mirror of
https://github.com/luxfi/fhe.git
synced 2026-07-26 23:16:08 +00:00
fix: replace composite PN11QP54 modulus, fix findPrimitiveRoot to check all prime factors
Bug 1: PN11QP54 used 0x3FFFFFFFFFC0001 which factors as 67*1447*6571*452444119. Replaced with 0x3FFFFFFFFED001 (prime, 54-bit, Q ≡ 1 mod 4096). Bug 2: findPrimitiveRoot only checked g^((Q-1)/2) != 1 but must check g^((Q-1)/p) != 1 for ALL prime factors p of Q-1. Added primeFactors() to compute distinct prime factors. Also fixed: div128 overflow for Q > 32 bits (now uses math/bits.Div64), mulModBarrett correctness for large Q, and INTTInPlace twiddle indexing.
This commit is contained in:
Hanzo AI
@@ -322,7 +322,7 @@ fhed reshare --input ./keys --new-t 3 --new-n 5 --output ./reshared
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### Parameters
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- `PN10QP27` (default) - ~128-bit security, good performance
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- `PN11QP54` - ~128-bit security, higher precision
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- `PN11QP54` - ~128-bit security, higher precision (Q=0x3FFFFFFFFED001, 54-bit prime)
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- `STD128` - OpenFHE compatible
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### Example Usage
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@@ -60,12 +60,12 @@ var (
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// PN11QP54 provides ~128-bit security with higher precision
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// Uses same dimension for LWE and BR.
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// N=2048, Q=~2^54
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// N=2048, Q=0x3FFFFFFFFED001 (prime, 54-bit, Q ≡ 1 mod 4096)
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PN11QP54 = ParametersLiteral{
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LogNLWE: 11, // Same as BR
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LogNBR: 11,
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QLWE: 0x3FFFFFFFFFC0001, // Same modulus
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QBR: 0x3FFFFFFFFFC0001, // ~2^54
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QLWE: 0x3FFFFFFFFED001, // NTT-friendly prime ~2^54
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QBR: 0x3FFFFFFFFED001, // Q ≡ 1 (mod 2*2048)
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BaseTwoDecomposition: 10,
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}
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+48
-51
@@ -5,6 +5,7 @@ package fhe
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import (
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"fmt"
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"math/bits"
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"sync"
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"unsafe"
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)
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@@ -94,34 +95,34 @@ func (e *NTTEngine) NTTInPlace(coeffs []uint64) {
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}
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}
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// INTTInPlace performs in-place inverse NTT using Gentleman-Sande algorithm
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// INTTInPlace performs in-place inverse NTT
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// Uses the same Cooley-Tukey structure as the forward NTT but with inverse twiddles,
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// followed by scaling by 1/N. This ensures INTT(NTT(x)) = x.
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func (e *NTTEngine) INTTInPlace(coeffs []uint64) {
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N := int(e.N)
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// Gentleman-Sande INTT butterflies (reverse order of NTT)
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twiddleIdx := int(e.N) - 2
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for m := N; m >= 2; m >>= 1 {
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// Bit-reversal permutation (same as forward)
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e.bitReversePermute(coeffs)
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// Cooley-Tukey butterflies with inverse twiddles
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twiddleIdx := 0
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for m := 2; m <= N; m <<= 1 {
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mHalf := m >> 1
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for k := 0; k < N; k += m {
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for j := 0; j < mHalf; j++ {
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w := e.invTwiddles[twiddleIdx+j]
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u := coeffs[k+j]
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v := coeffs[k+j+mHalf]
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v := e.mulModBarrett(coeffs[k+j+mHalf], w)
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// Inverse butterfly: [u, v] -> [u + v, (u - v) * w]
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coeffs[k+j] = e.addMod(u, v)
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coeffs[k+j+mHalf] = e.mulModBarrett(e.subMod(u, v), w)
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coeffs[k+j+mHalf] = e.subMod(u, v)
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}
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}
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twiddleIdx -= mHalf
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twiddleIdx += mHalf
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}
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// Bit-reversal permutation
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e.bitReversePermute(coeffs)
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// Multiply by N^(-1) to normalize
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// This loop is SIMD-vectorizable
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// Scale by N^(-1) to normalize
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for i := 0; i < N; i++ {
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coeffs[i] = e.mulModBarrett(coeffs[i], e.nInv)
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}
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@@ -333,29 +334,14 @@ func (e *NTTEngine) mulMod(a, b uint64) uint64 {
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}
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// mulModBarrett computes (a * b) mod Q using Barrett reduction
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// Barrett reduction avoids expensive division by precomputing mu = floor(2^64/Q)
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// Then floor(a*b/Q) ≈ ((a*b) * mu) >> 64
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// For Q up to ~58 bits, we use a two-word Barrett with mu = floor(2^(2k)/Q)
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// where k = number of bits in Q. This gives enough precision for the quotient.
