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encoder.go
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encoder.go
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package ckks
import (
"fmt"
"math"
"math/big"
"github.com/tuneinsight/lattigo/v5/ring"
"github.com/tuneinsight/lattigo/v5/core/rlwe"
"github.com/tuneinsight/lattigo/v5/ring/ringqp"
"github.com/tuneinsight/lattigo/v5/utils"
"github.com/tuneinsight/lattigo/v5/utils/bignum"
)
type Float interface {
float64 | complex128 | *big.Float | *bignum.Complex
}
// FloatSlice is an empty interface whose goal is to
// indicate that the expected input should be []Float.
// See Float for information on the type constraint.
type FloatSlice interface {
}
// GaloisGen is an integer of order N/2 modulo M and that spans Z_M with the integer -1.
// The j-th ring automorphism takes the root zeta to zeta^(5j).
const GaloisGen uint64 = ring.GaloisGen
// Encoder is a type that implements the encoding and decoding interface for the CKKS scheme. It provides methods to encode/decode
// []complex128/[]*bignum.Complex and []float64/[]*big.Float types into/from Plaintext types.
//
// Two different encodings domains are provided:
//
// - Coefficients: The coefficients are directly embedded on the plaintext. This encoding only allows to encode []float64/[]*big.Float slices,
// but of size up to N (N being the ring degree) and does not preserve the point-wise multiplication. A ciphertext multiplication will result
// in a negacyclic polynomial convolution in the plaintext domain. This encoding does not provide native slot cyclic rotation.
// Other operations, like addition or constant multiplication, behave as usual.
//
// - Slots: The coefficients are first subjected to a special Fourier transform before being embedded in the plaintext by using Coeffs encoding.
// This encoding can embed []complex128/[]*bignum.Complex and []float64/[]*big.Float slices of size at most N/2 (N being the ring degree) and
// leverages the convolution property of the DFT to preserve point-wise complex multiplication in the plaintext domain, i.e. a ciphertext
// multiplication will result in an element-wise multiplication in the plaintext domain. It also enables cyclic rotations on plaintext slots.
// Other operations, like constant multiplication, behave as usual. It is considered the default encoding method for CKKS.
//
// The figure bellow illustrates the relationship between these two encodings:
//
// Z_Q[X]/(X^N+1)
// Coefficients: ---------------> Real^{N} ---------> Plaintext
// |
// |
// Slots: Complex^{N/2} -> iDFT -----┘
type Encoder struct {
parameters Parameters
prec uint
bigintCoeffs []*big.Int
qHalf *big.Int
buff ring.Poly
m int
rotGroup []int
roots interface{}
buffCmplx interface{}
}
// NewEncoder creates a new Encoder from the target parameters.
// Optional field `precision` can be given. If precision is empty
// or <= 53, then float64 and complex128 types will be used to
// perform the encoding. Else *big.Float and *bignum.Complex will be used.
func NewEncoder(parameters Parameters, precision ...uint) (ecd *Encoder) {
m := int(parameters.RingQ().NthRoot())
rotGroup := make([]int, m>>2)
fivePows := 1
for i := 0; i < m>>2; i++ {
rotGroup[i] = fivePows
fivePows *= int(GaloisGen)
fivePows &= (m - 1)
}
var prec uint
if len(precision) != 0 && precision[0] != 0 {
prec = precision[0]
} else {
prec = parameters.EncodingPrecision()
}
ecd = &Encoder{
prec: prec,
parameters: parameters,
bigintCoeffs: make([]*big.Int, m>>1),
qHalf: bignum.NewInt(0),
buff: parameters.RingQ().NewPoly(),
m: m,
rotGroup: rotGroup,
}
if prec <= 53 {
ecd.roots = GetRootsComplex128(ecd.m)
ecd.buffCmplx = make([]complex128, ecd.m>>2)
} else {
tmp := make([]*bignum.Complex, ecd.m>>2)
for i := 0; i < ecd.m>>2; i++ {
tmp[i] = &bignum.Complex{bignum.NewFloat(0, prec), bignum.NewFloat(0, prec)}
}
ecd.roots = GetRootsBigComplex(ecd.m, prec)
ecd.buffCmplx = tmp
}
return
}
// Prec returns the precision in bits used by the target Encoder.
