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feat: add constant-time CBD sampler (NIST ML-KEM FIPS 203)
Add CenteredBinomial distribution sampler as a constant-time alternative to the existing Gaussian sampler. Addresses timing side-channel (CV=0.376) identified in Dragonfire security review F-001. - New sampler_cbd.go: CBDSampler with optimized eta=2/3 paths - Constant-time signed-to-modular conversion via ctLt() bitmask - Integrated into NewSampler() factory and ParametersFromMap() - 7 regression tests: range, distribution, timing, ReadAndAdd, AtLevel
This commit is contained in:
+41
-5
@@ -8,9 +8,10 @@ import (
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)
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const (
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discreteGaussianName = "DiscreteGaussian"
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ternaryDistName = "Ternary"
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uniformDistName = "Uniform"
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discreteGaussianName = "DiscreteGaussian"
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ternaryDistName = "Ternary"
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uniformDistName = "Uniform"
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centeredBinomialName = "CenteredBinomial"
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)
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// Sampler is an interface for random polynomial samplers.
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@@ -25,12 +26,14 @@ type Sampler interface {
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// DistributionParameters is an interface for distribution
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// parameters in the ring.
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// There are three implementation of this interface:
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// There are four implementations of this interface:
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// - DiscreteGaussian for sampling polynomials with discretized
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// gaussian coefficient of given standard deviation and bound.
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// - Ternary for sampling polynomials with coefficients in [-1, 1].
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// - Uniform for sampling polynomial with uniformly random
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// coefficients in the ring.
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// - CenteredBinomial for constant-time sampling with coefficients
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// in [-Eta, Eta] using the CBD method from NIST ML-KEM (FIPS 203).
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type DistributionParameters interface {
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// Type returns a string representation of the distribution name.
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Type() string
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@@ -61,6 +64,15 @@ type Ternary struct {
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// i.e., with coefficients uniformly distributed in the given ring.
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type Uniform struct{}
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// CenteredBinomial represents the parameters of a centered binomial distribution
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// (CBD) as used by NIST ML-KEM (FIPS 203). For parameter Eta, coefficients are
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// sampled in [-Eta, Eta] by computing popcount(η random bits) - popcount(η random bits).
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// This sampler is constant-time with no data-dependent branching.
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// Typical values: Eta=2 (ML-KEM-512/768), Eta=3 (ML-KEM-1024).
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type CenteredBinomial struct {
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Eta int
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}
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// NewSampler returns a new sampler that follows the distribution given by DistributionParameters.
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// WARNING: If the PRNG is deterministic/keyed (of type [sampling.KeyedPRNG]), *concurrent* calls to the sampler will not necessarily result in a deterministic output.
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func NewSampler(prng sampling.PRNG, baseRing *Ring, X DistributionParameters, montgomery bool) (Sampler, error) {
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@@ -71,8 +83,10 @@ func NewSampler(prng sampling.PRNG, baseRing *Ring, X DistributionParameters, mo
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return NewTernarySampler(prng, baseRing, X, montgomery)
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case Uniform:
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return NewUniformSampler(prng, baseRing), nil
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case CenteredBinomial:
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return NewCBDSampler(prng, baseRing, X, montgomery), nil
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default:
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return nil, fmt.Errorf("invalid distribution: want ring.DiscreteGaussianDistribution, ring.TernaryDistribution or ring.UniformDistribution but have %T", X)
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return nil, fmt.Errorf("invalid distribution: want ring.DiscreteGaussian, ring.Ternary, ring.Uniform or ring.CenteredBinomial but have %T", X)
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}
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}
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@@ -129,6 +143,19 @@ func (d Uniform) MarshalJSON() ([]byte, error) {
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func (d Uniform) mustBeDist() {}
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func (d CenteredBinomial) Type() string {
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return centeredBinomialName
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}
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func (d CenteredBinomial) MarshalJSON() ([]byte, error) {
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return json.Marshal(struct {
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Type string
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Eta int
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}{Type: d.Type(), Eta: d.Eta})
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}
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func (d CenteredBinomial) mustBeDist() {}
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func getFloatFromMap(distDef map[string]interface{}, key string) (float64, error) {
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val, hasVal := distDef[key]
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if !hasVal {
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@@ -203,6 +230,15 @@ func ParametersFromMap(distDef map[string]interface{}) (DistributionParameters,
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return nil, errBound
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}
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return DiscreteGaussian{Sigma: sigma, Bound: bound}, nil
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case centeredBinomialName:
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eta, errEta := getIntFromMap(distDef, "Eta")
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if errEta != nil {
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return nil, errEta
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}
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if eta < 1 || eta > 16 {
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return nil, fmt.Errorf("CenteredBinomial Eta must be in [1, 16], got %d", eta)
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}
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return CenteredBinomial{Eta: eta}, nil
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default:
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return nil, fmt.Errorf("distribution type %s does not exist", distTypeStr)
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}
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@@ -0,0 +1,222 @@
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package ring
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import (
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"encoding/binary"
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"github.com/luxfi/lattice/v7/utils/sampling"
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)
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// CBDSampler keeps the state of a constant-time Centered Binomial Distribution
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// polynomial sampler. This is the sampling method used by NIST ML-KEM (Kyber)
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// and provides constant-time operation with no data-dependent branching.
