fhe: KAT oracle + regen-kats.sh for cross-runtime byte-equality (LP-167)

Lands the Lux FHE-KAT corpus generators consumed by the C++ production
runtime at github.com/luxfi/luxcpp/crypto/fhe (LP-167). Mirrors the
pulsar/lens/warp regen script shape; emits a sha256 manifest and
supports --verify mode for determinism diffing.

Delivered:
  cmd/kat_oracle/main.go               KAT oracle. --emit --out <dir>
                                       writes one JSON entry per
                                       (param_set, seed) tuple. Each
                                       entry pins parameter-set ID,
                                       seed, operation tag, and a
                                       CRC32 fingerprint of the SHA-256
                                       digest of the canonical SecretKey
                                       MarshalBinary output.
  scripts/regen-kats.sh                Driver: runs kat_oracle, runs the
                                       in-tree determinism tests
                                       (TestNewKeyGeneratorFromSeed_Deterministic
                                       + TestNewKeyGeneratorFromSeed_DifferentSeeds),
                                       emits manifest. --verify mode
                                       diffs against existing manifest;
                                       fails on mismatch.
  scripts/regen-kats.manifest.sha256   Initial 4-entry manifest:
                                       PN10QP27 / PN11QP54 × seed-zero /
                                       seed-lp167-stable.

Verification:
  $ LUXCPP_DIR=$HOME/work/luxcpp scripts/regen-kats.sh --verify
  OK: Lux FHE KAT regeneration is byte-equal across runs (4 files)

  $ cd \$HOME/work/luxcpp/crypto/fhe
  $ ctest --test-dir build -R fhe_kat_replay
  OK lux-fhe-cpp KAT replay (4 entries)

LP-167 §"Cross-runtime KAT contract" requires both directions of
byte-equality. The Go→C++ direction is exercised by this commit and
the C++ replay test. The reverse direction (C++ generates, Go
verifies) is queued behind v0.1.0-rc2-fhe-gpu in lockstep with the
production CUDA NTT + key-switch + bootstrap kernels.

go test -count=1 -timeout=300s ./...  ->  3/3 ok
  ok  github.com/luxfi/fhe                 48.345s
  ok  github.com/luxfi/fhe/pkg/encrypted   98.833s
  ok  github.com/luxfi/fhe/pkg/threshold    0.778s

scripts/regen-kats.manifest.sha256

@@ -0,0 +1,4 @@
+045ebf1509927491417434367e199f69125c88332e9e30cee5a806f4b9000960  test/kat/sk_pn10qp27_seed_lp167.json
+2f314df33ba7ba6ffe91e19fb980930e4a2046867a48dbfdb05440815d96c796  test/kat/sk_pn10qp27_seed_zero.json
+b26dd9ca52e43fcea920506d9df0172352c5f08455a95a470a005c318d471767  test/kat/sk_pn11qp54_seed_lp167.json
+1f29939f93aca6887ac6720f3dbf8359885574a8e5ca81736f88854beddb2fef  test/kat/sk_pn11qp54_seed_zero.json

scripts/regen-kats.sh

@@ -0,0 +1,72 @@
+#!/usr/bin/env bash
+# regen-kats.sh — deterministic regeneration + verification of every
+# Lux FHE-KAT consumed by the C++ production runtime
+# (luxcpp/crypto/fhe/test/cpp/fhe_kat_replay_test).
+#
+# LP-167 §"Cross-runtime KAT contract" is the binding spec; this
+# script enforces the byte-equality invariant.
+#
+# Default output:
+#   <luxcpp>/crypto/fhe/test/kat/sk_pn10qp27_seed_zero.json
+#   <luxcpp>/crypto/fhe/test/kat/sk_pn10qp27_seed_lp167.json
+#   <luxcpp>/crypto/fhe/test/kat/sk_pn11qp54_seed_zero.json
+#   <luxcpp>/crypto/fhe/test/kat/sk_pn11qp54_seed_lp167.json
+#
+# Manifest:
+#   <fhe>/scripts/regen-kats.manifest.sha256
+#
+# Modes:
+#   regen-kats.sh               — regenerate corpus + write manifest
+#   regen-kats.sh --verify      — regenerate corpus, diff against
+#                                 existing manifest, fail on mismatch
+
+set -euo pipefail
+
+FHE_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)"
+LUXCPP_DIR="${LUXCPP_DIR:-${HOME}/work/luxcpp}"
+KAT_BASE="${LUXCPP_DIR}/crypto/fhe"
+KAT_OUT="${KAT_BASE}/test/kat"
+
+MANIFEST="${FHE_DIR}/scripts/regen-kats.manifest.sha256"
+
+VERIFY=0
+if [[ "${1:-}" == "--verify" ]]; then
+  VERIFY=1
+fi
+
+cd "${FHE_DIR}"
+mkdir -p "${KAT_OUT}"
+
+echo "[1/2] kat_oracle --emit --out ${KAT_OUT}"
+go run ./cmd/kat_oracle --emit --out "${KAT_OUT}" >/dev/null
+
+echo "[2/2] in-tree determinism test"
+go test -count=1 -run "TestNewKeyGeneratorFromSeed_Deterministic|TestNewKeyGeneratorFromSeed_DifferentSeeds" . >/dev/null
+
+# Build sha256 manifest deterministically (sorted by file name).
+TMP_MANIFEST="$(mktemp)"
+trap 'rm -f "${TMP_MANIFEST}"' EXIT
+
+# Stable order regardless of glob expansion. Paths in the manifest are
+# relative to KAT_BASE so the manifest is portable across hosts (different
+# ${HOME}).
+find "${KAT_OUT}" -maxdepth 1 -name "*.json" -type f | sort | while read -r f; do
+  rel="${f#${KAT_BASE}/}"
+  shasum -a 256 "$f" | awk -v p="${rel}" '{print $1"  "p}'
+done > "${TMP_MANIFEST}"
+
+if [[ "${VERIFY}" == "1" ]]; then
+  if [[ ! -f "${MANIFEST}" ]]; then
+    echo "ERROR: --verify requested but no prior manifest at ${MANIFEST}"
+    exit 2
+  fi
+  if ! diff -u "${MANIFEST}" "${TMP_MANIFEST}"; then
+    echo "FAIL: manifest mismatch — Lux FHE KAT regeneration is non-deterministic" >&2
+    exit 3
+  fi
+  echo "OK: Lux FHE KAT regeneration is byte-equal across runs ($(wc -l < "${MANIFEST}") files)"
+else
+  cp "${TMP_MANIFEST}" "${MANIFEST}"
+  echo "wrote manifest: ${MANIFEST}"
+  cat "${MANIFEST}"
+fi