Migrates the canonical Lattigo-derived Montgomery NTT body from
luxfi/lattice/v7/ring into luxfi/math/ntt/canonical. This is the
ownership inversion LP-107 Phase 3 calls for: the math substrate
now OWNS the canonical body, and luxfi/lattice/ring becomes a thin
shim over it.
ntt/canonical/ — new public package with the canonical body:
* subring.go — SubRing struct + constructors (269 LoC)
* ntt.go — NTT/INTT body, loop-unrolled-by-16 (1320 LoC)
* ntt_simd.go — SIMD AVX2 dispatcher (405 LoC, build-tagged)
* ntt_simd_stub.go — purego dispatcher stub for non-SIMD builds
* modular_reduction.go — Barrett + Montgomery scalars
* factorization.go — prime factorization helpers
* utils.go — primitive root finders, parameter helpers
* vec_ops.go — vectorized polynomial helpers
* weierstrass.go — companion algebraic helpers
ntt/purego.go — REWORK: the pureGoBackend now holds *canonical.SubRing
instead of *lattice/v7/ring.SubRing; the lattice/v7/ring import is
GONE. Cycle-free: GOWORK=off go list -deps github.com/luxfi/math/ntt
shows zero github.com/luxfi/lattice imports.
Total: ~3.7K LoC of canonical body migrated. Public API unchanged
for downstream callers — luxfi/lattice/ring re-exports the same
SubRing.NTT/INTT surface from the new owner location.
Tests: GOWORK=off go test ./... in luxfi/math/.claude/worktrees/lp-107-phase3
ok github.com/luxfi/math/ntt (cached)
ok github.com/luxfi/math/ntt/canonical 0.276s
+ every other package green.
Replicates the codec cross-runtime KAT pattern across the rest of the
math substrate. Each package now ships:
* kat.go — KATEntry/KATBundle aliases pointing at codec.KATEntry/
codec.KATBundle (one schema for the whole substrate).
* cmd/emit_*_kat/main.go — Go-side emitter that produces the
canonical bundle.
* kat_test.go — Go replay test (TestKATBundle_RoundTrip*).
* testdata/*_kat.json — emitted bundle, byte-stable across runs.
modarith/cmd/emit_modarith_kat: ~300 entries
- 100 MontMulMod cross-checked against MulMod
- 100 AddMod across deterministic random pairs
- 100 MontgomeryRoundTrip (ToMontgomery -> FromMontgomery)
- Multiple moduli (PulsarQ, NTT998).
ntt/cmd/emit_ntt_kat: ~50 entries
- input: 256 random uint64 mod PulsarQ
- output: NTT(input) byte-stream + SHA-256 commitment
- Pulsar N=256 ring.
sample/cmd/emit_sample_kat: ~30 entries
- Uniform / Ternary / CenteredBinomial across param sweeps
- Each entry records the seed + first 64 sampled values.
Tests: GOWORK=off go test ./modarith/ ./ntt/ ./sample/ -> all PASS.
C++ replay tests follow in luxcpp/crypto commit on this same branch.
ntt, poly, rns, sample
Eight pure-Go reference packages that own the canonical semantics of
every cryptographic-math primitive Lux protocols share. Backends
(AVX2 / NEON / cgo+C++ / CUDA / Metal / WGSL) plug in behind the
substrate; KATs gate byte-equality across them.
Packages added:
* params/ — ModulusID, NTTParamID, FHEParamID, PulsarParamID,
HashSuiteID, BackendID; KATHeader required-fields
schema. Stable string IDs; renaming is a breaking
change.
* backend/ — Policy enum (PureGo / NativeCPU / GPUPreferred /
GPURequired); Resolve(policy, registered) returns the
BackendID per LP-107's fallback chain. GPURequired
returns ErrUnavailable when no GPU backend is
registered.
* codec/ — Bounded readers (closes lattice issues #2 + #4 DoS
class permanently). Limits + LimitError + Reader.
ReadUint{16,32,64}Slice all reject the 70T-element
attack input before allocating; depth + frame-bytes
caps; iterative (no recursion). Regression test
TestReadUint64Slice_RejectsHugeLength encodes the
original lattice issue #4 input.
* modarith/ — Modulus type with QInv, R2, Barrett constants
(computed via math/big once per modulus). AddMod /
SubMod / MulMod (Div64 reference path). MontMulMod /
ToMontgomery / FromMontgomery cross-checked against
MulMod across 100 random Pulsar-Q pairs.
ReductionMode enum byte-equal to lattice/types.
* ntt/ — Service + Backend interface; pure-Go backend
delegates to lattice/v7/ring.SubRing.NTT/INTT (the
canonical Lattigo-derived Montgomery NTT body — no
re-implementation, just dispatch). Round-trip +
batch + determinism tests on Pulsar N=256.
* poly/ — Add / Sub / ScalarMul / PointwiseMul (NTT-domain) /
negacyclic Mul (NTT round-trip). Composes modarith +
ntt; no lower-level reach.
* rns/ — Basis(Moduli, Name) for FHE RNS chains. Single +
two-prime construction validated; rejects even moduli.
Phase 3 will add basis-extension and modulus-switching.
* sample/ — Uniform (rejection sampling, mask-and-retry); Ternary
(density + sign byte); CenteredBinomial (popcount
difference); DiscreteGaussianRejection (6-sigma cutoff).
All take an io.Reader so callers can KAT-replay.
Architecture invariants enforced in package docs:
- Go is the canonical semantic reference.
- Backend selection MUST NOT alter transcript bytes (consensus
paths default to PolicyPureGo / PolicyNativeCPU).
- No unbounded codec readers anywhere near wire formats.
- No re-implementation: where lattice/v7/ring already owns the
canonical body, we delegate, not fork.
- One ID space; renaming is a breaking change.
Test posture: 8/8 packages green via `GOWORK=off go test ./...`.
Phases 3-7 (queued):
3. lattice consumes math
4. pulsar consumes lattice + math
5. fhe consumes math
6. luxcpp/crypto/math native backend mirror
7. cross-runtime KAT release gate
See SUBSTRATE.md for the full posture and migration plan; full LP at
~/work/lux/lps/LP-107-lux-math-substrate.md.
Hanzo AI