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evaluator.go
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evaluator.go
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package ckks
import (
"errors"
"math"
"math/big"
"github.com/tuneinsight/lattigo/v4/ring"
"github.com/tuneinsight/lattigo/v4/rlwe"
"github.com/tuneinsight/lattigo/v4/rlwe/ringqp"
"github.com/tuneinsight/lattigo/v4/utils"
)
// Evaluator is an interface implementing the methods to conduct homomorphic operations between ciphertext and/or plaintexts.
type Evaluator interface {
// ========================
// === Basic Arithmetic ===
// ========================
// Addition
Add(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
AddNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext)
// Subtraction
Sub(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
SubNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext)
// Negation
Neg(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
NegNew(ctIn *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext)
// Constant Addition
AddConstNew(ctIn *rlwe.Ciphertext, constant interface{}) (ctOut *rlwe.Ciphertext)
AddConst(ctIn *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext)
// Constant Multiplication
MultByConstNew(ctIn *rlwe.Ciphertext, constant interface{}) (ctOut *rlwe.Ciphertext)
MultByConst(ctIn *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext)
MultByGaussianInteger(ctIn *rlwe.Ciphertext, cReal, cImag interface{}, ctOut *rlwe.Ciphertext)
// Constant Multiplication with Addition
MultByConstAndAdd(ctIn *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext)
MultByGaussianIntegerAndAdd(ctIn *rlwe.Ciphertext, cReal, cImag interface{}, ctOut *rlwe.Ciphertext)
// Multiplication by the imaginary unit
MultByiNew(ctIn *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext)
MultByi(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
DivByiNew(ctIn *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext)
DivByi(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
// Conjugation
ConjugateNew(ctIn *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext)
Conjugate(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
// Multiplication
Mul(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
MulNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext)
MulRelin(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
MulRelinNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext)
MulAndAdd(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
MulRelinAndAdd(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext)
// Slot Rotations
RotateNew(ctIn *rlwe.Ciphertext, k int) (ctOut *rlwe.Ciphertext)
Rotate(ctIn *rlwe.Ciphertext, k int, ctOut *rlwe.Ciphertext)
RotateHoistedNew(ctIn *rlwe.Ciphertext, rotations []int) (ctOut map[int]*rlwe.Ciphertext)
RotateHoisted(ctIn *rlwe.Ciphertext, rotations []int, ctOut map[int]*rlwe.Ciphertext)
RotateHoistedNoModDownNew(level int, rotations []int, c0 *ring.Poly, c2DecompQP []ringqp.Poly) (cOut map[int]rlwe.CiphertextQP)
// ===========================
// === Advanced Arithmetic ===
// ===========================
// Polynomial evaluation
EvaluatePoly(input interface{}, pol *Polynomial, targetScale rlwe.Scale) (ctOut *rlwe.Ciphertext, err error)
EvaluatePolyVector(input interface{}, pols []*Polynomial, encoder Encoder, slotIndex map[int][]int, targetScale rlwe.Scale) (ctOut *rlwe.Ciphertext, err error)
// Inversion
InverseNew(ctIn *rlwe.Ciphertext, steps int) (ctOut *rlwe.Ciphertext, err error)
// Linear Transformations
LinearTransformNew(ctIn *rlwe.Ciphertext, linearTransform interface{}) (ctOut []*rlwe.Ciphertext)
LinearTransform(ctIn *rlwe.Ciphertext, linearTransform interface{}, ctOut []*rlwe.Ciphertext)
MultiplyByDiagMatrix(ctIn *rlwe.Ciphertext, matrix LinearTransform, c2DecompQP []ringqp.Poly, ctOut *rlwe.Ciphertext)
MultiplyByDiagMatrixBSGS(ctIn *rlwe.Ciphertext, matrix LinearTransform, c2DecompQP []ringqp.Poly, ctOut *rlwe.Ciphertext)
// Inner sum
InnerSum(ctIn *rlwe.Ciphertext, batch, n int, ctOut *rlwe.Ciphertext)
Average(ctIn *rlwe.Ciphertext, batch int, ctOut *rlwe.Ciphertext)
// Replication (inverse of Inner sum)
Replicate(ctIn *rlwe.Ciphertext, batch, n int, ctOut *rlwe.Ciphertext)
// Trace
Trace(ctIn *rlwe.Ciphertext, logSlots int, ctOut *rlwe.Ciphertext)