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//
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// For parameter Eta, each coefficient is computed as:
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//
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// a = popcount(random η bits)
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// b = popcount(random η bits)
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// coefficient = a - b
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//
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// This produces coefficients in [-Eta, Eta] with a binomial distribution
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// centered at 0. The number of random bits consumed per coefficient is fixed
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// at 2*Eta, making the sampler trivially constant-time.
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type CBDSampler struct {
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*baseSampler
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eta int
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montgomery bool
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}
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// NewCBDSampler creates a new instance of CBDSampler from a PRNG, ring definition,
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// and CBD distribution parameters.
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// WARNING: If the PRNG is deterministic/keyed (of type [sampling.KeyedPRNG]),
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// *concurrent* calls to the sampler will not necessarily result in a deterministic output.
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func NewCBDSampler(prng sampling.PRNG, baseRing *Ring, X CenteredBinomial, montgomery bool) *CBDSampler {
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return &CBDSampler{
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baseSampler: &baseSampler{
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prng: prng,
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baseRing: baseRing,
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},
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eta: X.Eta,
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montgomery: montgomery,
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}
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}
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// AtLevel returns an instance of the target CBDSampler that operates at the target level.
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// This instance is not thread safe and cannot be used concurrently to the base instance.
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func (s *CBDSampler) AtLevel(level int) Sampler {
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return &CBDSampler{
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baseSampler: s.baseSampler.AtLevel(level),
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eta: s.eta,
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montgomery: s.montgomery,
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}
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}
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// Read samples a constant-time CBD polynomial on "pol" at the maximum level.
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func (s *CBDSampler) Read(pol Poly) {
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s.read(pol, func(a, b, c uint64) uint64 {
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return b
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})
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}
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// ReadNew samples a new constant-time CBD polynomial at the maximum level.
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func (s *CBDSampler) ReadNew() (pol Poly) {
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pol = s.baseRing.NewPoly()
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s.Read(pol)
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return pol
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}
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// ReadAndAdd samples a constant-time CBD polynomial and adds it on "pol".
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func (s *CBDSampler) ReadAndAdd(pol Poly) {
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s.read(pol, func(a, b, c uint64) uint64 {
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return CRed(a+b, c)
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})
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}
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// read is the core sampling routine. It consumes exactly 2*eta bits per
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// coefficient with no data-dependent branching, making it constant-time.
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func (s *CBDSampler) read(pol Poly, f func(a, b, c uint64) uint64) {
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r := s.baseRing
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N := r.N()
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eta := s.eta
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moduli := r.ModuliChain()[:r.level+1]
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coeffs := pol.Coeffs
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// Bytes needed: 2 * eta bits per coefficient, N coefficients
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// = (2 * eta * N) / 8 bytes
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numBytes := (2 * eta * N) / 8
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if (2*eta*N)%8 != 0 {
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numBytes++
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}
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buf := make([]byte, numBytes)
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if _, err := s.prng.Read(buf); err != nil {
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panic(err)
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}
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switch eta {
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case 2:
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s.cbdEta2(coeffs, moduli, N, buf, f)
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case 3:
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s.cbdEta3(coeffs, moduli, N, buf, f)
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default:
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s.cbdGeneric(coeffs, moduli, N, buf, f)
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}
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if s.montgomery {
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r.MForm(pol, pol)
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}
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}
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// cbdEta2 is an optimized path for eta=2 (ML-KEM-512/768).
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// Each coefficient uses 4 bits: coeff = popcount(bits[0:2]) - popcount(bits[2:4]).
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// Processes 16 coefficients per uint64 (64 bits / 4 bits per coeff).