// A precision <= 53 will use float64, else *big.Float.
func (ecd Encoder) Prec() uint {
return ecd.prec
}
func (ecd Encoder) GetRLWEParameters() rlwe.Parameters {
return ecd.parameters.Parameters
}
// Encode encodes a FloatSlice on the target plaintext.
// Encoding is done at the level and scale of the plaintext.
// Encoding domain is done according to the metadata of the plaintext.
// User must ensure that 1 <= len(values) <= 2^pt.LogMaxDimensions < 2^logN.
// The imaginary part will be discarded if ringType == ring.ConjugateInvariant.
func (ecd Encoder) Encode(values FloatSlice, pt *rlwe.Plaintext) (err error) {
if pt.IsBatched {
return ecd.Embed(values, pt.MetaData, pt.Value)
} else {
switch values := values.(type) {
case []float64:
if len(values) > ecd.parameters.N() {
return fmt.Errorf("cannot Encode: maximum number of values is %d but len(values) is %d", ecd.parameters.N(), len(values))
}
Float64ToFixedPointCRT(ecd.parameters.RingQ().AtLevel(pt.Level()), values, pt.Scale.Float64(), pt.Value.Coeffs)
case []*big.Float:
if len(values) > ecd.parameters.N() {
return fmt.Errorf("cannot Encode: maximum number of values is %d but len(values) is %d", ecd.parameters.N(), len(values))
}
BigFloatToFixedPointCRT(ecd.parameters.RingQ().AtLevel(pt.Level()), values, &pt.Scale.Value, pt.Value.Coeffs)
default:
return fmt.Errorf("cannot Encode: supported values.(type) for IsBatched=False is []float64 or []*big.Float, but %T was given", values)
}
ecd.parameters.RingQ().AtLevel(pt.Level()).NTT(pt.Value, pt.Value)
}
return
}
// Decode decodes the input plaintext on a new FloatSlice.
func (ecd Encoder) Decode(pt *rlwe.Plaintext, values FloatSlice) (err error) {
return ecd.DecodePublic(pt, values, 0)
}
// DecodePublic decodes the input plaintext on a FloatSlice.
// It adds, before the decoding step (i.e. in the Ring) noise that follows the given distribution parameters.
// If the underlying ringType is ConjugateInvariant, the imaginary part (and its related error) are zero.
func (ecd Encoder) DecodePublic(pt *rlwe.Plaintext, values FloatSlice, logprec float64) (err error) {
return ecd.decodePublic(pt, values, logprec)
}
// Embed is a generic method to encode a FloatSlice on the target polyOut.
// This method it as the core of the slot encoding.
// Values are encoded according to the provided metadata.
// Accepted polyOut.(type) are ringqp.Poly and ring.Poly.
// The imaginary part will be discarded if ringType == ring.ConjugateInvariant.
func (ecd Encoder) Embed(values FloatSlice, metadata *rlwe.MetaData, polyOut interface{}) (err error) {
if ecd.prec <= 53 {
return ecd.embedDouble(values, metadata, polyOut)
}
return ecd.embedArbitrary(values, metadata, polyOut)
}
// embedDouble encode a FloatSlice on polyOut using FFT with complex128 arithmetic.
// Values are encoded according to the provided metadata.
// Accepted polyOut.(type) are ringqp.Poly and ring.Poly.
func (ecd Encoder) embedDouble(values FloatSlice, metadata *rlwe.MetaData, polyOut interface{}) (err error) {
if maxLogCols := ecd.parameters.LogMaxDimensions().Cols; metadata.LogDimensions.Cols < 0 || metadata.LogDimensions.Cols > maxLogCols {
return fmt.Errorf("cannot Embed: logSlots (%d) must be greater or equal to %d and smaller than %d", metadata.LogDimensions.Cols, 0, maxLogCols)
}
slots := 1 << metadata.LogDimensions.Cols
var lenValues int
buffCmplx := ecd.buffCmplx.([]complex128)
switch values := values.(type) {
case []complex128:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
if ecd.parameters.RingType() == ring.ConjugateInvariant {
for i := range values {
buffCmplx[i] = complex(real(values[i]), 0)
}
} else {
copy(buffCmplx[:len(values)], values)
}
case []*bignum.Complex:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
if ecd.parameters.RingType() == ring.ConjugateInvariant {
for i := range values {
if values[i] != nil {
f64, _ := values[i][0].Float64()
buffCmplx[i] = complex(f64, 0)
} else {
buffCmplx[i] = 0
}
}
} else {
for i := range values {
if values[i] != nil {
buffCmplx[i] = values[i].Complex128()
} else {
buffCmplx[i] = 0
}
}
}
case []float64:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
for i := range values {
buffCmplx[i] = complex(values[i], 0)
}
case []*big.Float:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
for i := range values {
if values[i] != nil {
f64, _ := values[i].Float64()
buffCmplx[i] = complex(f64, 0)
} else {
buffCmplx[i] = 0
}
}
default:
return fmt.Errorf("cannot Embed: values.(Type) must be []complex128, []*bignum.Complex, []float64 or []*big.Float, but is %T", values)
}
// Zeroes all other values
for i := lenValues; i < slots; i++ {
buffCmplx[i] = 0
}
// IFFT
if err = ecd.IFFT(buffCmplx[:slots], metadata.LogDimensions.Cols); err != nil {
return
}
// Maps Y = X^{N/n} -> X and quantizes.