TraceNew(ctIn *rlwe.Ciphertext, logSlots int) (ctOut *rlwe.Ciphertext)
// =============================
// === Ciphertext Management ===
// =============================
// Key-Switching
SwitchKeysNew(ctIn *rlwe.Ciphertext, switchingKey *rlwe.SwitchingKey) (ctOut *rlwe.Ciphertext)
SwitchKeys(ctIn *rlwe.Ciphertext, switchingKey *rlwe.SwitchingKey, ctOut *rlwe.Ciphertext)
// Degree Management
RelinearizeNew(ctIn *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext)
Relinearize(ctIn *rlwe.Ciphertext, ctOut *rlwe.Ciphertext)
// Scale Management
ScaleUpNew(ctIn *rlwe.Ciphertext, scale rlwe.Scale) (ctOut *rlwe.Ciphertext)
ScaleUp(ctIn *rlwe.Ciphertext, scale rlwe.Scale, ctOut *rlwe.Ciphertext)
SetScale(ctIn *rlwe.Ciphertext, scale rlwe.Scale)
Rescale(ctIn *rlwe.Ciphertext, minScale rlwe.Scale, ctOut *rlwe.Ciphertext) (err error)
// Level Management
DropLevelNew(ctIn *rlwe.Ciphertext, levels int) (ctOut *rlwe.Ciphertext)
DropLevel(ctIn *rlwe.Ciphertext, levels int)
// ==============
// === Others ===
// ==============
GetRLWEEvaluator() *rlwe.Evaluator
BuffQ() [3]*ring.Poly
BuffCt() *rlwe.Ciphertext
ShallowCopy() Evaluator
WithKey(rlwe.EvaluationKey) Evaluator
}
// evaluator is a struct that holds the necessary elements to execute the homomorphic operations between Ciphertexts and/or Plaintexts.
// It also holds a memory buffer used to store intermediate computations.
type evaluator struct {
*evaluatorBase
*evaluatorBuffers
*rlwe.Evaluator
}
type evaluatorBase struct {
params Parameters
}
type evaluatorBuffers struct {
buffQ [3]*ring.Poly // Memory buffer in order: for MForm(c0), MForm(c1), c2
buffCt *rlwe.Ciphertext // Memory buffer for ciphertexts that need to be scaled up (to be eventually removed)
}
// BuffQ returns a pointer to the internal memory buffer buffQ.
func (eval *evaluator) BuffQ() [3]*ring.Poly {
return eval.buffQ
}
// BuffCt returns a pointer to the internal memory buffer buffCt.
func (eval *evaluator) BuffCt() *rlwe.Ciphertext {
return eval.buffCt
}
func newEvaluatorBase(params Parameters) *evaluatorBase {
ev := new(evaluatorBase)
ev.params = params
return ev
}
func newEvaluatorBuffers(evalBase *evaluatorBase) *evaluatorBuffers {
buff := new(evaluatorBuffers)
params := evalBase.params
ringQ := params.RingQ()
buff.buffQ = [3]*ring.Poly{ringQ.NewPoly(), ringQ.NewPoly(), ringQ.NewPoly()}
buff.buffCt = NewCiphertext(params, 2, params.MaxLevel())
return buff
}
// NewEvaluator creates a new Evaluator, that can be used to do homomorphic
// operations on the Ciphertexts and/or Plaintexts. It stores a memory buffer
// and Ciphertexts that will be used for intermediate values.
func NewEvaluator(params Parameters, evaluationKey rlwe.EvaluationKey) Evaluator {
eval := new(evaluator)
eval.evaluatorBase = newEvaluatorBase(params)
eval.evaluatorBuffers = newEvaluatorBuffers(eval.evaluatorBase)
eval.Evaluator = rlwe.NewEvaluator(params.Parameters, &evaluationKey)
return eval
}
// GetRLWEEvaluator returns the underlying *rlwe.Evaluator.
func (eval *evaluator) GetRLWEEvaluator() *rlwe.Evaluator {
return eval.Evaluator
}
func (eval *evaluator) PermuteNTTIndexesForKey(rtks *rlwe.RotationKeySet) *map[uint64][]uint64 {
if rtks == nil {
return &map[uint64][]uint64{}
}
PermuteNTTIndex := make(map[uint64][]uint64, len(rtks.Keys))
for galEl := range rtks.Keys {
PermuteNTTIndex[galEl] = eval.params.RingQ().PermuteNTTIndex(galEl)
}
return &PermuteNTTIndex
}
func (eval *evaluator) checkBinary(op0, op1, opOut rlwe.Operand, opOutMinDegree int) {
if op0 == nil || op1 == nil || opOut == nil {
panic("cannot checkBinary: rlwe.Operands cannot be nil")
}
if op0.Degree()+op1.Degree() == 0 {
panic("cannot checkBinary: rlwe.Operands cannot be both plaintext")
}
if opOut.Degree() < opOutMinDegree {
panic("cannot checkBinary: receiver rlwe.Operand degree is too small")
}
if !op0.El().IsNTT {
panic("cannot checkBinary: op0 must be in NTT")
}
if !op1.El().IsNTT {
panic("cannot checkBinary: op1 must be in NTT")
}
}
func (eval *evaluator) newCiphertextBinary(op0, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext) {
maxDegree := utils.MaxInt(op0.Degree(), op1.Degree())
minLevel := utils.MinInt(op0.Level(), op1.Level())
return NewCiphertext(eval.params, maxDegree, minLevel)
}
// Add adds op1 to ctIn and returns the result in ctOut.