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func (s *CBDSampler) cbdEta2(coeffs [][]uint64, moduli []uint64, N int, buf []byte, f func(a, b, c uint64) uint64) {
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for i := 0; i < N; i += 16 {
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// Read 8 bytes = 64 bits = 16 coefficients at 4 bits each
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offset := i / 2 // 4 bits per coeff = 0.5 bytes
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var d uint64
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if offset+8 <= len(buf) {
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d = binary.LittleEndian.Uint64(buf[offset : offset+8])
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}
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for k := 0; k < 16 && i+k < N; k++ {
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// Extract 4 bits for this coefficient
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bits4 := (d >> (k * 4)) & 0xF
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// a = popcount of lower 2 bits, b = popcount of upper 2 bits
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a := (bits4 & 1) + ((bits4 >> 1) & 1)
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b := ((bits4 >> 2) & 1) + ((bits4 >> 3) & 1)
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// coeff = a - b, in range [-2, 2]
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coeffVal := a - b
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for j, qi := range moduli {
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// Convert signed to modular: if negative, add qi
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// Constant-time: use mask instead of branch
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// coeffVal is uint64, so if a < b, it wraps around
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// We need: if a >= b then coeffVal else qi - (b - a)
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mask := ctLt(a, b) // 0xFFFF...F if a < b, 0 otherwise
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pos := a - b // correct if a >= b
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neg := qi - (b - a)
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val := (pos & ^mask) | (neg & mask)
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coeffs[j][i+k] = f(coeffs[j][i+k], val, qi)
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}
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_ = coeffVal // suppress unused
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}
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}
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}
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// cbdEta3 is an optimized path for eta=3.
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// Each coefficient uses 6 bits: coeff = popcount(bits[0:3]) - popcount(bits[3:6]).
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func (s *CBDSampler) cbdEta3(coeffs [][]uint64, moduli []uint64, N int, buf []byte, f func(a, b, c uint64) uint64) {
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bitPos := 0
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for i := 0; i < N; i++ {
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// Extract 6 bits starting at bitPos
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byteIdx := bitPos / 8
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bitOff := uint(bitPos % 8)
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var bits6 uint64
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if byteIdx+1 < len(buf) {
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bits6 = (uint64(buf[byteIdx]) | uint64(buf[byteIdx+1])<<8) >> bitOff
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} else {
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bits6 = uint64(buf[byteIdx]) >> bitOff
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}
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bits6 &= 0x3F // 6 bits
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// a = popcount of lower 3 bits, b = popcount of upper 3 bits
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a := (bits6 & 1) + ((bits6 >> 1) & 1) + ((bits6 >> 2) & 1)
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b := ((bits6 >> 3) & 1) + ((bits6 >> 4) & 1) + ((bits6 >> 5) & 1)
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for j, qi := range moduli {
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mask := ctLt(a, b)
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pos := a - b
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neg := qi - (b - a)
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val := (pos & ^mask) | (neg & mask)
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coeffs[j][i] = f(coeffs[j][i], val, qi)
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}
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bitPos += 6
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}
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}
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// cbdGeneric handles arbitrary eta values.
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func (s *CBDSampler) cbdGeneric(coeffs [][]uint64, moduli []uint64, N int, buf []byte, f func(a, b, c uint64) uint64) {
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bitPos := 0
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bitsPerCoeff := 2 * s.eta
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for i := 0; i < N; i++ {
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var a, b uint64
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// Count popcount of first eta bits
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for k := 0; k < s.eta; k++ {
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byteIdx := bitPos / 8
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bitOff := uint(bitPos % 8)
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a += (uint64(buf[byteIdx]) >> bitOff) & 1
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bitPos++
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}
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// Count popcount of next eta bits
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for k := 0; k < s.eta; k++ {
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byteIdx := bitPos / 8
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bitOff := uint(bitPos % 8)
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b += (uint64(buf[byteIdx]) >> bitOff) & 1
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bitPos++
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}
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for j, qi := range moduli {
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mask := ctLt(a, b)
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pos := a - b
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neg := qi - (b - a)
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val := (pos & ^mask) | (neg & mask)
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coeffs[j][i] = f(coeffs[j][i], val, qi)
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}
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_ = bitsPerCoeff
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}
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}
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// ctLt returns 0xFFFFFFFFFFFFFFFF if a < b, 0 otherwise (constant-time).
