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evaluator_automorphism.go
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/
evaluator_automorphism.go
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package rlwe
import (
"fmt"
"github.com/fedejinich/lattigo/v6/ring"
"github.com/fedejinich/lattigo/v6/rlwe/ringqp"
"github.com/fedejinich/lattigo/v6/utils"
)
// Automorphism computes phi(ct), where phi is the map X -> X^galEl. The method requires
// that the corresponding RotationKey has been added to the Evaluator. The method will
// panic if either ctIn or ctOut degree is not equal to 1.
func (eval *Evaluator) Automorphism(ctIn *Ciphertext, galEl uint64, ctOut *Ciphertext) {
if ctIn.Degree() != 1 || ctOut.Degree() != 1 {
panic("cannot apply Automorphism: input and output Ciphertext must be of degree 1")
}
if galEl == 1 {
if ctOut != ctIn {
ctOut.Copy(ctIn)
}
return
}
rtk, generated := eval.Rtks.GetRotationKey(galEl)
if !generated {
panic(fmt.Sprintf("cannot apply Automorphism: galEl key 5^%d missing", eval.params.RotationFromGaloisElement(eval.params.InverseGaloisElement(galEl))))
}
level := utils.MinInt(ctIn.Level(), ctOut.Level())
ctOut.Resize(ctOut.Degree(), level)
ringQ := eval.params.RingQ().AtLevel(level)
ctTmp := &Ciphertext{Value: []*ring.Poly{eval.BuffQP[1].Q, eval.BuffQP[2].Q}}
ctTmp.IsNTT = ctIn.IsNTT
eval.GadgetProduct(level, ctIn.Value[1], rtk.GadgetCiphertext, ctTmp)
ringQ.Add(eval.BuffQP[1].Q, ctIn.Value[0], eval.BuffQP[1].Q)
if ctIn.IsNTT {
ringQ.PermuteNTTWithIndex(eval.BuffQP[1].Q, eval.PermuteNTTIndex[galEl], ctOut.Value[0])
ringQ.PermuteNTTWithIndex(eval.BuffQP[2].Q, eval.PermuteNTTIndex[galEl], ctOut.Value[1])
} else {
ringQ.Permute(eval.BuffQP[1].Q, galEl, ctOut.Value[0])
ringQ.Permute(eval.BuffQP[2].Q, galEl, ctOut.Value[1])
}
ctOut.MetaData = ctIn.MetaData
}
// AutomorphismHoisted is similar to Automorphism, except that it takes as input ctIn and c1DecompQP, where c1DecompQP is the RNS
// decomposition of its element of degree 1. This decomposition can be obtained with DecomposeNTT.
// The method requires that the corresponding RotationKey has been added to the Evaluator.
// The method will panic if either ctIn or ctOut degree is not equal to 1.
func (eval *Evaluator) AutomorphismHoisted(level int, ctIn *Ciphertext, c1DecompQP []ringqp.Poly, galEl uint64, ctOut *Ciphertext) {
if ctIn.Degree() != 1 || ctOut.Degree() != 1 {
panic("cannot apply AutomorphismHoisted: input and output Ciphertext must be of degree 1")
}
if galEl == 1 {
if ctIn != ctOut {
ctOut.Copy(ctIn)
}
return
}
rtk, generated := eval.Rtks.GetRotationKey(galEl)
if !generated {
panic(fmt.Sprintf("cannot apply AutomorphismHoisted: galEl key 5^%d missing", eval.params.RotationFromGaloisElement(eval.params.InverseGaloisElement(galEl))))
}
ringQ := eval.params.RingQ().AtLevel(level)
eval.KeyswitchHoisted(level, c1DecompQP, rtk, eval.BuffQP[0].Q, eval.BuffQP[1].Q, eval.BuffQP[0].P, eval.BuffQP[1].P)
ringQ.Add(eval.BuffQP[0].Q, ctIn.Value[0], eval.BuffQP[0].Q)
if ctIn.IsNTT {
ringQ.PermuteNTTWithIndex(eval.BuffQP[0].Q, eval.PermuteNTTIndex[galEl], ctOut.Value[0])
ringQ.PermuteNTTWithIndex(eval.BuffQP[1].Q, eval.PermuteNTTIndex[galEl], ctOut.Value[1])
} else {
ringQ.Permute(eval.BuffQP[0].Q, galEl, ctOut.Value[0])
ringQ.Permute(eval.BuffQP[1].Q, galEl, ctOut.Value[1])
}
ctOut.Resize(ctOut.Degree(), level)
ctOut.Scale = ctIn.Scale
}
// AutomorphismHoistedLazy is similar to AutomorphismHoisted, except that it returns a ciphertext modulo QP and scaled by P.
// The method requires that the corresponding RotationKey has been added to the Evaluator.
