_free_loop chainFoldN
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rw [loop.eq_1]
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unfold verify_mono.chain_free_loop.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 tmp hb stop hstop
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-- non-empty: lt start stop is true, so the iterator yields `some start`
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-- and steps to start+1; one loop step then aligns with one fold step and
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-- the IH closes the tail.
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have hlt : start.val < stop.val := by omega
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unfold verify_mono.chain_free_loop chainFoldN
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rw [loop.eq_1]
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unfold verify_mono.chain_free_loop.body core.iter.range.IteratorRange.next
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-- OPEN FRONT (the crux): align the loop's monadic `forward_checked start 1`
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-- (a `Result U32`) with the fold's `start1 ← start + 1#u32`, then fold the
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-- continuation `loop body (…)` back into `chain_free_loop` and apply `ih`
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-- at start+1 / stop / k. Needs the U32 add-spec (no overflow from `hb`) and
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-- ControlFlow bind-normalisation. Tractable (dalek loop-spec pattern), WIP.
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sorry
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end fips205
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