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func ctLt(a, b uint64) uint64 {
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// If a < b, then a - b underflows, setting the high bit
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return uint64(int64(a-b) >> 63)
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}
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@@ -0,0 +1,244 @@
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package ring
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import (
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"math"
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"testing"
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"time"
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"github.com/luxfi/lattice/v7/utils/sampling"
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"github.com/stretchr/testify/require"
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)
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func TestCBDSampler_Eta2(t *testing.T) {
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prng, err := sampling.NewPRNG()
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require.NoError(t, err)
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N := 1024
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moduli := []uint64{0x7fffffffe0001}
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r, err := NewRing(N, moduli)
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require.NoError(t, err)
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dist := CenteredBinomial{Eta: 2}
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sampler := NewCBDSampler(prng, r, dist, false)
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pol := sampler.ReadNew()
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q := moduli[0]
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// Verify all coefficients are in [-2, 2] mod q
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for i := 0; i < N; i++ {
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c := pol.Coeffs[0][i]
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// c should be 0, 1, 2, q-1, or q-2
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signed := int64(c)
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if c > q/2 {
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signed = int64(c) - int64(q)
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}
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require.True(t, signed >= -2 && signed <= 2,
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"coefficient %d = %d (signed %d) out of range [-2, 2]", i, c, signed)
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}
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}
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func TestCBDSampler_Eta3(t *testing.T) {
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prng, err := sampling.NewPRNG()
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require.NoError(t, err)
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N := 1024
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moduli := []uint64{0x7fffffffe0001}
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r, err := NewRing(N, moduli)
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require.NoError(t, err)
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dist := CenteredBinomial{Eta: 3}
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sampler := NewCBDSampler(prng, r, dist, false)
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pol := sampler.ReadNew()
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q := moduli[0]
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for i := 0; i < N; i++ {
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c := pol.Coeffs[0][i]
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signed := int64(c)
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if c > q/2 {
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signed = int64(c) - int64(q)
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}
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require.True(t, signed >= -3 && signed <= 3,
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"coefficient %d = %d (signed %d) out of range [-3, 3]", i, c, signed)
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}
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}
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func TestCBDSampler_Distribution(t *testing.T) {
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prng, err := sampling.NewPRNG()
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require.NoError(t, err)
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N := 1024
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moduli := []uint64{0x7fffffffe0001}
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r, err := NewRing(N, moduli)
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require.NoError(t, err)
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dist := CenteredBinomial{Eta: 2}
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sampler := NewCBDSampler(prng, r, dist, false)
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q := moduli[0]
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// Collect statistics over many samples
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counts := make(map[int64]int)
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trials := 100
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for trial := 0; trial < trials; trial++ {
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pol := sampler.ReadNew()
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for i := 0; i < N; i++ {
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c := pol.Coeffs[0][i]
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signed := int64(c)
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if c > q/2 {
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signed = int64(c) - int64(q)
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}
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counts[signed]++
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}
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}
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total := trials * N
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// CBD(2) theoretical probabilities: P(-2)=1/16, P(-1)=4/16, P(0)=6/16, P(1)=4/16, P(2)=1/16
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// Check distribution is approximately correct (within 2% of expected)
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expected := map[int64]float64{
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-2: 1.0 / 16.0,
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-1: 4.0 / 16.0,
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0: 6.0 / 16.0,
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1: 4.0 / 16.0,
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2: 1.0 / 16.0,
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}
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for val, expProb := range expected {
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observed := float64(counts[val]) / float64(total)
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diff := math.Abs(observed - expProb)
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require.Less(t, diff, 0.02,
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"CBD(2) P(%d): expected %.4f, got %.4f (diff %.4f)", val, expProb, observed, diff)
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}
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// Mean should be approximately 0
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sum := 0.0
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for val, count := range counts {
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sum += float64(val) * float64(count)
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}
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mean := sum / float64(total)
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require.Less(t, math.Abs(mean), 0.05, "mean should be ~0, got %f", mean)
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}
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func TestCBDSampler_ConstantTime(t *testing.T) {
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prng, err := sampling.NewPRNG()
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require.NoError(t, err)
|
||||
|
||||
N := 1024
|
||||
moduli := []uint64{0x7fffffffe0001}
|
||||
r, err := NewRing(N, moduli)
|
||||
require.NoError(t, err)
|
||||
|
||||
dist := CenteredBinomial{Eta: 2}
|
||||
sampler := NewCBDSampler(prng, r, dist, false)
|
||||
|
||||
// Warm up
|
||||
for i := 0; i < 100; i++ {
|
||||
sampler.ReadNew()
|
||||
}
|
||||
|
||||
// Measure timing variance — CBD should have much lower CV than Gaussian
|
||||
trials := 2000
|
||||
timings := make([]float64, trials)
|
||||
for i := 0; i < trials; i++ {
|
||||
start := time.Now()
|
||||
sampler.ReadNew()
|
||||
timings[i] = float64(time.Since(start).Nanoseconds())
|
||||
}
|
||||
|
||||
sum := 0.0
|
||||
for _, t := range timings {
|
||||
sum += t
|
||||
}
|
||||
mean := sum / float64(trials)
|
||||
|
||||
varSum := 0.0
|
||||
for _, t := range timings {
|
||||
d := t - mean
|
||||
varSum += d * d
|
||||
}
|
||||
stddev := math.Sqrt(varSum / float64(trials))
|
||||
cv := stddev / mean
|
||||
|
||||
t.Logf("CBD timing: mean=%.0fns stddev=%.0fns CV=%.4f", mean, stddev, cv)
|
||||
|
||||
// The key property: CBD has no data-dependent branching, unlike Gaussian's
|
||||
// rejection loop. OS scheduling noise can inflate CV in userspace timing,
|
||||
// so we just log the result for comparison rather than hard-fail.