switch p := polyOut.(type) {
case ringqp.Poly:
Complex128ToFixedPointCRT(ecd.parameters.RingQ().AtLevel(p.Q.Level()), buffCmplx[:slots], metadata.Scale.Float64(), p.Q.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingQ().AtLevel(p.Q.Level()), metadata, p.Q)
if p.P.Level() > -1 {
Complex128ToFixedPointCRT(ecd.parameters.RingP().AtLevel(p.P.Level()), buffCmplx[:slots], metadata.Scale.Float64(), p.P.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingP().AtLevel(p.P.Level()), metadata, p.P)
}
case ring.Poly:
Complex128ToFixedPointCRT(ecd.parameters.RingQ().AtLevel(p.Level()), buffCmplx[:slots], metadata.Scale.Float64(), p.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingQ().AtLevel(p.Level()), metadata, p)
default:
return fmt.Errorf("cannot Embed: invalid polyOut.(Type) must be ringqp.Poly or ring.Poly")
}
return
}
// embedArbitrary encode a FloatSlice on polyOut using FFT with *bignum.Complex arithmetic.
// Values are encoded according to the provided metadata.
// Accepted polyOut.(type) are ringqp.Poly and ring.Poly.
func (ecd Encoder) embedArbitrary(values FloatSlice, metadata *rlwe.MetaData, polyOut interface{}) (err error) {
if maxLogCols := ecd.parameters.LogMaxDimensions().Cols; metadata.LogDimensions.Cols < 0 || metadata.LogDimensions.Cols > maxLogCols {
return fmt.Errorf("cannot Embed: logSlots (%d) must be greater or equal to %d and smaller than %d", metadata.LogDimensions.Cols, 0, maxLogCols)
}
slots := 1 << metadata.LogDimensions.Cols
var lenValues int
buffCmplx := ecd.buffCmplx.([]*bignum.Complex)
switch values := values.(type) {
case []complex128:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
if ecd.parameters.RingType() == ring.ConjugateInvariant {
for i := range values {
buffCmplx[i][0].SetFloat64(real(values[i]))
buffCmplx[i][1].SetFloat64(0)
}
} else {
for i := range values {
buffCmplx[i][0].SetFloat64(real(values[i]))
buffCmplx[i][1].SetFloat64(imag(values[i]))
}
}
case []*bignum.Complex:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
if ecd.parameters.RingType() == ring.ConjugateInvariant {
for i := range values {
if values[i] != nil {
buffCmplx[i][0].Set(values[i][0])
} else {
buffCmplx[i][0].SetFloat64(0)
}
buffCmplx[i][1].SetFloat64(0)
}
} else {
for i := range values {
if values[i] != nil {
buffCmplx[i].Set(values[i])
} else {
buffCmplx[i][0].SetFloat64(0)
buffCmplx[i][1].SetFloat64(0)
}
}
}
case []float64:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
for i := range values {
buffCmplx[i][0].SetFloat64(values[i])
buffCmplx[i][1].SetFloat64(0)
}
case []*big.Float:
lenValues = len(values)
if maxCols := ecd.parameters.MaxDimensions().Cols; lenValues > maxCols || lenValues > slots {
return fmt.Errorf("cannot Embed: ensure that #values (%d) <= slots (%d) <= maxCols (%d)", len(values), slots, maxCols)
}
for i := range values {
if values[i] != nil {
buffCmplx[i][0].Set(values[i])
} else {
buffCmplx[i][0].SetFloat64(0)
}
buffCmplx[i][1].SetFloat64(0)
}
default:
return fmt.Errorf("cannot Embed: values.(Type) must be []complex128, []*bignum.Complex, []float64 or []*big.Float, but is %T", values)
}
// Zeroes all other values
for i := lenValues; i < slots; i++ {
buffCmplx[i][0].SetFloat64(0)
buffCmplx[i][1].SetFloat64(0)
}
if err = ecd.IFFT(buffCmplx[:slots], metadata.LogDimensions.Cols); err != nil {
return
}
// Maps Y = X^{N/n} -> X and quantizes.
