mirror of
https://github.com/luxfi/math.git
synced 2026-07-27 03:38:49 +00:00
Hanzo AI
e018a9c3d1
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.
54 lines
1.8 KiB
Go
54 lines
1.8 KiB
Go
// Copyright (c) 2026 Lux Industries Inc.
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// SPDX-License-Identifier: BSD-3-Clause
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// Package rns provides the Residue Number System primitives that FHE
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// schemes use to operate over a chain of small primes instead of one
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// large modulus.
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//
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// LP-107 §"Polynomial and RNS operations" — the canonical motivation.
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// FHE PN10QP27 / PN11QP54 ring chains are RNS towers; their basis-
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// extension and modulus-switching primitives live here.
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//
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// Phase 2 (this file): defines the public surface for RNS Basis,
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// Tower, and basis-extension. Concrete bodies delegate to
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// github.com/luxfi/lattice/v7/ringqp; Phase 3 of LP-107 inverts that.
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package rns
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import (
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"fmt"
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"github.com/luxfi/math/modarith"
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)
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// Basis describes one RNS basis: a list of pairwise coprime primes
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// q_0, q_1, ..., q_{k-1}. Numbers are represented as their CRT
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// projections (x mod q_0, x mod q_1, ..., x mod q_{k-1}).
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type Basis struct {
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// Moduli is the tuple of primes. Each entry MUST satisfy
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// gcd(q_i, q_j) = 1 for i != j; we don't re-check this at every
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// op (it's a parameter-set property).
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Moduli []*modarith.Modulus
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// Name is a stable identifier (e.g. "fhe-pn10qp27").
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Name string
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}
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// NewBasis constructs an RNS basis from a list of primes. Returns an
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// error if any modulus fails modarith.NewModulus.
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func NewBasis(primes []uint64, name string) (*Basis, error) {
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if len(primes) == 0 {
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return nil, fmt.Errorf("rns.NewBasis: empty prime list")
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}
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mods := make([]*modarith.Modulus, len(primes))
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for i, q := range primes {
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m, err := modarith.NewModulus(q, fmt.Sprintf("%s.q[%d]", name, i))
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if err != nil {
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return nil, fmt.Errorf("rns.NewBasis: prime[%d]=%d: %w", i, q, err)
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}
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mods[i] = m
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}
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return &Basis{Moduli: mods, Name: name}, nil
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}
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// Levels returns the number of primes in the basis.
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func (b *Basis) Levels() int { return len(b.Moduli) }
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