anza-ed25519-verified/verification/check-scalar.sh
mrwulf 7dc6bdc40d Signature layer, first bricks: canonicity closure + hash-to-scalar foundation
Canonicity pass (the layer is now closed under its own preconditions):
- sub_val_spec post carries the exact value equation
  (exists beta <= 1, scVal r + scVal b = scVal a + ell*beta, with the
  underflow guard beta = 1 -> scVal a < scVal b)
- add/montgomery_reduce/mul/aggregate posts all carry scVal r < ell:
  canonical inputs give canonical outputs everywhere. Needed because
  from_bytes_wide (hash-to-scalar) feeds Montgomery outputs into add.

Hash-to-scalar foundation (toward Scalar::from_hash / EdDSA verify):
- extraction scope + from_bytes_wide (brings constants::R); regenerated gen
- source repos carry a documented Aeneas-compat patch: the bare
  `hi[4] = words[7] >> 20` extracts ill-typed at pin bf13c42e; masked
  (semantic no-op, words[7] >> 20 < 2^44)
- Proofs/ScalarWideSpec.lean: R constant lemmas (R = 2^260 mod ell,
  witness 2^260 = R + 255*ell) and montgomery_mul_spec, the single
  Montgomery round: [r]*2^260 = [a]*[b], canonical bounded output

check-scalar.sh: 10 proof files, 11 kernel audits, all exactly
[propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
2026-07-03 23:18:31 +02:00

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#!/usr/bin/env bash
# Scalar-layer check (Scalar52 arithmetic mod ). Compiles the gen model + the
# proven foundation. add/sub (Range-loop reductions) and the Montgomery mul
# path are in progress — see README. Guarded compiles throughout.
set -uo pipefail
source ~/aeneas-toolchain/env.sh
HERE="$(cd "$(dirname "$0")" && pwd)"
AENEAS_LEAN="$AENEAS_HOME/backends/lean"
GEN=(CurveScalar/TypesExternal CurveScalar/Types CurveScalar/FunsExternal CurveScalar/Funs)
PROOFS=(ScalarDenote ScalarLoop ScalarSubSpec ScalarAddSpec ScalarMulSpec ScalarMontSpec ScalarReduceSpec ScalarFullMulSpec ScalarMain ScalarWideSpec)
echo "=== stub/axiom audit ==="
grep -rnE '^(private |protected |noncomputable )*axiom ' "$HERE"/Proofs/Scalar*.lean 2>/dev/null && { echo "axiom under Proofs/"; exit 1; }
echo " clean"
echo "=== compile (guarded) ==="
cd "$AENEAS_LEAN"
lake env bash -c "
set -uo pipefail
cd '$HERE/gen' && export LEAN_PATH=\"\$LEAN_PATH:\$PWD:$HERE\"
for m in ${GEN[*]}; do echo \" · gen \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=6144 '$HERE/lean-guard' \"\$m.lean\" || exit 1; done
cd '$HERE'
for m in ${PROOFS[*]}; do echo \" · proof \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=4096 '$HERE/lean-guard' \"Proofs/\$m.lean\" || exit 1; done
" || { echo FAIL; exit 1; }
echo "=== Phase 3: axiom audit (kernel-level) ==="
cd "$AENEAS_LEAN"
lake env bash -c "
set -uo pipefail
export LEAN_PATH=\"\$LEAN_PATH:$HERE/gen:$HERE\"
cd '$HERE'
AUD=\$(mktemp '$HERE/.audit-scalar-XXXX.lean')
{ echo 'import Proofs.ScalarMain'; echo 'import Proofs.ScalarWideSpec'; echo '#print axioms ScalarProofs.L_val'
echo '#print axioms ScalarProofs.sub_loop_spec'
echo '#print axioms ScalarProofs.cond_add_l_one_spec'; echo '#print axioms ScalarProofs.sub_val_spec'; echo '#print axioms ScalarProofs.add_val_spec'; echo '#print axioms ScalarProofs.mul_internal_spec'
echo '#print axioms ScalarProofs.part1_spec'; echo '#print axioms ScalarProofs.montgomery_reduce_spec'; echo '#print axioms ScalarProofs.mul_spec'; echo '#print axioms ScalarProofs.scalarImplementation'; echo '#print axioms ScalarProofs.montgomery_mul_spec'; } > \"\$AUD\"
OUT=\$(LEAN_TIMEOUT=120 LEAN_MEM_MB=4096 '$HERE/lean-guard' \"\$AUD\" 2>&1)
echo \"\$OUT\"
rm -f \"\$AUD\" \"\${AUD%.lean}.olean\"
N=\$(echo \"\$OUT\" | grep -cF \"depends on axioms: [propext, Classical.choice, Quot.sound]\" || true)
[ \"\$N\" -eq 11 ] || { echo \"AXIOM AUDIT FAILED: \$N/11 clean\"; exit 1; }
" || { echo FAIL; exit 1; }
echo " L_val axiom-clean"
echo ""
echo "SCALAR LAYER COMPLETE: add, sub, mul (Montgomery reduction, double round through RR) proven mod ; aggregate certificate scalarImplementation kernel-audited."