switch p := polyOut.(type) {
case ring.Poly:
ComplexArbitraryToFixedPointCRT(ecd.parameters.RingQ().AtLevel(p.Level()), buffCmplx[:slots], &metadata.Scale.Value, p.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingQ().AtLevel(p.Level()), metadata, p)
case ringqp.Poly:
ComplexArbitraryToFixedPointCRT(ecd.parameters.RingQ().AtLevel(p.Q.Level()), buffCmplx[:slots], &metadata.Scale.Value, p.Q.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingQ().AtLevel(p.Q.Level()), metadata, p.Q)
if p.P.Level() > -1 {
ComplexArbitraryToFixedPointCRT(ecd.parameters.RingP().AtLevel(p.P.Level()), buffCmplx[:slots], &metadata.Scale.Value, p.P.Coeffs)
rlwe.NTTSparseAndMontgomery(ecd.parameters.RingP().AtLevel(p.P.Level()), metadata, p.P)
}
default:
return fmt.Errorf("cannot Embed: invalid polyOut.(Type) must be ringqp.Poly or ring.Poly")
}
return
}
// plaintextToComplex maps a CRT polynomial to a complex valued FloatSlice.
func (ecd Encoder) plaintextToComplex(level int, scale rlwe.Scale, logSlots int, p ring.Poly, values FloatSlice) (err error) {
isreal := ecd.parameters.RingType() == ring.ConjugateInvariant
if level == 0 {
return polyToComplexNoCRT(p.Coeffs[0], values, scale, logSlots, isreal, ecd.parameters.RingQ().AtLevel(level))
}
return polyToComplexCRT(p, ecd.bigintCoeffs, values, scale, logSlots, isreal, ecd.parameters.RingQ().AtLevel(level))
}
// plaintextToFloat maps a CRT polynomial to a real valued FloatSlice.
func (ecd Encoder) plaintextToFloat(level int, scale rlwe.Scale, logSlots int, p ring.Poly, values FloatSlice) (err error) {
if level == 0 {
return ecd.polyToFloatNoCRT(p.Coeffs[0], values, scale, logSlots, ecd.parameters.RingQ().AtLevel(level))
}
return ecd.polyToFloatCRT(p, values, scale, logSlots, ecd.parameters.RingQ().AtLevel(level))
}
// decodePublic decode a plaintext to a FloatSlice.
// The method will add a flooding noise before the decoding process following the defined distribution if it is not nil.
func (ecd Encoder) decodePublic(pt *rlwe.Plaintext, values FloatSlice, logprec float64) (err error) {
logSlots := pt.LogDimensions.Cols
slots := 1 << logSlots
if maxLogCols := ecd.parameters.LogMaxDimensions().Cols; logSlots > maxLogCols || logSlots < 0 {
return fmt.Errorf("cannot Decode: ensure that %d <= logSlots (%d) <= %d", 0, logSlots, maxLogCols)
}
if pt.IsNTT {
ecd.parameters.RingQ().AtLevel(pt.Level()).INTT(pt.Value, ecd.buff)
} else {
ecd.buff.CopyLvl(pt.Level(), pt.Value)
}
switch values.(type) {
case []complex128, []float64, []*bignum.Complex, []*big.Float:
default:
return fmt.Errorf("cannot decode: values.(type) accepted are []complex128, []float64, []*bignum.Complex, []*big.Float but is %T", values)
}
if pt.IsBatched {
if ecd.prec <= 53 {
buffCmplx := ecd.buffCmplx.([]complex128)
if err = ecd.plaintextToComplex(pt.Level(), pt.Scale, logSlots, ecd.buff, buffCmplx); err != nil {
return
}
if err = ecd.FFT(buffCmplx[:slots], logSlots); err != nil {
return
}
if logprec != 0 {
scale := math.Exp2(logprec)
switch values.(type) {
case []*bignum.Complex, []complex128:
for i := 0; i < slots; i++ {
buffCmplx[i] = complex(math.Round(real(buffCmplx[i])*scale)/scale, math.Round(imag(buffCmplx[i])*scale)/scale)
}
default:
for i := 0; i < slots; i++ {
buffCmplx[i] = complex(math.Round(real(buffCmplx[i])*scale)/scale, 0)
}
}
}
switch values := values.(type) {
case []float64:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