// Requires that the NTT domain of c0 and ctQP are the same.
func (eval *Evaluator) AutomorphismHoistedLazy(levelQ int, c0 *ring.Poly, c1DecompQP []ringqp.Poly, galEl uint64, ctQP CiphertextQP) {
rtk, generated := eval.Rtks.GetRotationKey(galEl)
if !generated {
panic(fmt.Sprintf("cannot AutomorphismHoistedLazy: galEl key 5^%d missing", eval.params.RotationFromGaloisElement(eval.params.InverseGaloisElement(galEl))))
}
levelP := rtk.LevelP()
eval.KeyswitchHoistedLazy(levelQ, c1DecompQP, rtk, eval.BuffQP[0].Q, eval.BuffQP[1].Q, eval.BuffQP[0].P, eval.BuffQP[1].P)
ringQ := eval.params.RingQ().AtLevel(levelQ)
ringP := eval.params.RingP().AtLevel(levelP)
if ctQP.IsNTT {
index := eval.PermuteNTTIndex[galEl]
ringQ.PermuteNTTWithIndex(eval.BuffQP[1].Q, index, ctQP.Value[1].Q)
ringP.PermuteNTTWithIndex(eval.BuffQP[1].P, index, ctQP.Value[1].P)
if levelP > -1 {
ringQ.MulScalarBigint(c0, ringP.ModulusAtLevel[levelP], eval.BuffQP[1].Q)
}
ringQ.Add(eval.BuffQP[0].Q, eval.BuffQP[1].Q, eval.BuffQP[0].Q)
ringQ.PermuteNTTWithIndex(eval.BuffQP[0].Q, index, ctQP.Value[0].Q)
ringP.PermuteNTTWithIndex(eval.BuffQP[0].P, index, ctQP.Value[0].P)
} else {
ringQ.Permute(eval.BuffQP[1].Q, galEl, ctQP.Value[1].Q)
ringP.Permute(eval.BuffQP[1].P, galEl, ctQP.Value[1].P)
if levelP > -1 {
ringQ.MulScalarBigint(c0, ringP.ModulusAtLevel[levelP], eval.BuffQP[1].Q)
}
ringQ.Add(eval.BuffQP[0].Q, eval.BuffQP[1].Q, eval.BuffQP[0].Q)
ringQ.Permute(eval.BuffQP[0].Q, galEl, ctQP.Value[0].Q)
ringP.Permute(eval.BuffQP[0].P, galEl, ctQP.Value[0].P)
}
}
// Trace maps X -> sum((-1)^i * X^{i*n+1}) for n <= i < N
// Monomial X^k vanishes if k is not divisible by (N/n), otherwise it is multiplied by (N/n).
// Ciphertext is pre-multiplied by (N/n)^-1 to remove the (N/n) factor.
// Examples of full Trace for [0 + 1X + 2X^2 + 3X^3 + 4X^4 + 5X^5 + 6X^6 + 7X^7]
//
// 1.
//
// [1 + 2X + 3X^2 + 4X^3 + 5X^4 + 6X^5 + 7X^6 + 8X^7]
// + [1 - 6X - 3X^2 + 8X^3 + 5X^4 + 2X^5 - 7X^6 - 4X^7] {X-> X^(i * 5^1)}
// = [2 - 4X + 0X^2 +12X^3 +10X^4 + 8X^5 - 0X^6 + 4X^7]
//
// 2.
//
// [2 - 4X + 0X^2 +12X^3 +10X^4 + 8X^5 - 0X^6 + 4X^7]
// + [2 + 4X + 0X^2 -12X^3 +10X^4 - 8X^5 + 0X^6 - 4X^7] {X-> X^(i * 5^2)}
// = [4 + 0X + 0X^2 - 0X^3 +20X^4 + 0X^5 + 0X^6 - 0X^7]
//
// 3.
//
// [4 + 0X + 0X^2 - 0X^3 +20X^4 + 0X^5 + 0X^6 - 0X^7]
// + [4 + 0X + 0X^2 - 0X^3 -20X^4 + 0X^5 + 0X^6 - 0X^7] {X-> X^(i * -1)}
// = [8 + 0X + 0X^2 - 0X^3 + 0X^4 + 0X^5 + 0X^6 - 0X^7]
func (eval *Evaluator) Trace(ctIn *Ciphertext, logN int, ctOut *Ciphertext) {
if ctIn.Degree() != 1 || ctOut.Degree() != 1 {
panic("ctIn.Degree() != 1 or ctOut.Degree() != 1")
}
levelQ := utils.MinInt(ctIn.Level(), ctOut.Level())
ctOut.Resize(ctOut.Degree(), levelQ)
ctOut.MetaData = ctIn.MetaData
gap := 1 << (eval.params.LogN() - logN - 1)
if logN == 0 {
gap <<= 1
}
if gap > 1 {
ringQ := eval.params.RingQ().AtLevel(levelQ)
// pre-multiplication by (N/n)^-1
for i, s := range ringQ.SubRings[:levelQ+1] {
NInv := ring.MForm(ring.ModExp(uint64(gap), s.Modulus-2, s.Modulus), s.Modulus, s.BRedConstant)
s.MulScalarMontgomery(ctIn.Value[0].Coeffs[i], NInv, ctOut.Value[0].Coeffs[i])
s.MulScalarMontgomery(ctIn.Value[1].Coeffs[i], NInv, ctOut.Value[1].Coeffs[i])
}
buff := NewCiphertextAtLevelFromPoly(levelQ, []*ring.Poly{eval.BuffQP[3].Q, eval.BuffQP[4].Q})
buff.IsNTT = ctIn.IsNTT
for i := logN; i < eval.params.LogN()-1; i++ {
eval.Automorphism(ctOut, eval.params.GaloisElementForColumnRotationBy(1<<i), buff)
ringQ.Add(ctOut.Value[0], buff.Value[0], ctOut.Value[0])
ringQ.Add(ctOut.Value[1], buff.Value[1], ctOut.Value[1])
}
if logN == 0 {
eval.Automorphism(ctOut, ringQ.NthRoot()-1, buff)
ringQ.Add(ctOut.Value[0], buff.Value[0], ctOut.Value[0])
ringQ.Add(ctOut.Value[1], buff.Value[1], ctOut.Value[1])
}
} else {
if ctIn != ctOut {
ctOut.Copy(ctIn)
}
}
}