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Published: Nov 15, 2023 License: Apache-2.0 Imports: 8 Imported by: 0

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Constants

View Source
const (
	CoeffsToSlots = LinearTransformType(0) // Homomorphic Encoding
	SlotsToCoeffs = LinearTransformType(1) // Homomorphic Decoding
)

CoeffsToSlots and SlotsToCoeffs are two linear transformations.

View Source
const (
	Sin  = SineType(0) // Standard Chebyshev approximation of (1/2pi) * sin(2pix)
	Cos1 = SineType(1) // Special approximation (Han and Ki) of pow((1/2pi), 1/2^r) * cos(2pi(x-0.25)/2^r); this method requires a minimum degree of 2*(K-1).
	Cos2 = SineType(2) // Standard Chebyshev approximation of pow((1/2pi), 1/2^r) * cos(2pi(x-0.25)/2^r)
)

Sin and Cos are the two proposed functions for SineType

Variables

This section is empty.

Functions

func ApproximateCos

func ApproximateCos(K, degree int, dev float64, scnum int) []complex128

ApproximateCos computes a polynomial approximation of degree "degree" in Chevyshev basis of the function cos(2*pi*x/2^"scnum") in the range -"K" to "K" The nodes of the Chevyshev approximation are are located from -dev to +dev at each integer value between -K and -K

func BigintCos

func BigintCos(x *big.Float) (cosx *big.Float)

BigintCos is an iterative arbitrary precision computation of Cos(x) Iterative process with an error of ~10^{−0.60206*k} after k iterations. ref : Johansson, B. Tomas, An elementary algorithm to evaluate trigonometric functions to high precision, 2018

func BigintSin

func BigintSin(x *big.Float) (sinx *big.Float)

BigintSin is an iterative arbitrary precision computation of Sin(x)

func NewFloat

func NewFloat(x float64) (y *big.Float)

NewFloat creates a new big.Float element with 1000 bits of precision

Types

type EncodingMatrix

type EncodingMatrix struct {
	EncodingMatrixLiteral
	// contains filtered or unexported fields
}

EncodingMatrix is a struct storing the factorized DFT matrix

func NewHomomorphicEncodingMatrixFromLiteral

func NewHomomorphicEncodingMatrixFromLiteral(mParams EncodingMatrixLiteral, encoder ckks.Encoder) EncodingMatrix

NewHomomorphicEncodingMatrixFromLiteral generates the factorized encoding matrix. scaling : constant by witch the all the matrices will be multuplied by. encoder : ckks.Encoder.

type EncodingMatrixLiteral

type EncodingMatrixLiteral struct {
	LinearTransformType LinearTransformType
	LogN                int     // log(RingDegree)
	LogSlots            int     // log(slots)
	Scaling             float64 // constant by which the matrix is multiplied with
	LevelStart          int     // Encoding level
	BitReversed         bool    // Flag for bit-reverseed input to the DFT (with bit-reversed output), by default false.
	BSGSRatio           float64 // n1/n2 ratio for the bsgs algo for matrix x vector eval
	ScalingFactor       [][]float64
}

EncodingMatrixLiteral is a struct storing the parameters to generate the factorized DFT matrix.

func (*EncodingMatrixLiteral) Depth

func (mParams *EncodingMatrixLiteral) Depth(actual bool) (depth int)

Depth returns the number of levels allocated. If actual == true then returns the number of moduli consumed, else returns the factorization depth.

func (*EncodingMatrixLiteral) Levels

func (mParams *EncodingMatrixLiteral) Levels() (levels []int)

Levels returns the index of the Qi used int CoeffsToSlots.

func (*EncodingMatrixLiteral) MarshalBinary

func (mParams *EncodingMatrixLiteral) MarshalBinary() (data []byte, err error)

MarshalBinary encode the target EncodingMatrixParameters on a slice of bytes.

func (*EncodingMatrixLiteral) Rotations

func (mParams *EncodingMatrixLiteral) Rotations(logN, logSlots int) (rotations []int)

Rotations returns the list of rotations performed during the CoeffsToSlot operation.

func (*EncodingMatrixLiteral) UnmarshalBinary

func (mParams *EncodingMatrixLiteral) UnmarshalBinary(data []byte) error

UnmarshalBinary decodes a slice of bytes on the target EncodingMatrixParameters.

type EvalModLiteral

type EvalModLiteral struct {
	Q             uint64   // Q to reduce by during EvalMod
	LevelStart    int      // Starting level of EvalMod
	ScalingFactor float64  // Scaling factor used during EvalMod
	SineType      SineType // Chose betwenn [Sin(2*pi*x)] or [cos(2*pi*x/r) with double angle formula]
	MessageRatio  float64  // Ratio between Q0 and m, i.e. Q[0]/|m|
	K             int      // K parameter (interpolation in the range -K to K)
	SineDeg       int      // Degree of the interpolation
	DoubleAngle   int      // Number of rescale and double angle formula (only applies for cos)
	ArcSineDeg    int      // Degree of the Taylor arcsine composed with f(2*pi*x) (if zero then not used)
}

EvalModLiteral a struct for the paramters of the EvalMod step of the bootstrapping

func (*EvalModLiteral) Depth

func (evm *EvalModLiteral) Depth() (depth int)

Depth returns the depth of the SineEval. If true, then also counts the double angle formula.

func (*EvalModLiteral) MarshalBinary

func (evmParams *EvalModLiteral) MarshalBinary() (data []byte, err error)

MarshalBinary encode the target EvalModParameters on a slice of bytes.

func (*EvalModLiteral) QDiff

func (evm *EvalModLiteral) QDiff() float64

QDiff return Q/ClosestedPow2 This is the error introduced by the approximate division by Q

func (*EvalModLiteral) UnmarshalBinary

func (evmParams *EvalModLiteral) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a slice of bytes on the target EvalModParameters.

type EvalModPoly

type EvalModPoly struct {
	// contains filtered or unexported fields
}

EvalModPoly is a struct storing the EvalModLiteral with the polynomials.

func NewEvalModPolyFromLiteral

func NewEvalModPolyFromLiteral(evm EvalModLiteral) EvalModPoly

NewEvalModPolyFromLiteral generates an EvalModPoly fromt the EvalModLiteral.

func (*EvalModPoly) A

func (evp *EvalModPoly) A() float64

A returns the left bound of the sine approximation (scaled by 1/2^r).

func (*EvalModPoly) B

func (evp *EvalModPoly) B() float64

B returns the right bound of the sine approximation (scaled by 1/2^r).

func (*EvalModPoly) K

func (evp *EvalModPoly) K() float64

K return the sine approximation range.

func (*EvalModPoly) LevelStart

func (evp *EvalModPoly) LevelStart() int

LevelStart returns the starting level of the EvalMod.

func (*EvalModPoly) MessageRatio

func (evp *EvalModPoly) MessageRatio() float64

MessageRatio returns the pre-set ratio Q[0]/|m|.

func (*EvalModPoly) QDiff

func (evp *EvalModPoly) QDiff() float64

QDiff return Q/ClosestedPow2 This is the error introduced by the approximate division by Q.

func (*EvalModPoly) ScFac

func (evp *EvalModPoly) ScFac() float64

ScFac returns 1/2^r where r is the number of double angle evaluation.

func (*EvalModPoly) ScalingFactor

func (evp *EvalModPoly) ScalingFactor() float64

ScalingFactor returns scaling factor used during the EvalMod.

type Evaluator

type Evaluator interface {
	Add(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	AddNoMod(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	AddNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	AddNoModNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	Sub(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	SubNoMod(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	SubNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	SubNoModNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	Neg(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext)
	NegNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	AddConstNew(ctIn *ckks.Ciphertext, constant interface{}) (ctOut *ckks.Ciphertext)
	AddConst(ctIn *ckks.Ciphertext, constant interface{}, ctOut *ckks.Ciphertext)
	MultByConstNew(ctIn *ckks.Ciphertext, constant interface{}) (ctOut *ckks.Ciphertext)
	MultByConst(ctIn *ckks.Ciphertext, constant interface{}, ctOut *ckks.Ciphertext)
	MultByGaussianInteger(ctIn *ckks.Ciphertext, cReal, cImag interface{}, ctOut *ckks.Ciphertext)
	MultByConstAndAdd(ctIn *ckks.Ciphertext, constant interface{}, ctOut *ckks.Ciphertext)
	MultByGaussianIntegerAndAdd(ctIn *ckks.Ciphertext, cReal, cImag interface{}, ctOut *ckks.Ciphertext)
	MultByiNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	MultByi(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext)
	DivByiNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	DivByi(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext)
	ConjugateNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	Conjugate(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext)
	Mul(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	MulNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	MulRelin(op0, op1 ckks.Operand, ctOut *ckks.Ciphertext)
	MulRelinNew(op0, op1 ckks.Operand) (ctOut *ckks.Ciphertext)
	RotateNew(ctIn *ckks.Ciphertext, k int) (ctOut *ckks.Ciphertext)
	Rotate(ctIn *ckks.Ciphertext, k int, ctOut *ckks.Ciphertext)
	RotateHoistedNew(ctIn *ckks.Ciphertext, rotations []int) (ctOut map[int]*ckks.Ciphertext)
	RotateHoisted(ctIn *ckks.Ciphertext, rotations []int, ctOut map[int]*ckks.Ciphertext)
	MulByPow2New(ctIn *ckks.Ciphertext, pow2 int) (ctOut *ckks.Ciphertext)
	MulByPow2(ctIn *ckks.Ciphertext, pow2 int, ctOut *ckks.Ciphertext)
	PowerOf2(ctIn *ckks.Ciphertext, logPow2 int, ctOut *ckks.Ciphertext)
	Power(ctIn *ckks.Ciphertext, degree int, ctOut *ckks.Ciphertext)
	PowerNew(ctIn *ckks.Ciphertext, degree int) (ctOut *ckks.Ciphertext)
	EvaluatePoly(ctIn *ckks.Ciphertext, pol *ckks.Polynomial, targetScale float64) (ctOut *ckks.Ciphertext, err error)
	EvaluatePolyVector(ctIn *ckks.Ciphertext, pols []*ckks.Polynomial, encoder ckks.Encoder, slotIndex map[int][]int, targetScale float64) (ctOut *ckks.Ciphertext, err error)
	InverseNew(ctIn *ckks.Ciphertext, steps int) (ctOut *ckks.Ciphertext)
	LinearTransformNew(ctIn *ckks.Ciphertext, linearTransform interface{}) (ctOut []*ckks.Ciphertext)
	LinearTransform(ctIn *ckks.Ciphertext, linearTransform interface{}, ctOut []*ckks.Ciphertext)
	MultiplyByDiagMatrix(ctIn *ckks.Ciphertext, matrix ckks.LinearTransform, c2DecompQP []rlwe.PolyQP, ctOut *ckks.Ciphertext)
	MultiplyByDiagMatrixBSGS(ctIn *ckks.Ciphertext, matrix ckks.LinearTransform, c2DecompQP []rlwe.PolyQP, ctOut *ckks.Ciphertext)
	InnerSumLog(ctIn *ckks.Ciphertext, batch, n int, ctOut *ckks.Ciphertext)
	InnerSum(ctIn *ckks.Ciphertext, batch, n int, ctOut *ckks.Ciphertext)
	ReplicateLog(ctIn *ckks.Ciphertext, batch, n int, ctOut *ckks.Ciphertext)
	Replicate(ctIn *ckks.Ciphertext, batch, n int, ctOut *ckks.Ciphertext)
	TraceNew(ctIn *ckks.Ciphertext, logSlotsStart, logSlotsEnd int) *ckks.Ciphertext
	Trace(ctIn *ckks.Ciphertext, logSlotsStart, logSlotsEnd int, ctOut *ckks.Ciphertext)
	SwitchKeysNew(ctIn *ckks.Ciphertext, switchingKey *rlwe.SwitchingKey) (ctOut *ckks.Ciphertext)
	SwitchKeys(ctIn *ckks.Ciphertext, switchingKey *rlwe.SwitchingKey, ctOut *ckks.Ciphertext)
	RelinearizeNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	Relinearize(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext)
	ScaleUpNew(ctIn *ckks.Ciphertext, scale float64) (ctOut *ckks.Ciphertext)
	ScaleUp(ctIn *ckks.Ciphertext, scale float64, ctOut *ckks.Ciphertext)
	SetScale(ctIn *ckks.Ciphertext, scale float64)
	Rescale(ctIn *ckks.Ciphertext, minScale float64, ctOut *ckks.Ciphertext) (err error)
	DropLevelNew(ctIn *ckks.Ciphertext, levels int) (ctOut *ckks.Ciphertext)
	DropLevel(ctIn *ckks.Ciphertext, levels int)
	ReduceNew(ctIn *ckks.Ciphertext) (ctOut *ckks.Ciphertext)
	Reduce(ctIn *ckks.Ciphertext, ctOut *ckks.Ciphertext) error

	CoeffsToSlotsNew(ctIn *ckks.Ciphertext, ctsMatrices EncodingMatrix) (ctReal, ctImag *ckks.Ciphertext)
	CoeffsToSlots(ctIn *ckks.Ciphertext, ctsMatrices EncodingMatrix, ctReal, ctImag *ckks.Ciphertext)
	SlotsToCoeffsNew(ctReal, ctImag *ckks.Ciphertext, stcMatrices EncodingMatrix) (ctOut *ckks.Ciphertext)
	SlotsToCoeffs(ctReal, ctImag *ckks.Ciphertext, stcMatrices EncodingMatrix, ctOut *ckks.Ciphertext)
	EvalModNew(ctIn *ckks.Ciphertext, evalModPoly EvalModPoly) (ctOut *ckks.Ciphertext)

	GetKeySwitcher() *rlwe.KeySwitcher
	PoolQMul() [3]*ring.Poly
	CtxPool() *ckks.Ciphertext
	ShallowCopy() Evaluator
	WithKey(rlwe.EvaluationKey) Evaluator
}

Evaluator is an interface embeding the ckks.Evaluator interface with additional advanced arithmetic features.

func NewEvaluator

func NewEvaluator(params ckks.Parameters, evaluationKey rlwe.EvaluationKey) Evaluator

NewEvaluator creates a new Evaluator.

type LinearTransformType

type LinearTransformType int

LinearTransformType is a type used to distinguish different linear transformations.

type SineType

type SineType uint64

SineType is the type of function used during the bootstrapping for the homomorphic modular reduction

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