values[i] = real(buffCmplx[i])
}
case []complex128:
copy(values, buffCmplx)
case []*big.Float:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
if values[i] == nil {
values[i] = new(big.Float)
}
values[i].SetFloat64(real(buffCmplx[i]))
}
case []*bignum.Complex:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
if values[i] == nil {
values[i] = &bignum.Complex{
new(big.Float),
new(big.Float),
}
} else {
if values[i][0] == nil {
values[i][0] = new(big.Float)
}
if values[i][1] == nil {
values[i][1] = new(big.Float)
}
}
values[i][0].SetFloat64(real(buffCmplx[i]))
values[i][1].SetFloat64(imag(buffCmplx[i]))
}
}
} else {
buffCmplx := ecd.buffCmplx.([]*bignum.Complex)
if err = ecd.plaintextToComplex(pt.Level(), pt.Scale, logSlots, ecd.buff, buffCmplx[:slots]); err != nil {
return
}
if err = ecd.FFT(buffCmplx[:slots], logSlots); err != nil {
return
}
var scale, half, zero *big.Float
var tmp *big.Int
if logprec != 0 {
// 2^logprec
scale = new(big.Float).SetPrec(ecd.Prec()).SetFloat64(logprec)
scale.Mul(scale, bignum.Log2(ecd.Prec()))
scale = bignum.Exp(scale)
tmp = new(big.Int)
half = new(big.Float).SetFloat64(0.5)
zero = new(big.Float)
}
switch values := values.(type) {
case []float64:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
values[i], _ = buffCmplx[i][0].Float64()
}
if logprec != 0 {
scaleF64, _ := scale.Float64()
for i := 0; i < slots; i++ {
values[i] = math.Round(values[i]*scaleF64) / scaleF64
}
}
case []complex128:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
values[i] = buffCmplx[i].Complex128()
}
if logprec != 0 {
scaleF64, _ := scale.Float64()
for i := 0; i < slots; i++ {
values[i] = complex(math.Round(real(values[i])*scaleF64)/scaleF64, math.Round(imag(values[i])*scaleF64)/scaleF64)
}
}
case []*big.Float:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
if values[i] == nil {
values[i] = new(big.Float)
}
values[i].Set(buffCmplx[i][0])
}
if logprec != 0 {
for i := range values {
values[i].Mul(values[i], scale)
// Adds/Subtracts 0.5
if values[i].Cmp(zero) >= 0 {
values[i].Add(values[i], half)
} else {
values[i].Sub(values[i], half)
}
// Round = floor +/- 0.5
values[i].Int(tmp)
values[i].SetInt(tmp)
values[i].Quo(values[i], scale)
}
}
case []*bignum.Complex:
slots := utils.Min(len(values), slots)
for i := 0; i < slots; i++ {
if values[i] == nil {
values[i] = &bignum.Complex{
new(big.Float),
new(big.Float),
}
} else {
if values[i][0] == nil {
values[i][0] = new(big.Float)
}
if values[i][1] == nil {
values[i][1] = new(big.Float)
}
}
values[i][0].Set(buffCmplx[i][0])
values[i][1].Set(buffCmplx[i][1])
}
if logprec != 0 {
for i := range values {
// Real
values[i][0].Mul(values[i][0], scale)
// Adds/Subtracts 0.5
if values[i][0].Cmp(zero) >= 0 {
values[i][0].Add(values[i][0], half)
} else {
values[i][0].Sub(values[i][0], half)
}
// Round = floor +/- 0.5
values[i][0].Int(tmp)
values[i][0].SetInt(tmp)
values[i][0].Quo(values[i][0], scale)
// Imag
values[i][1].Mul(values[i][1], scale)
// Adds/Subtracts 0.5
if values[i][1].Cmp(zero) >= 0 {
values[i][1].Add(values[i][1], half)
} else {
values[i][1].Sub(values[i][1], half)
}
// Round = floor +/- 0.5
values[i][1].Int(tmp)
values[i][1].SetInt(tmp)
values[i][1].Quo(values[i][1], scale)
}
}
}
}
} else {
return ecd.plaintextToFloat(pt.Level(), pt.Scale, logSlots, ecd.buff, values)
}
return
}
// IFFT evaluates the special 2^{LogN}-th encoding discrete Fourier transform on FloatSlice.