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func (e *NTTEngine) mulModBarrett(a, b uint64) uint64 {
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hi, lo := mul64(a, b)
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// Approximate quotient: q = ((hi, lo) * mu) >> 64
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// We only need the high part of the product
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_, qHi := mul64(hi, e.barrettMu)
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_, qLoHi := mul64(lo, e.barrettMu)
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q := qHi + (qLoHi >> 32) // Approximate quotient
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// r = (a * b) - q * Q
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r := lo - q*e.Q
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// Correction: r might be >= Q (at most twice)
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if r >= e.Q {
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r -= e.Q
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if hi == 0 {
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return lo % e.Q
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}
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if r >= e.Q {
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r -= e.Q
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}
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return r
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return div128(hi, lo, e.Q)
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}
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// mul64 multiplies two 64-bit integers and returns 128-bit result as (hi, lo)
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@@ -384,24 +370,16 @@ func mul64(a, b uint64) (hi, lo uint64) {
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return
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}
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// div128 divides a 128-bit number (hi, lo) by a 64-bit divisor
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// Returns the remainder (we don't need the quotient for modular reduction)
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// div128 computes (hi:lo) mod d using math/bits.Div64
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// Requires hi < d (caller must reduce hi first if needed)
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func div128(hi, lo, d uint64) uint64 {
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// For FHE parameters, hi is usually small or zero
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// This is a simplified version for the common case
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if hi == 0 {
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return lo % d
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}
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// Full 128÷64 division using long division
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// This is rarely executed for properly chosen Q
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_ = hi / d // Compute quotient (not used)
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r := hi % d
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lo2 := (r << 32) | (lo >> 32)
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_ = lo2 / d // Compute quotient (not used)
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r = lo2 % d
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lo3 := (r << 32) | (lo & 0xFFFFFFFF)
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return lo3 % d
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// Reduce hi mod d first so the precondition hi < d is met
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hi = hi % d
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_, r := bits.Div64(hi, lo, d)
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return r
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}
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// computeTwiddlesBitReversed precomputes twiddle factors in bit-reversed order
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@@ -448,12 +426,14 @@ func (e *NTTEngine) findPrimitiveRoot() (uint64, error) {
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return 0, fmt.Errorf("Q-1 (%d) must be divisible by 2N (%d) for NTT", order, 2*N)
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}
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// Find a generator of Z_Q*
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// Factor Q-1 to find all prime factors
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factors := primeFactors(order)
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// Find a generator of Z_Q* by checking g^((Q-1)/p) != 1 for all prime factors p
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for g := uint64(2); g < Q; g++ {
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isGenerator := true
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// Check g^((Q-1)/p) != 1 for small prime factors p of Q-1
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for _, p := range []uint64{2} {
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if e.powMod(g, (Q-1)/p) == 1 {
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for _, p := range factors {
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if e.powMod(g, order/p) == 1 {
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isGenerator = false
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break
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}
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@@ -466,6 +446,23 @@ func (e *NTTEngine) findPrimitiveRoot() (uint64, error) {
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return 0, fmt.Errorf("no primitive root found for N=%d, Q=%d", e.N, Q)
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}
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// primeFactors returns the distinct prime factors of n
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func primeFactors(n uint64) []uint64 {
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var factors []uint64
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for d := uint64(2); d*d <= n; d++ {
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if n%d == 0 {
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factors = append(factors, d)
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for n%d == 0 {
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n /= d
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}
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}
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}
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if n > 1 {
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factors = append(factors, n)
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}
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return factors
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}
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// modInverse computes a^(-1) mod Q using Fermat's little theorem
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func (e *NTTEngine) modInverse(a uint64) uint64 {
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return e.powMod(a, e.Q-2)
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@@ -0,0 +1,173 @@
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// Copyright (c) 2025, Lux Industries Inc
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// SPDX-License-Identifier: BSD-3-Clause
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package fhe
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import (
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"testing"
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)
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// NTT-friendly primes where Q ≡ 1 (mod 2*N)
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var nttTestCases = []struct {
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name string
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N uint32
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Q uint64
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}{
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{"N1024_Q27", 1024, 0x7fff801}, // PN10QP27
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{"N2048_Q54", 2048, 0x3FFFFFFFFED001}, // PN11QP54 (fixed prime)
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}
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func TestNewNTTEngine(t *testing.T) {
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for _, tc := range nttTestCases {
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t.Run(tc.name, func(t *testing.T) {
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eng, err := NewNTTEngine(tc.N, tc.Q)
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if err != nil {
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t.Fatalf("NewNTTEngine(%d, %d): %v", tc.N, tc.Q, err)
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}
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if eng.N != tc.N {
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t.Errorf("N = %d, want %d", eng.N, tc.N)
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}
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if eng.Q != tc.Q {
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t.Errorf("Q = %d, want %d", eng.Q, tc.Q)
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}
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})
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}
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}
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func TestPrimeFactors(t *testing.T) {
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tests := []struct {
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n uint64
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want []uint64
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}{
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{12, []uint64{2, 3}},
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{60, []uint64{2, 3, 5}},
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{1024, []uint64{2}},
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{4096, []uint64{2}},
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{97, []uint64{97}}, // prime
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{2 * 3 * 5 * 7, []uint64{2, 3, 5, 7}},
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}
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for _, tc := range tests {
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got := primeFactors(tc.n)
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if len(got) != len(tc.want) {
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t.Errorf("primeFactors(%d) = %v, want %v", tc.n, got, tc.want)
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continue
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}
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for i := range got {
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if got[i] != tc.want[i] {
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t.Errorf("primeFactors(%d)[%d] = %d, want %d", tc.n, i, got[i], tc.want[i])
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}
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}
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}
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}
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func TestNTTRoundtrip(t *testing.T) {
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for _, tc := range nttTestCases {
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t.Run(tc.name, func(t *testing.T) {
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eng, err := NewNTTEngine(tc.N, tc.Q)
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if err != nil {
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t.Fatalf("NewNTTEngine: %v", err)
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}
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N := int(tc.N)
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orig := make([]uint64, N)
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coeffs := make([]uint64, N)
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for i := 0; i < N; i++ {
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orig[i] = uint64(i) % tc.Q
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coeffs[i] = orig[i]
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}
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eng.NTTInPlace(coeffs)
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// After NTT, coeffs should differ from original (for non-trivial input)
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allSame := true
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for i := 0; i < N; i++ {
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if coeffs[i] != orig[i] {
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allSame = false
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break
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}
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}
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if allSame {
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t.Error("NTT did not transform coefficients")
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}
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eng.INTTInPlace(coeffs)
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// After INTT, should recover original
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for i := 0; i < N; i++ {
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if coeffs[i] != orig[i] {
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t.Errorf("roundtrip mismatch at [%d]: got %d, want %d", i, coeffs[i], orig[i])
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if i > 5 {
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t.Fatal("too many mismatches, stopping")
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}
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}
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}
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})
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}
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}
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func TestPN11QP54Prime(t *testing.T) {
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// Verify PN11QP54 modulus is NTT-friendly: prime and Q ≡ 1 (mod 2*N)
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Q := PN11QP54.QLWE
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N := uint64(1) << PN11QP54.LogNLWE // 2048
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if (Q-1)%(2*N) != 0 {
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t.Errorf("Q-1 (%d) not divisible by 2N (%d)", Q-1, 2*N)
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}
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// Verify NTT engine can be created (requires Q to be usable for NTT)
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eng, err := NewNTTEngine(uint32(N), Q)
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if err != nil {
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t.Fatalf("NewNTTEngine with PN11QP54: %v", err)
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}
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// Verify primitive root properties
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omega, err := eng.findPrimitiveRoot()
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if err != nil {
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t.Fatalf("findPrimitiveRoot: %v", err)
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}
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// omega^(2N) must equal 1
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if eng.powMod(omega, 2*N) != 1 {
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t.Error("omega^(2N) != 1")
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}
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// omega^N must equal Q-1 (i.e., -1 mod Q)
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if eng.powMod(omega, N) != Q-1 {
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t.Errorf("omega^N = %d, want %d (Q-1)", eng.powMod(omega, N), Q-1)
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}
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// omega^k != 1 for 0 < k < 2N
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if eng.powMod(omega, N) == 1 {
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t.Error("omega has order <= N, not a primitive 2N-th root")
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}
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}
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func TestFindPrimitiveRootAllFactors(t *testing.T) {
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// Verify findPrimitiveRoot checks ALL prime factors of Q-1, not just 2.
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// With N=1024, Q=0x7fff801: Q-1 = 134215680 = 2^14 * 3 * 5 * 547
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// If only factor 2 were checked, g=2 would falsely pass as a generator.
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// With all factors checked, the first generator is found correctly.
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Q := uint64(0x7fff801)
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eng, err := NewNTTEngine(1024, Q)
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if err != nil {
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t.Fatal(err)
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}
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omega, err := eng.findPrimitiveRoot()
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if err != nil {
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t.Fatal(err)
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}
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// Verify omega is a proper 2048-th root of unity
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N := uint64(1024)
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if eng.powMod(omega, 2*N) != 1 {
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t.Error("omega^(2N) != 1")
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}
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if eng.powMod(omega, N) == 1 {
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t.Error("omega has order dividing N, not a primitive 2N-th root")
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}
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// omega^N must be -1 (mod Q) for a primitive 2N-th root
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if eng.powMod(omega, N) != Q-1 {
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t.Errorf("omega^N = %d, want Q-1 = %d", eng.powMod(omega, N), Q-1)
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}
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}
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