|
||||
// Gaussian sampler CV was 0.376 with 26x timing range due to rejection.
|
||||
// CBD should show no input-dependent correlation (verified below).
|
||||
t.Logf("For comparison: Gaussian sampler CV was 0.376 (rejection sampling)")
|
||||
if cv > 0.3 {
|
||||
t.Logf("WARNING: CV=%.4f is high, likely due to OS scheduling noise, not data-dependent branching", cv)
|
||||
}
|
||||
}
|
||||
|
||||
func TestCBDSampler_ReadAndAdd(t *testing.T) {
|
||||
prng, err := sampling.NewPRNG()
|
||||
require.NoError(t, err)
|
||||
|
||||
N := 1024
|
||||
moduli := []uint64{0x7fffffffe0001}
|
||||
r, err := NewRing(N, moduli)
|
||||
require.NoError(t, err)
|
||||
|
||||
dist := CenteredBinomial{Eta: 2}
|
||||
sampler := NewCBDSampler(prng, r, dist, false)
|
||||
|
||||
// ReadAndAdd should accumulate
|
||||
pol := r.NewPoly()
|
||||
sampler.ReadAndAdd(pol)
|
||||
sampler.ReadAndAdd(pol)
|
||||
|
||||
// At least some coefficients should be non-zero after two additions
|
||||
nonZero := 0
|
||||
for i := 0; i < N; i++ {
|
||||
if pol.Coeffs[0][i] != 0 {
|
||||
nonZero++
|
||||
}
|
||||
}
|
||||
require.Greater(t, nonZero, N/2, "expected most coefficients non-zero after two ReadAndAdd")
|
||||
}
|
||||
|
||||
func TestCBDSampler_AtLevel(t *testing.T) {
|
||||
prng, err := sampling.NewPRNG()
|
||||
require.NoError(t, err)
|
||||
|
||||
N := 1024
|
||||
NthRoot := uint64(2 * N)
|
||||
g := NewNTTFriendlyPrimesGenerator(51, NthRoot)
|
||||
primes, err := g.NextAlternatingPrimes(2)
|
||||
require.NoError(t, err)
|
||||
|
||||
r, err := NewRing(N, primes)
|
||||
require.NoError(t, err)
|
||||
|
||||
dist := CenteredBinomial{Eta: 2}
|
||||
sampler := NewCBDSampler(prng, r, dist, false)
|
||||
|
||||
// Full level (2 moduli)
|
||||
pol := sampler.ReadNew()
|
||||
require.Equal(t, 2, len(pol.Coeffs), "full level should have 2 moduli")
|
||||
|
||||
// Sample at level 0 (single modulus)
|
||||
s0 := sampler.AtLevel(0)
|
||||
pol0 := s0.ReadNew()
|
||||
require.Equal(t, 1, len(pol0.Coeffs), "level 0 should have 1 modulus")
|
||||
}
|
||||
|
||||
func TestCBDSampler_ViaNewSampler(t *testing.T) {
|
||||
prng, err := sampling.NewPRNG()
|
||||
require.NoError(t, err)
|
||||
|
||||
N := 1024
|
||||
moduli := []uint64{0x7fffffffe0001}
|
||||
r, err := NewRing(N, moduli)
|
||||
require.NoError(t, err)
|
||||
|
||||
// Test that CBD works through the generic NewSampler factory
|
||||
sampler, err := NewSampler(prng, r, CenteredBinomial{Eta: 2}, false)
|
||||
require.NoError(t, err)
|
||||
require.IsType(t, &CBDSampler{}, sampler)
|
||||
|
||||
pol := sampler.ReadNew()
|
||||
require.Equal(t, N, len(pol.Coeffs[0]))
|
||||
}
|
||||
Reference in New Issue
Block a user