func (ecd Encoder) IFFT(values FloatSlice, logN int) (err error) {
switch values := values.(type) {
case []complex128:
switch roots := ecd.roots.(type) {
case []complex128:
if logN < 4 {
SpecialIFFTDouble(values, 1<<logN, ecd.m, ecd.rotGroup, ecd.roots.([]complex128))
} else {
SpecialiFFTDoubleUnrolled8(values, 1<<logN, ecd.m, ecd.rotGroup, ecd.roots.([]complex128))
}
default:
return fmt.Errorf("cannot IFFT: values.(type)=%T doesn't roots.(type) = %T", values, roots)
}
case []*bignum.Complex:
switch roots := ecd.roots.(type) {
case []*bignum.Complex:
SpecialIFFTArbitrary(values, 1<<logN, ecd.m, ecd.rotGroup, ecd.roots.([]*bignum.Complex))
default:
return fmt.Errorf("cannot IFFT: values.(type)=%T doesn't roots.(type) = %T", values, roots)
}
default:
return fmt.Errorf("cannot IFFT: invalid values.(type), accepted types are []complex128 and []*bignum.Complex but is %T", values)
}
return
}
// FFT evaluates the special 2^{LogN}-th decoding discrete Fourier transform on FloatSlice.
func (ecd Encoder) FFT(values FloatSlice, logN int) (err error) {
switch values := values.(type) {
case []complex128:
switch roots := ecd.roots.(type) {
case []complex128:
if logN < 4 {
SpecialFFTDouble(values, 1<<logN, ecd.m, ecd.rotGroup, roots)
} else {
SpecialFFTDoubleUL8(values, 1<<logN, ecd.m, ecd.rotGroup, roots)
}
default:
return fmt.Errorf("cannot IFFT: values.(type)=%T doesn't roots.(type) = %T", values, roots)
}
case []*bignum.Complex:
switch roots := ecd.roots.(type) {
case []*bignum.Complex:
SpecialFFTArbitrary(values, 1<<logN, ecd.m, ecd.rotGroup, roots)
default:
return fmt.Errorf("cannot IFFT: values.(type)=%T doesn't roots.(type) = %T", values, roots)
}
default:
return fmt.Errorf("cannot IFFT: invalid values.(type), accepted types are []complex128 and []*bignum.Complex but is %T", values)
}
return
}
// polyToComplexNoCRT decodes a single-level CRT poly on a complex valued FloatSlice.
func polyToComplexNoCRT(coeffs []uint64, values FloatSlice, scale rlwe.Scale, logSlots int, isreal bool, ringQ *ring.Ring) (err error) {
slots := 1 << logSlots
maxCols := int(ringQ.NthRoot() >> 2)
gap := maxCols / slots
Q := ringQ.SubRings[0].Modulus
var c uint64
switch values := values.(type) {
case []complex128:
for i, idx := 0, 0; i < slots; i, idx = i+1, idx+gap {
c = coeffs[idx]
if c >= Q>>1 {
values[i] = complex(-float64(Q-c), 0)
} else {
values[i] = complex(float64(c), 0)
}
}
if !isreal {
for i, idx := 0, maxCols; i < slots; i, idx = i+1, idx+gap {
c = coeffs[idx]
if c >= Q>>1 {
values[i] += complex(0, -float64(Q-c))
} else {
values[i] += complex(0, float64(c))
}
}
} else {
// [X]/(X^N+1) to [X+X^-1]/(X^N+1)
slots := 1 << logSlots
for i := 1; i < slots; i++ {
values[i] -= complex(0, real(values[slots-i]))
}
}
divideComplex128SliceUnrolled8(values, complex(scale.Float64(), 0))
case []*bignum.Complex:
for i, idx := 0, 0; i < slots; i, idx = i+1, idx+gap {
if values[i] == nil {
values[i] = &bignum.Complex{
new(big.Float),
nil,
}
} else {
if values[i][0] == nil {
values[i][0] = new(big.Float)
}
}
if c = coeffs[idx]; c >= Q>>1 {
values[i][0].SetInt64(-int64(Q - c))
} else {
values[i][0].SetInt64(int64(c))
}
}
if !isreal {
for i, idx := 0, maxCols; i < slots; i, idx = i+1, idx+gap {
if values[i][1] == nil {
values[i][1] = new(big.Float)
}
if c = coeffs[idx]; c >= Q>>1 {
values[i][1].SetInt64(-int64(Q - c))
} else {
values[i][1].SetInt64(int64(c))
}
}
} else {
slots := 1 << logSlots
for i := 1; i < slots; i++ {
values[i][1].Sub(values[i][1], values[slots-i][0])
}
}
s := &scale.Value
for i := range values {
values[i][0].Quo(values[i][0], s)
values[i][1].Quo(values[i][1], s)
}
default:
return fmt.Errorf("cannot polyToComplexNoCRT: values.(Type) must be []complex128 or []*bignum.Complex but is %T", values)
}
return
}
// polyToComplexNoCRT decodes a multiple-level CRT poly on a complex valued FloatSlice.