func (eval *evaluator) Add(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext) {
eval.checkBinary(ctIn, op1, ctOut, utils.MaxInt(ctIn.Degree(), op1.Degree()))
eval.evaluateInPlace(ctIn, op1, ctOut, eval.params.RingQ().AddLvl)
}
// AddNew adds op1 to ctIn and returns the result in a newly created element.
func (eval *evaluator) AddNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext) {
ctOut = eval.newCiphertextBinary(ctIn, op1)
eval.Add(ctIn, op1, ctOut)
return
}
// Sub subtracts op1 from ctIn and returns the result in ctOut.
func (eval *evaluator) Sub(ctIn *rlwe.Ciphertext, op1 rlwe.Operand, ctOut *rlwe.Ciphertext) {
eval.checkBinary(ctIn, op1, ctOut, utils.MaxInt(ctIn.Degree(), op1.Degree()))
eval.evaluateInPlace(ctIn, op1, ctOut, eval.params.RingQ().SubLvl)
level := utils.MinInt(utils.MinInt(ctIn.Level(), op1.Level()), ctOut.Level())
if ctIn.Degree() < op1.Degree() {
for i := ctIn.Degree() + 1; i < op1.Degree()+1; i++ {
eval.params.RingQ().NegLvl(level, ctOut.Value[i], ctOut.Value[i])
}
}
}
// SubNew subtracts op1 from ctIn and returns the result in a newly created element.
func (eval *evaluator) SubNew(ctIn *rlwe.Ciphertext, op1 rlwe.Operand) (ctOut *rlwe.Ciphertext) {
ctOut = eval.newCiphertextBinary(ctIn, op1)
eval.Sub(ctIn, op1, ctOut)
return
}
func (eval *evaluator) evaluateInPlace(c0 *rlwe.Ciphertext, c1 rlwe.Operand, ctOut *rlwe.Ciphertext, evaluate func(int, *ring.Poly, *ring.Poly, *ring.Poly)) {
var tmp0, tmp1 *rlwe.Ciphertext
level := utils.MinInt(utils.MinInt(c0.Level(), c1.Level()), ctOut.Level())
maxDegree := utils.MaxInt(c0.Degree(), c1.Degree())
minDegree := utils.MinInt(c0.Degree(), c1.Degree())
// Else resizes the receiver element
ctOut.El().Resize(maxDegree, ctOut.Level())
c0Scale := c0.GetScale().Float64()
c1Scale := c1.GetScale().Float64()
if ctOut.Level() > level {
eval.DropLevel(ctOut, ctOut.Level()-utils.MinInt(c0.Level(), c1.Level()))
}
cmp := c0.GetScale().Cmp(c1.GetScale())
// Checks whether or not the receiver element is the same as one of the input elements
// and acts accordingly to avoid unnecessary element creation or element overwriting,
// and scales properly the element before the evaluation.
if ctOut == c0 {
if cmp == 1 && math.Floor(c0Scale/c1Scale) > 1 {
tmp1 = eval.buffCt.El()
tmp1.Scale = ctOut.Scale
eval.MultByConst(c1.El(), math.Floor(c0Scale/c1Scale), tmp1)
} else if cmp == -1 && math.Floor(c1Scale/c0Scale) > 1 {
eval.MultByConst(c0, math.Floor(c1Scale/c0Scale), c0)
ctOut.Scale = c1.GetScale()
tmp1 = c1.El()
} else {
tmp1 = c1.El()
}
tmp0 = c0.El()
} else if ctOut == c1 {
if cmp == 1 && math.Floor(c0Scale/c1Scale) > 1 {
eval.MultByConst(c1.El(), math.Floor(c0Scale/c1Scale), ctOut)
ctOut.Scale = c0.Scale
tmp0 = c0.El()
} else if cmp == -1 && math.Floor(c1Scale/c0Scale) > 1 {
tmp0 = eval.buffCt.El()
tmp0.Scale = ctOut.Scale
eval.MultByConst(c0, math.Floor(c1Scale/c0Scale), tmp0)
} else {
tmp0 = c0.El()
}
tmp1 = c1.El()
} else {
if cmp == 1 && math.Floor(c0Scale/c1Scale) > 1 {
tmp1 = eval.buffCt.El()
tmp1.Scale = ctOut.Scale
eval.MultByConst(c1.El(), math.Floor(c0Scale/c1Scale), tmp1)
tmp0 = c0.El()
} else if cmp == -1 && math.Floor(c1Scale/c0Scale) > 1 {
tmp0 = eval.buffCt.El()
tmp0.Scale = ctOut.Scale
eval.MultByConst(c0, math.Floor(c1Scale/c0Scale), tmp0)
tmp1 = c1.El()
} else {
tmp0 = c0.El()
tmp1 = c1.El()
}
}
for i := 0; i < minDegree+1; i++ {
evaluate(level, tmp0.Value[i], tmp1.Value[i], ctOut.El().Value[i])
}
ctOut.MetaData = c0.MetaData
ctOut.Scale = c0.Scale.Max(c1.GetScale())
// If the inputs degrees differ, it copies the remaining degree on the receiver.
// Also checks that the receiver is not one of the inputs to avoid unnecessary work.
if c0.Degree() > c1.Degree() && tmp0 != ctOut.El() {
for i := minDegree + 1; i < maxDegree+1; i++ {
ring.CopyLvl(level, tmp0.Value[i], ctOut.El().Value[i])
}
} else if c1.Degree() > c0.Degree() && tmp1 != ctOut.El() {
for i := minDegree + 1; i < maxDegree+1; i++ {
ring.CopyLvl(level, tmp1.Value[i], ctOut.El().Value[i])
}
}
}
// Neg negates the value of ct0 and returns the result in ctOut.
func (eval *evaluator) Neg(ct0 *rlwe.Ciphertext, ctOut *rlwe.Ciphertext) {
level := utils.MinInt(ct0.Level(), ctOut.Level())
if ct0.Degree() != ctOut.Degree() {
panic("cannot Negate: invalid receiver Ciphertext does not match input Ciphertext degree")
}
for i := range ct0.Value {
eval.params.RingQ().NegLvl(level, ct0.Value[i], ctOut.Value[i])
}
ctOut.MetaData = ct0.MetaData
}
// NegNew negates ct0 and returns the result in a newly created element.
func (eval *evaluator) NegNew(ct0 *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext) {
ctOut = NewCiphertext(eval.params, ct0.Degree(), ct0.Level())
eval.Neg(ct0, ctOut)
return
}
// AddConstNew adds the input constant (which can be a uint64, int64, float64 or complex128) to ct0 and returns the result in a new element.
func (eval *evaluator) AddConstNew(ct0 *rlwe.Ciphertext, constant interface{}) (ctOut *rlwe.Ciphertext) {
ctOut = ct0.CopyNew()
eval.AddConst(ct0, constant, ctOut)
return ctOut
}
func (eval *evaluator) getConstAndScale(level int, constant interface{}) (cReal, cImag, scale float64) {
// Converts to float64 and determines if a scaling is required (which is the case if either real or imag have a rational part)
scale = 1
switch constant := constant.(type) {
case complex128:
cReal = real(constant)
cImag = imag(constant)
if cReal != 0 {
valueInt := int64(cReal)
valueFloat := cReal - float64(valueInt)
if valueFloat != 0 {
scale = float64(eval.params.RingQ().Modulus[level])
}
}
if cImag != 0 {
valueInt := int64(cImag)
valueFloat := cImag - float64(valueInt)
if valueFloat != 0 {
scale = float64(eval.params.RingQ().Modulus[level])
}
}
case float64:
cReal = constant
cImag = float64(0)
if cReal != 0 {
valueInt := int64(cReal)
valueFloat := cReal - float64(valueInt)
if valueFloat != 0 {
scale = float64(eval.params.RingQ().Modulus[level])
}
}
case *big.Float:
cf64, _ := constant.Float64()
return eval.getConstAndScale(level, cf64)
case uint64:
cReal = float64(constant)
cImag = float64(0)
case int64:
cReal = float64(constant)
cImag = float64(0)
case int:
cReal = float64(constant)
cImag = float64(0)
}
if eval.params.RingType() == ring.ConjugateInvariant {
cImag = float64(0)
}
return
}
// AddConst adds the input constant (which can be a uint64, int64, float64 or complex128) to ct0 and returns the result in ctOut.
func (eval *evaluator) AddConst(ct0 *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext) {
var level = utils.MinInt(ct0.Level(), ctOut.Level())
var scaledConst, scaledConstReal, scaledConstImag, qi uint64
cReal, cImag, _ := eval.getConstAndScale(level, constant)
ringQ := eval.params.RingQ()
cf64 := ctOut.Scale.Float64()
ctOut.MetaData = ct0.MetaData
// Component wise addition of the following vector to the ciphertext:
// [a + b*psi_qi^2, ....., a + b*psi_qi^2, a - b*psi_qi^2, ...., a - b*psi_qi^2] mod Qi
// [{ N/2 }{ N/2 }]
// Which is equivalent outside of the NTT domain to adding a to the first coefficient of ct0 and b to the N/2-th coefficient of ct0.
for i := 0; i < level+1; i++ {
scaledConstReal, scaledConstImag, scaledConst = 0, 0, 0
qi = ringQ.Modulus[i]
if cReal != 0 {
scaledConstReal = scaleUpExact(cReal, cf64, qi)
scaledConst = scaledConstReal
}
if cImag != 0 {
scaledConstImag = ring.MRed(scaleUpExact(cImag, cf64, qi), ringQ.NttPsi[i][1], qi, ringQ.MredParams[i])
scaledConst = ring.CRed(scaledConst+scaledConstImag, qi)
}
p0tmp := ct0.Value[0].Coeffs[i]
p1tmp := ctOut.Value[0].Coeffs[i]
ring.AddScalarVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], scaledConst, qi)
if cImag != 0 {
scaledConst = ring.CRed(scaledConstReal+(qi-scaledConstImag), qi)
}
ring.AddScalarVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], scaledConst, qi)
}
}
// MultByConstAndAdd multiplies ct0 by the input constant, and adds it to the receiver element (it does not modify the input
// element), e.g., ctOut(x) = ctOut(x) + ct0(x) * (a+bi). This functions removes the need of storing the intermediate value c(x) * (a+bi).
// This function will modify the level and the scale of the receiver element depending on the level and the scale of the input
// element and the type of the constant. The level of the receiver element will be set to min(input.level, receiver.level).
// The scale of the receiver element will be set to the scale that the input element would have after the multiplication by the constant.
func (eval *evaluator) MultByConstAndAdd(ct0 *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext) {
var level = utils.MinInt(ct0.Level(), ctOut.Level())
// Forces a drop of ctOut level to ct0 level
if ctOut.Level() > level {
eval.DropLevel(ctOut, ctOut.Level()-level)
}
cReal, cImag, scale := eval.getConstAndScale(level, constant)
var scaledConst, scaledConstReal, scaledConstImag uint64
c0f64 := ct0.Scale.Float64()
c1f64 := ctOut.Scale.Float64()
ringQ := eval.params.RingQ()
// If a scaling would be required to multiply by the constant,
// it equalizes scales such that the scales match in the end.
if scale != 1 {
// If ctOut scaling is smaller than ct0's scale + the default scaling,
// then brings ctOut scale to ct0's scale.
if c1f64 < c0f64*scale {
if scale := math.Floor((scale * c0f64) / c1f64); scale > 1 {
eval.MultByConst(ctOut, scale, ctOut)
}
ctOut.MetaData = ct0.MetaData
ctOut.Scale = ct0.Scale.Mul(rlwe.NewScale(scale))
// If ctOut.scale > ((a+bi)*scale)*ct0(x), then it sets the scale to
// bring c(x)*scale to the level of ctOut(x) scale
} else if c1f64 > c0f64*scale {
scale = c1f64 / c0f64
}
// If no scaling is required, then it sets the appropriate scale such that
// ct0(x)*scale matches ctOut(x) scale without modifying ct0(x) scale.
} else {
if c1f64 > c0f64 {
scale = c1f64 / c0f64
} else if c0f64 > c1f64 {
if scale := math.Floor(c0f64 / c1f64); scale > 1 {
eval.MultByConst(ctOut, scale, ctOut)
}
ctOut.MetaData = ct0.MetaData
ctOut.Scale = ct0.Scale
}
}
// Component-wise multiplication of the following vector to the ciphertext:
// [a + b*psi_qi^2, ....., a + b*psi_qi^2, a - b*psi_qi^2, ...., a - b*psi_qi^2] mod Qi
// [{ N/2 }{ N/2 }]
// Which is equivalent outside of the NTT domain to adding a to the first coefficient of ct0 and b to the N/2-th coefficient of ct0.
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
mredParams := ringQ.MredParams[i]
bredParams := ringQ.BredParams[i]
scaledConstReal = 0
scaledConstImag = 0
scaledConst = 0
if cReal != 0 {
scaledConstReal = scaleUpExact(cReal, scale, qi)
scaledConst = scaledConstReal
}
if cImag != 0 {
scaledConstImag = scaleUpExact(cImag, scale, qi)
scaledConstImag = ring.MRed(scaledConstImag, ringQ.NttPsi[i][1], qi, mredParams)
scaledConst = ring.CRed(scaledConst+scaledConstImag, qi)
}
scaledConst = ring.MForm(scaledConst, qi, bredParams)
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryAndAddVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], scaledConst, qi, mredParams)
}
if cImag != 0 {
scaledConst = ring.CRed(scaledConstReal+(qi-scaledConstImag), qi)
scaledConst = ring.MForm(scaledConst, qi, bredParams)
}
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryAndAddVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], scaledConst, qi, mredParams)
}
}
}
// MultByConstNew multiplies ct0 by the input constant and returns the result in a newly created element.
// The scale of the output element will depend on the scale of the input element and the constant (if the constant
// needs to be scaled (its rational part is not zero)). The constant can be a uint64, int64, float64 or complex128.
func (eval *evaluator) MultByConstNew(ct0 *rlwe.Ciphertext, constant interface{}) (ctOut *rlwe.Ciphertext) {
ctOut = NewCiphertext(eval.params, ct0.Degree(), ct0.Level())
eval.MultByConst(ct0, constant, ctOut)
return
}
// MultByConst multiplies ct0 by the input constant and returns the result in ctOut.
// The scale of the output element will depend on the scale of the input element and the constant (if the constant
// needs to be scaled (its rational part is not zero)). The constant can be a uint64, int64, float64 or complex128.
func (eval *evaluator) MultByConst(ct0 *rlwe.Ciphertext, constant interface{}, ctOut *rlwe.Ciphertext) {
var level = utils.MinInt(ct0.Level(), ctOut.Level())
cReal, cImag, scale := eval.getConstAndScale(level, constant)
// Component wise multiplication of the following vector with the ciphertext:
// [a + b*psi_qi^2, ....., a + b*psi_qi^2, a - b*psi_qi^2, ...., a - b*psi_qi^2] mod Qi
// [{ N/2 }{ N/2 }]
// Which is equivalent outside of the NTT domain to adding a to the first coefficient of ct0 and b to the N/2-th coefficient of ct0.
ringQ := eval.params.RingQ()
var scaledConst, scaledConstReal, scaledConstImag uint64
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
bredParams := ringQ.BredParams[i]
mredParams := ringQ.MredParams[i]
scaledConstReal = 0
scaledConstImag = 0
scaledConst = 0
if cReal != 0 {
scaledConstReal = scaleUpExact(cReal, scale, qi)
scaledConst = scaledConstReal
}
if cImag != 0 {
scaledConstImag = scaleUpExact(cImag, scale, qi)
scaledConstImag = ring.MRed(scaledConstImag, ringQ.NttPsi[i][1], qi, mredParams)
scaledConst = ring.CRed(scaledConst+scaledConstImag, qi)
}
scaledConst = ring.MForm(scaledConst, qi, bredParams)
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], scaledConst, qi, mredParams)
}
if cImag != 0 {
scaledConst = ring.CRed(scaledConstReal+(qi-scaledConstImag), qi)
scaledConst = ring.MForm(scaledConst, qi, bredParams)
}
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], scaledConst, qi, mredParams)
}
}
ctOut.MetaData = ct0.MetaData
ctOut.Scale = ct0.Scale.Mul(rlwe.NewScale(scale))
}
// MultByGaussianInteger multiples the ct0 by the gaussian integer cReal + i*cImag and returns the result on ctOut.
// Accepted types for cReal and cImag are uint64, int64 and big.Int.
func (eval *evaluator) MultByGaussianInteger(ct0 *rlwe.Ciphertext, cReal, cImag interface{}, ctOut *rlwe.Ciphertext) {
ringQ := eval.params.RingQ()
level := utils.MinInt(ct0.Level(), ctOut.Level())
var scaledConst, scaledConstReal, scaledConstImag uint64
ctOut.MetaData = ct0.MetaData
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
bredParams := ringQ.BredParams[i]
mredParams := ringQ.MredParams[i]
scaledConstReal = interfaceMod(cReal, qi)
if eval.params.RingType() != ring.ConjugateInvariant {
scaledConstImag = interfaceMod(cImag, qi)
}
scaledConst = scaledConstReal
if scaledConstImag != 0 {
scaledConstImag = ring.MRed(scaledConstImag, ringQ.NttPsi[i][1], qi, mredParams)
scaledConst = ring.CRed(scaledConst+scaledConstImag, qi)
}
scaledConst = ring.MForm(scaledConst, qi, bredParams)
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], scaledConst, qi, mredParams)
}
if cImag != 0 {
scaledConst = ring.CRed(scaledConstReal+(qi-scaledConstImag), qi)
scaledConst = ring.MForm(scaledConst, qi, bredParams)
}
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], scaledConst, qi, mredParams)
}
}
}
// MultByGaussianIntegerAndAdd multiples the ct0 by the gaussian integer cReal + i*cImag and adds the result on ctOut.
// Accepted types for cReal and cImag are uint64, int64 and big.Int.
func (eval *evaluator) MultByGaussianIntegerAndAdd(ct0 *rlwe.Ciphertext, cReal, cImag interface{}, ctOut *rlwe.Ciphertext) {
ringQ := eval.params.RingQ()
level := utils.MinInt(ct0.Level(), ctOut.Level())
var scaledConst, scaledConstReal, scaledConstImag uint64
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
bredParams := ringQ.BredParams[i]
mredParams := ringQ.MredParams[i]
scaledConstReal = interfaceMod(cReal, qi)
if eval.params.RingType() != ring.ConjugateInvariant {
scaledConstImag = interfaceMod(cImag, qi)
}
scaledConst = scaledConstReal
if scaledConstImag != 0 {
scaledConstImag = ring.MRed(scaledConstImag, ringQ.NttPsi[i][1], qi, mredParams)
scaledConst = ring.CRed(scaledConst+scaledConstImag, qi)
}
scaledConst = ring.MForm(scaledConst, qi, bredParams)
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryAndAddVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], scaledConst, qi, mredParams)
}
if cImag != 0 {
scaledConst = ring.CRed(scaledConstReal+(qi-scaledConstImag), qi)
scaledConst = ring.MForm(scaledConst, qi, bredParams)
}
for u := range ct0.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryAndAddVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], scaledConst, qi, mredParams)
}
}
}
// MultByiNew multiplies ct0 by the imaginary number i, and returns the result in a newly created element.
// It does not change the scale.
func (eval *evaluator) MultByiNew(ct0 *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext) {
if eval.params.RingType() == ring.ConjugateInvariant {
panic("cannot MultByiNew: method not supported when params.RingType() == ring.ConjugateInvariant")
}
ctOut = NewCiphertext(eval.params, 1, ct0.Level())
eval.MultByi(ct0, ctOut)
return ctOut
}
// MultByi multiplies ct0 by the imaginary number i, and returns the result in ctOut.
// It does not change the scale.
func (eval *evaluator) MultByi(ct0 *rlwe.Ciphertext, ctOut *rlwe.Ciphertext) {
if eval.params.RingType() == ring.ConjugateInvariant {
panic("cannot MultByi: method not supported when params.RingType() == ring.ConjugateInvariant")
}
var level = utils.MinInt(ct0.Level(), ctOut.Level())
ctOut.MetaData = ct0.MetaData
ringQ := eval.params.RingQ()
var imag uint64
// Equivalent to a product by the monomial x^(n/2) outside of the NTT domain
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
mredParams := ringQ.MredParams[i]
imag = ringQ.NttPsi[i][1] // Psi^2
for u := range ctOut.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], imag, qi, mredParams)
}
imag = qi - imag
for u := range ctOut.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], imag, qi, mredParams)
}
}
}
// DivByiNew multiplies ct0 by the imaginary number 1/i = -i, and returns the result in a newly created element.
// It does not change the scale.
func (eval *evaluator) DivByiNew(ct0 *rlwe.Ciphertext) (ctOut *rlwe.Ciphertext) {
if eval.params.RingType() == ring.ConjugateInvariant {
panic("cannot DivByiNew: method not supported when params.RingType() == ring.ConjugateInvariant")
}
ctOut = NewCiphertext(eval.params, 1, ct0.Level())
eval.DivByi(ct0, ctOut)
return
}
// DivByi multiplies ct0 by the imaginary number 1/i = -i, and returns the result in ctOut.
// It does not change the scale.
func (eval *evaluator) DivByi(ct0 *rlwe.Ciphertext, ctOut *rlwe.Ciphertext) {
if eval.params.RingType() == ring.ConjugateInvariant {
panic("cannot DivByi: method not supported when params.RingType() == ring.ConjugateInvariant")
}
var level = utils.MinInt(ct0.Level(), ctOut.Level())
ringQ := eval.params.RingQ()
ctOut.MetaData = ct0.MetaData
var imag uint64
// Equivalent to a product by the monomial x^(3*n/2) outside of the NTT domain
for i := 0; i < level+1; i++ {
qi := ringQ.Modulus[i]
mredParams := ringQ.MredParams[i]
imag = qi - ringQ.NttPsi[i][1] // -Psi^2
for u := range ctOut.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[:ringQ.N>>1], p1tmp[:ringQ.N>>1], imag, qi, mredParams)
}
imag = ringQ.NttPsi[i][1] // Psi^2
for u := range ctOut.Value {
p0tmp := ct0.Value[u].Coeffs[i]
p1tmp := ctOut.Value[u].Coeffs[i]
ring.MulScalarMontgomeryVec(p0tmp[ringQ.N>>1:], p1tmp[ringQ.N>>1:], imag, qi, mredParams)
}
}
}
// ScaleUpNew multiplies ct0 by 2^scale and sets its scale to its previous scale
// plus 2^n. It returns the result in a newly created element.
func (eval *evaluator) ScaleUpNew(ct0 *rlwe.Ciphertext, scale rlwe.Scale) (ctOut *rlwe.Ciphertext) {
ctOut = NewCiphertext(eval.params, ct0.Degree(), ct0.Level())
eval.ScaleUp(ct0, scale, ctOut)
return
}
// ScaleUp multiplies ct0 by 2^scale and sets its scale to its previous scale
// plus 2^n. It returns the result in ctOut.
func (eval *evaluator) ScaleUp(ct0 *rlwe.Ciphertext, scale rlwe.Scale, ctOut *rlwe.Ciphertext) {
eval.MultByConst(ct0, scale.Uint64(), ctOut)
ctOut.MetaData = ct0.MetaData
ctOut.Scale = ct0.Scale.Mul(scale)
}
// SetScale sets the scale of the ciphertext to the input scale (consumes a level)
func (eval *evaluator) SetScale(ct *rlwe.Ciphertext, scale rlwe.Scale) {
eval.MultByConst(ct, scale.Float64()/ct.Scale.Float64(), ct)
if err := eval.Rescale(ct, scale, ct); err != nil {
panic(err)
}
ct.Scale = scale
}
// DropLevelNew reduces the level of ct0 by levels and returns the result in a newly created element.
// No rescaling is applied during this procedure.
func (eval *evaluator) DropLevelNew(ct0 *rlwe.Ciphertext, levels int) (ctOut *rlwe.Ciphertext) {
ctOut = ct0.CopyNew()
eval.DropLevel(ctOut, levels)
return
}
// DropLevel reduces the level of ct0 by levels and returns the result in ct0.
// No rescaling is applied during this procedure.
func (eval *evaluator) DropLevel(ct0 *rlwe.Ciphertext, levels int) {
ct0.Resize(ct0.Degree(), ct0.Level()-levels)
}
// RescaleNew divides ct0 by the last modulus in the moduli chain, and repeats this
// procedure (consuming one level each time) until the scale reaches the original scale or before it goes below it, and returns the result
// in a newly created element. Since all the moduli in the moduli chain are generated to be close to the
// original scale, this procedure is equivalent to dividing the input element by the scale and adding
// some error.
// Returns an error if "threshold <= 0", ct.scale = 0, ct.Level() = 0, ct.IsNTT() != true
func (eval *evaluator) RescaleNew(ct0 *rlwe.Ciphertext, minScale rlwe.Scale) (ctOut *rlwe.Ciphertext, err error) {
ctOut = NewCiphertext(eval.params, ct0.Degree(), ct0.Level())
return ctOut, eval.Rescale(ct0, minScale, ctOut)
}
// Rescale divides ct0 by the last modulus in the moduli chain, and repeats this
// procedure (consuming one level each time) until the scale reaches the original scale or before it goes below it, and returns the result
// in ctOut. Since all the moduli in the moduli chain are generated to be close to the
// original scale, this procedure is equivalent to dividing the input element by the scale and adding
// some error.
// Returns an error if "minScale <= 0", ct.scale = 0, ct.Level() = 0, ct.IsNTT() != true or if ct.Leve() != ctOut.Level()
func (eval *evaluator) Rescale(ctIn *rlwe.Ciphertext, minScale rlwe.Scale, ctOut *rlwe.Ciphertext) (err error) {
ringQ := eval.params.RingQ()
if minScale.Cmp(rlwe.NewScale(0)) != 1 {
return errors.New("cannot Rescale: minScale is <0")
}
minScale = minScale.Div(rlwe.NewScale(2))
if ctIn.Scale.Cmp(rlwe.NewScale(0)) != 1 {
return errors.New("cannot Rescale: ciphertext scale is <0")
}
if ctIn.Level() == 0 {
return errors.New("cannot Rescale: input Ciphertext already at level 0")
}
if ctOut.Degree() != ctIn.Degree() {
return errors.New("cannot Rescale: ctIn.Degree() != ctOut.Degree()")
}
ctOut.MetaData = ctIn.MetaData
currentLevel := ctIn.Level()
// Divides the scale by each moduli of the modulus chain as long as the scale isn't smaller than minScale/2
// or until the output Level() would be zero
var nbRescales int
for currentLevel >= 0 {
scale := ctOut.Scale.Div(rlwe.NewScale(ringQ.Modulus[currentLevel]))