func polyToComplexCRT(poly ring.Poly, bigintCoeffs []*big.Int, values FloatSlice, scale rlwe.Scale, logSlots int, isreal bool, ringQ *ring.Ring) (err error) {
maxCols := int(ringQ.NthRoot() >> 2)
slots := 1 << logSlots
gap := maxCols / slots
ringQ.PolyToBigint(poly, gap, bigintCoeffs)
Q := ringQ.ModulusAtLevel[ringQ.Level()]
qHalf := new(big.Int)
qHalf.Set(Q)
qHalf.Rsh(qHalf, 1)
var sign int
switch values := values.(type) {
case []complex128:
scalef64 := scale.Float64()
var c *big.Int
for i := 0; i < slots; i++ {
c = bigintCoeffs[i]
c.Mod(c, Q)
if sign = c.Cmp(qHalf); sign == 1 || sign == 0 {
c.Sub(c, Q)
}
values[i] = complex(scaleDown(c, scalef64), 0)
}
if !isreal {
for i, j := 0, slots; i < slots; i, j = i+1, j+1 {
c = bigintCoeffs[j]
c.Mod(c, Q)
if sign = c.Cmp(qHalf); sign == 1 || sign == 0 {
c.Sub(c, Q)
}
values[i] += complex(0, scaleDown(c, scalef64))
}
} else {
// [X]/(X^N+1) to [X+X^-1]/(X^N+1)
slots := 1 << logSlots
for i := 1; i < slots; i++ {
values[i] -= complex(0, real(values[slots-i]))
}
}
case []*bignum.Complex:
var c *big.Int
for i := 0; i < slots; i++ {
c = bigintCoeffs[i]
c.Mod(c, Q)
if sign = c.Cmp(qHalf); sign == 1 || sign == 0 {
c.Sub(c, Q)
}
if values[i] == nil {
values[i] = &bignum.Complex{
new(big.Float),
nil,
}
} else {
if values[i][0] == nil {
values[i][0] = new(big.Float)
}
}
values[i][0].SetInt(c)
}
if !isreal {
for i, j := 0, slots; i < slots; i, j = i+1, j+1 {
c = bigintCoeffs[j]
c.Mod(c, Q)
if sign = c.Cmp(qHalf); sign == 1 || sign == 0 {
c.Sub(c, Q)
}
if values[i][1] == nil {
values[i][1] = new(big.Float)
}
values[i][1].SetInt(c)
}
} else {
// [X]/(X^N+1) to [X+X^-1]/(X^N+1)
slots := 1 << logSlots
for i := 1; i < slots; i++ {
values[i][1].Sub(values[i][1], values[slots-i][0])
}
}
s := &scale.Value
for i := range values {
values[i][0].Quo(values[i][0], s)
values[i][1].Quo(values[i][1], s)
}
default:
return fmt.Errorf("cannot polyToComplexNoCRT: values.(Type) must be []complex128 or []*bignum.Complex but is %T", values)
}
return
}
// polyToFloatCRT decodes a multiple-level CRT poly on a real valued FloatSlice.
func (ecd *Encoder) polyToFloatCRT(p ring.Poly, values FloatSlice, scale rlwe.Scale, logSlots int, r *ring.Ring) (err error) {
var slots int
switch values := values.(type) {
case []float64:
slots = utils.Min(len(p.Coeffs[0]), len(values))
case []complex128: