rlwe

package
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 Go to latest Published: Aug 10, 2023 License: Apache-2.0 Imports: 10 Imported by: 0

Documentation

Overview

Package rlwe implements the generic operations that are common to R-LWE schemes. The other implemented schemes extend this package with their specific operations and structures.

Index

Constants

View Source 
const DefaultSigma = 3.2

DefaultSigma is the default error distribution standard deviation

View Source 
const GaloisGen uint64 = ring.GaloisGen

GaloisGen is an integer of order N=2^d modulo M=2N and that spans Z_M with the integer -1. The j-th ring automorphism takes the root zeta to zeta^(5j).

View Source 
const MaxLogN = 17

MaxLogN is the log2 of the largest supported polynomial modulus degree.

View Source 
const MaxModuliCount = 34

MaxModuliCount is the largest supported number of moduli in the RNS representation.

View Source 
const MaxModuliSize = 60

MaxModuliSize is the largest bit-length supported for the moduli in the RNS representation.

View Source 
const MinLogN = 4

MinLogN is the log2 of the smallest supported polynomial modulus degree (needed to ensure the NTT correctness).

Variables

View Source 
var (

	// TestPN10QP27 is a set of default parameters with logN=10 and logQP=27
	TestPN10QP27 = ParametersLiteral{
		LogN:     10,
		Q:        []uint64{0x7fff801},
		Pow2Base: 2,
	}

	// TestPN11QP54 is a set of default parameters with logN=11 and logQP=54
	TestPN11QP54 = ParametersLiteral{
		LogN:     11,
		Q:        []uint64{0x15400000001},
		P:        []uint64{0x3001},
		Pow2Base: 14,
	}
	// TestPN12QP109 is a set of default parameters with logN=12 and logQP=109
	TestPN12QP109 = ParametersLiteral{
		LogN:     12,
		Q:        []uint64{0x7ffffffec001, 0x400000008001},
		P:        []uint64{0xa001},
		Pow2Base: 16,
	}
	// TestPN13QP218 is a set of default parameters with logN=13 and logQP=218
	TestPN13QP218 = ParametersLiteral{
		LogN: 13,
		Q:    []uint64{0x3fffffffef8001, 0x4000000011c001, 0x40000000120001},
		P:    []uint64{0x7ffffffffb4001},
	}

	// TestPN14QP438 is a set of default parameters with logN=14 and logQP=438
	TestPN14QP438 = ParametersLiteral{
		LogN: 14,
		Q: []uint64{0x100000000060001, 0x80000000068001, 0x80000000080001,
			0x3fffffffef8001, 0x40000000120001, 0x3fffffffeb8001},
		P: []uint64{0x80000000130001, 0x7fffffffe90001},
	}

	// TestPN15QP880 is a set of default parameters with logN=15 and logQP=880
	TestPN15QP880 = ParametersLiteral{
		LogN: 15,
		Q: []uint64{0x7ffffffffe70001, 0x7ffffffffe10001, 0x7ffffffffcc0001,
			0x400000000270001, 0x400000000350001, 0x400000000360001,
			0x3ffffffffc10001, 0x3ffffffffbe0001, 0x3ffffffffbd0001,
			0x4000000004d0001, 0x400000000570001, 0x400000000660001},
		P: []uint64{0xffffffffffc0001, 0x10000000001d0001, 0x10000000006e0001},
	}

	// TestPN16QP240 is a set of default parameters with logN=16 and logQP=240
	TestPN16QP240 = ParametersLiteral{
		LogN: 16,
		LogQ: []int{60, 60, 60},
		LogP: []int{60},
	}

	// TestPN17QP360 is a set of default parameters with logN=17 and logQP=360
	TestPN17QP360 = ParametersLiteral{
		LogN: 17,
		LogQ: []int{60, 60, 60, 60},
		LogP: []int{60, 60},
	}

	DefaultParams = []ParametersLiteral{TestPN10QP27, TestPN11QP54, TestPN12QP109, TestPN13QP218, TestPN14QP438, TestPN15QP880, TestPN16QP240, TestPN17QP360}
)

Functions

func AddPolyTimesGadgetVectorToGadgetCiphertext 

func AddPolyTimesGadgetVectorToGadgetCiphertext(pt *ring.Poly, cts []GadgetCiphertext, ringQP ringqp.Ring, logbase2 int, buff *ring.Poly)

AddPolyTimesGadgetVectorToGadgetCiphertext takes a plaintext polynomial and a list of Ciphertexts and adds the plaintext times the RNS and BIT decomposition to the i-th element of the i-th Ciphertexts. This method panics if len(cts) > 2.

func AddPolyToGadgetMatrix 

func AddPolyToGadgetMatrix(pt *ring.Poly, gm [][]ringqp.Poly, ringQP ringqp.Ring, logbase2 int, buff *ring.Poly)

AddPolyToGadgetMatrix takes a plaintext polynomial and a list of ringqp.Poly and adds the plaintext times the RNS and BIT decomposition to the list of ringqp.Poly.

func CheckModuli 

func CheckModuli(q, p []uint64) error

CheckModuli checks that the provided q and p correspond to a valid moduli chain.

func GenModuli 

func GenModuli(logN int, logQ, logP []int) (q, p []uint64, err error)

GenModuli generates a valid moduli chain from the provided moduli sizes.

func PopulateElementRandom 

func PopulateElementRandom(prng utils.PRNG, params Parameters, el *Ciphertext)

PopulateElementRandom creates a new rlwe.Element with random coefficients

func PublicKeyIsCorrect 

func PublicKeyIsCorrect(pk *PublicKey, sk *SecretKey, params Parameters, log2Bound int) bool

PublicKeyIsCorrect returns true if pk is a correct RLWE public-key for secret-key sk and parameters params.

func RelinearizationKeyIsCorrect 

func RelinearizationKeyIsCorrect(rlk *SwitchingKey, skIdeal *SecretKey, params Parameters, log2Bound int) bool

RelinearizationKeyIsCorrect returns true if swk is a correct RLWE relinearization-key for secret-key sk and parameters params.

func RotationKeyIsCorrect 

func RotationKeyIsCorrect(swk *SwitchingKey, galEl uint64, skIdeal *SecretKey, params Parameters, log2Bound int) bool

RotationKeyIsCorrect returns true if swk is a correct RLWE switching-key for galois element galEl, secret-key sk and parameters params.

func SwitchCiphertextRingDegree 

func SwitchCiphertextRingDegree(ctIn *Ciphertext, ctOut *Ciphertext)

SwitchCiphertextRingDegree changes the ring degree of ctIn to the one of ctOut. Maps Y^{N/n} -> X^{N} or X^{N} -> Y^{N/n}. If the ring degree of ctOut is larger than the one of ctIn, then the ringQ of ctIn must be provided (else a nil pointer).

func SwitchCiphertextRingDegreeNTT 

func SwitchCiphertextRingDegreeNTT(ctIn *Ciphertext, ringQSmallDim, ringQLargeDim *ring.Ring, ctOut *Ciphertext)

SwitchCiphertextRingDegreeNTT changes the ring degree of ctIn to the one of ctOut. Maps Y^{N/n} -> X^{N} or X^{N} -> Y^{N/n}. If the ring degree of ctOut is larger than the one of ctIn, then the ringQ of ctIn must be provided (else a nil pointer). The ctIn must be in the NTT domain and ctOut will be in the NTT domain.

func SwitchingKeyIsCorrect 

func SwitchingKeyIsCorrect(swk *SwitchingKey, skIn, skOut *SecretKey, params Parameters, log2Bound int) bool

SwitchingKeyIsCorrect returns true if swk is a correct RLWE switching-key for input key skIn, output key skOut and parameters params.

Types

type AdditiveShare 

type AdditiveShare struct {
	Value ring.Poly
}

AdditiveShare is a type for storing additively shared values in Z_Q[X] (RNS domain)

func NewAdditiveShare 

func NewAdditiveShare(params Parameters) *AdditiveShare

NewAdditiveShare instantiates a new additive share struct for the ring defined by the given parameters at maximum level.

func NewAdditiveShareAtLevel 

func NewAdditiveShareAtLevel(params Parameters, level int) *AdditiveShare

NewAdditiveShareAtLevel instantiates a new additive share struct for the ring defined by the given parameters at level `level`.

type AdditiveShareBigint 

type AdditiveShareBigint struct {
	Value []*big.Int
}

AdditiveShareBigint is a type for storing additively shared values in Z (positional domain)

func NewAdditiveShareBigint 

func NewAdditiveShareBigint(params Parameters, n int) *AdditiveShareBigint

NewAdditiveShareBigint instantiates a new additive share struct composed of "n" big.Int elements

type Ciphertext 

type Ciphertext struct {
	Value []*ring.Poly
}

Ciphertext is a generic type for RLWE ciphertexts.

func GetSmallestLargest 

func GetSmallestLargest(el0, el1 *Ciphertext) (smallest, largest *Ciphertext, sameDegree bool)

GetSmallestLargest returns the provided element that has the smallest degree as a first returned value and the largest degree as second return value. If the degree match, the order is the same as for the input.

func NewCiphertext 

func NewCiphertext(params Parameters, degree, level int) *Ciphertext

NewCiphertext returns a new Element with zero values.

func NewCiphertextAtLevelFromPoly 

func NewCiphertextAtLevelFromPoly(level int, poly [2]*ring.Poly) *Ciphertext

NewCiphertextAtLevelFromPoly constructs a new Ciphetext at a specific level where the message is set to the passed poly. No checks are performed on poly and the returned Ciphertext will share its backing array of coefficient.

func NewCiphertextNTT 

func NewCiphertextNTT(params Parameters, degree, level int) *Ciphertext

NewCiphertextNTT returns a new Element with zero values and the NTT flags set.

func NewCiphertextRandom 

func NewCiphertextRandom(prng utils.PRNG, params Parameters, degree, level int) (ciphertext *Ciphertext)

NewCiphertextRandom generates a new uniformly distributed Ciphertext of degree, level.

func (*Ciphertext) Copy 

func (el *Ciphertext) Copy(ctxCopy *Ciphertext)

Copy copies the input element and its parameters on the target element.

func (*Ciphertext) CopyNew 

func (el *Ciphertext) CopyNew() *Ciphertext

CopyNew creates a new element as a copy of the target element.

func (*Ciphertext) Degree 

func (el *Ciphertext) Degree() int

Degree returns the degree of the target element.

func (*Ciphertext) El 

func (el *Ciphertext) El() *Ciphertext

El returns a pointer to this Element

func (*Ciphertext) GetDataLen 

func (el *Ciphertext) GetDataLen(WithMetaData bool) (dataLen int)

GetDataLen returns the length in bytes of the target Ciphertext.

func (*Ciphertext) Level 

func (el *Ciphertext) Level() int

Level returns the level of the target element.

func (*Ciphertext) MarshalBinary 

func (el *Ciphertext) MarshalBinary() (data []byte, err error)

MarshalBinary encodes a Ciphertext on a byte slice. The total size in byte is 4 + 8* N * numberModuliQ * (degree + 1).

func (*Ciphertext) RLWEElement 

func (el *Ciphertext) RLWEElement() *Ciphertext

RLWEElement returns a pointer to this Element

func (*Ciphertext) Resize 

func (el *Ciphertext) Resize(degree, level int)

Resize resizes the degree of the target element. Sets the NTT flag of the added poly equal to the NTT flag to the poly at degree zero.

func (*Ciphertext) SetValue 

func (el *Ciphertext) SetValue(value []*ring.Poly)

SetValue sets the input slice of polynomials as the value of the target element.

func (*Ciphertext) UnmarshalBinary 

func (el *Ciphertext) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a previously marshaled Ciphertext on the target Ciphertext.

type CiphertextQP 

type CiphertextQP struct {
	Value [2]ringqp.Poly
}

CiphertextQP is a generic type for RLWE ciphertexts in R_qp.

func (*CiphertextQP) CopyNew 

func (el *CiphertextQP) CopyNew() *CiphertextQP

type Decryptor 

type Decryptor interface {
	Decrypt(ciphertext *Ciphertext, plaintext *Plaintext)
	ShallowCopy() Decryptor
	WithKey(sk *SecretKey) Decryptor
}

Decryptor is an interface generic RLWE encryption.

func NewDecryptor 

func NewDecryptor(params Parameters, sk *SecretKey) Decryptor

NewDecryptor instantiates a new generic RLWE Decryptor.

type Encryptor 

type Encryptor interface {
	Encrypt(pt *Plaintext, ct interface{})
	EncryptZero(ct interface{})

	ShallowCopy() Encryptor
	WithKey(key interface{}) Encryptor
}

Encryptor a generic RLWE encryption interface.

func NewEncryptor 

func NewEncryptor(params Parameters, key interface{}) Encryptor

NewEncryptor creates a new Encryptor Accepts either a secret-key or a public-key.

type EvaluationKey 

type EvaluationKey struct {
	Rlk  *RelinearizationKey
	Rtks *RotationKeySet
}

EvaluationKey is a type for storing generic RLWE public evaluation keys. An evaluation key is a union of a relinearization key and a set of rotation keys.

type Evaluator 

type Evaluator struct {
	Rlk             *RelinearizationKey
	Rtks            *RotationKeySet
	PermuteNTTIndex map[uint64][]uint64

	BasisExtender *ring.BasisExtender
	Decomposer    *ring.Decomposer
	// contains filtered or unexported fields
}

Evaluator is a struct that holds the necessary elements to execute general homomorphic operation on RLWE ciphertexts, such as automorphisms, key-switching and relinearization.

func NewEvaluator 

func NewEvaluator(params Parameters, evaluationKey *EvaluationKey) (eval *Evaluator)

NewEvaluator creates a new Evaluator.

func (*Evaluator) Automorphism 

func (eval *Evaluator) Automorphism(ctIn *Ciphertext, galEl uint64, ctOut *Ciphertext)

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 (*Evaluator) AutomorphismHoisted 

func (eval *Evaluator) AutomorphismHoisted(level int, ctIn *Ciphertext, c1DecompQP []ringqp.Poly, galEl uint64, ctOut *Ciphertext)

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 (*Evaluator) AutomorphismHoistedNoModDown 

func (eval *Evaluator) AutomorphismHoistedNoModDown(levelQ int, c0 *ring.Poly, c1DecompQP []ringqp.Poly, galEl uint64, ct0OutQ, ct1OutQ, ct0OutP, ct1OutP *ring.Poly)

AutomorphismHoistedNoModDown 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.The method will panic if either ctIn or ctOut degree is not equal to 1.

func (*Evaluator) DecomposeNTT 

func (eval *Evaluator) DecomposeNTT(levelQ, levelP, nbPi int, c2 *ring.Poly, BuffDecompQP []ringqp.Poly)

DecomposeNTT applies the full RNS basis decomposition on c2. Expects the IsNTT flag of c2 to correctly reflect the domain of c2. BuffQPDecompQ and BuffQPDecompQ are vectors of polynomials (mod Q and mod P) that store the special RNS decomposition of c2 (in the NTT domain)

func (*Evaluator) DecomposeSingleNTT 

func (eval *Evaluator) DecomposeSingleNTT(levelQ, levelP, nbPi, decompRNS int, c2NTT, c2InvNTT, c2QiQ, c2QiP *ring.Poly)

DecomposeSingleNTT takes the input polynomial c2 (c2NTT and c2InvNTT, respectively in the NTT and out of the NTT domain) modulo the RNS basis, and returns the result on c2QiQ and c2QiP, the receiver polynomials respectively mod Q and mod P (in the NTT domain)

func (*Evaluator) ExpandRLWE 

func (eval *Evaluator) ExpandRLWE(ctIn *Ciphertext, logN int) (ctOut []*Ciphertext)

ExpandRLWE expands a RLWE ciphertext encrypting sum ai * X^i to 2^logN ciphertexts, each encrypting ai * X^0 for 0 <= i < 2^LogN. That is, it extracts the first 2^logN coefficients of ctIn and returns a RLWE ciphetext for each coefficient extracted.

func (*Evaluator) GadgetProduct 

func (eval *Evaluator) GadgetProduct(levelQ int, cx *ring.Poly, gadgetCt GadgetCiphertext, p0, p1 *ring.Poly)

GadgetProduct evaluates poly x Gadget -> RLWE where

p0 = dot(decomp(cx) * gadget[0]) mod Q p1 = dot(decomp(cx) * gadget[1]) mod Q

Expects the flag IsNTT of cx to correctly reflect the domain of cx.

func (*Evaluator) GadgetProductNoModDown 

func (eval *Evaluator) GadgetProductNoModDown(levelQ int, cx *ring.Poly, gadgetCt GadgetCiphertext, p0QP, p1QP ringqp.Poly)

GadgetProductNoModDown applies the gadget prodcut to the polynomial cx:

p0QP = dot(decomp(cx) * gadget[0]) mod QP (encrypted input is multiplied by P factor) p1QP = dot(decomp(cx) * gadget[1]) mod QP (encrypted input is multiplied by P factor)

Expects the flag IsNTT of cx to correctly reflect the domain of cx.

func (*Evaluator) GadgetProductSinglePAndBitDecompNoModDown 

func (eval *Evaluator) GadgetProductSinglePAndBitDecompNoModDown(levelQ int, cx *ring.Poly, gadgetCt GadgetCiphertext, p0QP, p1QP ringqp.Poly)

GadgetProductSinglePAndBitDecompNoModDown applies the key-switch to the polynomial cx:

p0QP = dot(decomp(cx) * evakey[0]) mod QP (encrypted input is multiplied by P factor) p1QP = dot(decomp(cx) * evakey[1]) mod QP (encrypted input is multiplied by P factor)

Expects the flag IsNTT of cx to correctly reflect the domain of cx.

func (*Evaluator) KeyswitchHoisted 

func (eval *Evaluator) KeyswitchHoisted(levelQ int, BuffQPDecompQP []ringqp.Poly, evakey *SwitchingKey, c0Q, c1Q, c0P, c1P *ring.Poly)

KeyswitchHoisted applies the key-switch to the decomposed polynomial c2 mod QP (BuffQPDecompQ and BuffQPDecompP) and divides the result by P, reducing the basis from QP to Q.

BuffQP2 = dot(BuffQPDecompQ||BuffQPDecompP * evakey[0]) mod Q BuffQP3 = dot(BuffQPDecompQ||BuffQPDecompP * evakey[1]) mod Q

func (*Evaluator) KeyswitchHoistedNoModDown 

func (eval *Evaluator) KeyswitchHoistedNoModDown(levelQ int, BuffQPDecompQP []ringqp.Poly, evakey *SwitchingKey, c0Q, c1Q, c0P, c1P *ring.Poly)

KeyswitchHoistedNoModDown applies the key-switch to the decomposed polynomial c2 mod QP (BuffQPDecompQ and BuffQPDecompP)

BuffQP2 = dot(BuffQPDecompQ||BuffQPDecompP * evakey[0]) mod QP BuffQP3 = dot(BuffQPDecompQ||BuffQPDecompP * evakey[1]) mod QP

func (*Evaluator) MergeRLWE 

func (eval *Evaluator) MergeRLWE(ctIn map[int]*Ciphertext) (ctOut *Ciphertext)

MergeRLWE merges a batch of RLWE, packing the first coefficient of each RLWE into a single RLWE. The operation will require N/gap + log(gap) key-switches, where gap is the minimum gap between two non-zero coefficients of the final Ciphertext. The method takes as input a map of Ciphertext, indexing in which coefficient of the final Ciphertext the first coefficient of each Ciphertext of the map must be packed.

func (*Evaluator) Parameters 

func (eval *Evaluator) Parameters() Parameters

Parameters returns the parameters used to instantiate the target evaluator.

func (*Evaluator) Relinearize 

func (eval *Evaluator) Relinearize(ctIn *Ciphertext, ctOut *Ciphertext)

Relinearize applies the relinearization procedure on ct0 and returns the result in ctOut. The method will panic if the corresponding relinearization key to the ciphertext degree is missing.

func (*Evaluator) ShallowCopy 

func (eval *Evaluator) ShallowCopy() *Evaluator

ShallowCopy creates a shallow copy of this Evaluator in which all the read-only data-structures are shared with the receiver and the temporary buffers are reallocated. The receiver and the returned Evaluators can be used concurrently.

func (*Evaluator) SwitchKeys 

func (eval *Evaluator) SwitchKeys(ctIn *Ciphertext, switchingKey *SwitchingKey, ctOut *Ciphertext)

SwitchKeys re-encrypts ctIn under a different key and returns the result in ctOut. It requires a SwitchingKey, which is computed from the key under which the Ciphertext is currently encrypted and the key under which the Ciphertext will be re-encrypted. The method will panic if either ctIn or ctOut degree isn't 1.

func (*Evaluator) Trace 

func (eval *Evaluator) Trace(ctIn *Ciphertext, logN int, ctOut *Ciphertext)

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 (*Evaluator) WithKey 

func (eval *Evaluator) WithKey(evaluationKey *EvaluationKey) *Evaluator

WithKey creates a shallow copy of the receiver Evaluator for which the new EvaluationKey is evaluationKey and where the temporary buffers are shared. The receiver and the returned Evaluators cannot be used concurrently.

type GadgetCiphertext 

type GadgetCiphertext struct {
	Value [][]CiphertextQP
}

GadgetCiphertext is a struct for storing an encrypted plaintext times the gadget power matrix.

func NewGadgetCiphertext 

func NewGadgetCiphertext(levelQ, levelP, decompRNS, decompBIT int, ringQP ringqp.Ring) (ct *GadgetCiphertext)

NewGadgetCiphertext returns a new Ciphertext key with pre-allocated zero-value. Ciphertext is always in the NTT domain.

func (*GadgetCiphertext) CopyNew 

func (ct *GadgetCiphertext) CopyNew() (ctCopy *GadgetCiphertext)

CopyNew creates a deep copy of the receiver Ciphertext and returns it.

func (*GadgetCiphertext) Decode 

func (ct *GadgetCiphertext) Decode(data []byte) (pointer int, err error)

Decode decodes a slice of bytes on the target ciphertext.

func (*GadgetCiphertext) Encode 

func (ct *GadgetCiphertext) Encode(pointer int, data []byte) (int, error)

Encode encodes the target ciphertext on a pre-allocated slice of bytes.

func (*GadgetCiphertext) Equals 

func (ct *GadgetCiphertext) Equals(other *GadgetCiphertext) bool

Equals checks two Ciphertexts for equality.

func (*GadgetCiphertext) GetDataLen 

func (ct *GadgetCiphertext) GetDataLen(WithMetadata bool) (dataLen int)

GetDataLen returns the length in bytes of the target Ciphertext.

func (*GadgetCiphertext) LevelP 

func (ct *GadgetCiphertext) LevelP() int

LevelP returns the level of the modulus P of the target Ciphertext.

func (*GadgetCiphertext) LevelQ 

func (ct *GadgetCiphertext) LevelQ() int

LevelQ returns the level of the modulus Q of the target Ciphertext.

func (*GadgetCiphertext) MarshalBinary 

func (ct *GadgetCiphertext) MarshalBinary() (data []byte, err error)

MarshalBinary encodes the target Ciphertext on a slice of bytes.

func (*GadgetCiphertext) UnmarshalBinary 

func (ct *GadgetCiphertext) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a slice of bytes on the target Ciphertext.

type GadgetPlaintext 

type GadgetPlaintext struct {
	Value []*ring.Poly
}

GadgetPlaintext stores a RGSW plaintext value.

func NewGadgetPlaintext 

func NewGadgetPlaintext(value interface{}, levelQ, levelP, logBase2, decompBIT int, ringQP ringqp.Ring) (pt *GadgetPlaintext)

NewGadgetPlaintext creates a new gadget plaintext from value, which can be either uint64, int64 or *ring.Poly. Plaintext is returned in the NTT and Mongtomery domain.

type KeyGenerator 

type KeyGenerator interface {
	GenSecretKey() (sk *SecretKey)
	GenSecretKeyGaussian() (sk *SecretKey)
	GenSecretKeyWithDistrib(p float64) (sk *SecretKey)
	GenSecretKeyWithHammingWeight(hw int) (sk *SecretKey)
	GenPublicKey(sk *SecretKey) (pk *PublicKey)
	GenKeyPair() (sk *SecretKey, pk *PublicKey)
	GenRelinearizationKey(sk *SecretKey, maxDegree int) (evk *RelinearizationKey)
	GenSwitchingKey(skInput, skOutput *SecretKey) (newevakey *SwitchingKey)
	GenSwitchingKeyForGalois(galEl uint64, sk *SecretKey) (swk *SwitchingKey)
	GenRotationKeys(galEls []uint64, sk *SecretKey) (rks *RotationKeySet)
	GenSwitchingKeyForRotationBy(k int, sk *SecretKey) (swk *SwitchingKey)
	GenRotationKeysForRotations(ks []int, inclueSwapRows bool, sk *SecretKey) (rks *RotationKeySet)
	GenSwitchingKeyForRowRotation(sk *SecretKey) (swk *SwitchingKey)
	GenRotationKeysForInnerSum(sk *SecretKey) (rks *RotationKeySet)
	GenSwitchingKeysForRingSwap(skCKKS, skCI *SecretKey) (swkStdToConjugateInvariant, swkConjugateInvariantToStd *SwitchingKey)
}

KeyGenerator is an interface implementing the methods of the KeyGenerator.

func NewKeyGenerator 

func NewKeyGenerator(params Parameters) KeyGenerator

NewKeyGenerator creates a new KeyGenerator, from which the secret and public keys, as well as the evaluation, rotation and switching keys can be generated.

type PRNGEncryptor 

type PRNGEncryptor interface {
	Encryptor
	WithPRNG(prng utils.PRNG) PRNGEncryptor
}

PRNGEncryptor is an interface for encrypting RLWE ciphertexts from a secret-key and a pre-determined PRNG. An Encryptor constructed from a secret-key complies to this interface.

func NewPRNGEncryptor 

func NewPRNGEncryptor(params Parameters, key *SecretKey) PRNGEncryptor

NewPRNGEncryptor creates a new PRNGEncryptor instance.

type Parameters 

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

Parameters represents a set of generic RLWE parameters. Its fields are private and immutable. See ParametersLiteral for user-specified parameters.

func NewParameters 

func NewParameters(logn int, q, p []uint64, pow2Base, h int, sigma float64, ringType ring.Type) (Parameters, error)

NewParameters returns a new set of generic RLWE parameters from the given ring degree logn, moduli q and p, and error distribution parameter sigma. It returns the empty parameters Parameters{} and a non-nil error if the specified parameters are invalid.

func NewParametersFromLiteral 

func NewParametersFromLiteral(paramDef ParametersLiteral) (Parameters, error)

NewParametersFromLiteral instantiate a set of generic RLWE parameters from a ParametersLiteral specification. It returns the empty parameters Parameters{} and a non-nil error if the specified parameters are invalid.

If the moduli chain is specified through the LogQ and LogP fields, the method generates a moduli chain matching the specified sizes (see `GenModuli`).

If the secrets' density parameter (H) is left unset, its value is set to 2^(paramDef.LogN-1) to match the standard ternary distribution.

If the error variance is left unset, its value is set to `DefaultSigma`.

If the RingType is left unset, the default value is ring.Standard.

func (Parameters) CopyNew deprecated 

func (p Parameters) CopyNew() Parameters

CopyNew makes a deep copy of the receiver and returns it.

Deprecated: Parameter is now a read-only struct, except for the UnmarshalBinary method: deep copying should only be required to save a Parameter struct before calling its UnmarshalBinary method and it will be deprecated when transitioning to a immutable serialization interface.

func (Parameters) DecompPw2 

func (p Parameters) DecompPw2(levelQ, levelP int) (c int)

DecompPw2 returns ceil(p.MaxBitQ(levelQ, levelP)/bitDecomp).

func (Parameters) DecompRNS 

func (p Parameters) DecompRNS(levelQ, levelP int) int

DecompRNS returns the number of element in the RNS decomposition basis: Ceil(lenQi / lenPi)

func (Parameters) Equals 

func (p Parameters) Equals(other Parameters) bool

Equals checks two Parameter structs for equality.

func (Parameters) GaloisElementForColumnRotationBy 

func (p Parameters) GaloisElementForColumnRotationBy(k int) uint64

GaloisElementForColumnRotationBy returns the Galois element for plaintext column rotations by k position to the left. Providing a negative k is equivalent to a right rotation.

func (Parameters) GaloisElementForExpandRLWE 

func (p Parameters) GaloisElementForExpandRLWE(logN int) (galEls []uint64)

GaloisElementForExpandRLWE returns the list of Galois elements required to perform the ExpandRLWE operation.

func (Parameters) GaloisElementForRowRotation 

func (p Parameters) GaloisElementForRowRotation() uint64

GaloisElementForRowRotation returns the Galois element for generating the row rotation automorphism

func (Parameters) GaloisElementsForMergeRLWE 

func (p Parameters) GaloisElementsForMergeRLWE() (galEls []uint64)

GaloisElementsForMergeRLWE returns the list of Galois elements required to perform the MergeRLWE operation.

func (Parameters) GaloisElementsForRowInnerSum 

func (p Parameters) GaloisElementsForRowInnerSum() (galEls []uint64)

GaloisElementsForRowInnerSum returns a list of all Galois elements required to perform an InnerSum operation. This corresponds to all the left rotations by k-positions where k is a power of two and the row-rotation element.

func (Parameters) GaloisElementsForTrace 

func (p Parameters) GaloisElementsForTrace(logN int) (galEls []uint64)

GaloisElementsForTrace generates the Galois elements for the Trace evaluation. Trace maps X -> sum((-1)^i * X^{i*n+1}) for 2^{LogN} <= i < N.

func (Parameters) HammingWeight 

func (p Parameters) HammingWeight() int

HammingWeight returns the number of non-zero coefficients in secret-keys.

func (Parameters) InverseGaloisElement 

func (p Parameters) InverseGaloisElement(galEl uint64) uint64

InverseGaloisElement takes a Galois element and returns the Galois element corresponding to the inverse automorphism

func (Parameters) LogN 

func (p Parameters) LogN() int

LogN returns the log of the degree of the polynomial ring

func (Parameters) LogP 

func (p Parameters) LogP() int

LogP returns the size of the extended modulus P in bits

func (Parameters) LogQ 

func (p Parameters) LogQ() int

LogQ returns the size of the extended modulus Q in bits

func (Parameters) LogQP 

func (p Parameters) LogQP() int

LogQP returns the size of the extended modulus QP in bits

func (Parameters) MarshalBinary 

func (p Parameters) MarshalBinary() ([]byte, error)

MarshalBinary returns a []byte representation of the parameter set.

func (Parameters) MarshalBinarySize 

func (p Parameters) MarshalBinarySize() int

MarshalBinarySize returns the length of the []byte encoding of the reciever.

func (Parameters) MarshalJSON 

func (p Parameters) MarshalJSON() ([]byte, error)

MarshalJSON returns a JSON representation of this parameter set. See `Marshal` from the `encoding/json` package.

func (Parameters) MaxBit 

func (p Parameters) MaxBit(levelQ, levelP int) (c int)

MaxBit returns max(max(bitLen(Q[:levelQ+1])), max(bitLen(P[:levelP+1])).

func (Parameters) MaxLevel 

func (p Parameters) MaxLevel() int

MaxLevel returns the maximum level of a ciphertext

func (Parameters) N 

func (p Parameters) N() int

N returns the ring degree

func (Parameters) NoiseBound 

func (p Parameters) NoiseBound() uint64

NoiseBound returns truncation bound for the noise distribution.

func (Parameters) P 

func (p Parameters) P() []uint64

P returns a new slice with the factors of the ciphertext modulus extension P

func (Parameters) PBigInt 

func (p Parameters) PBigInt() *big.Int

PBigInt return the ciphertext-space extention modulus P in big.Integer, reconstructed, representation.

func (Parameters) PCount 

func (p Parameters) PCount() int

PCount returns the number of factors of the ciphertext modulus extension P

func (Parameters) ParametersLiteral 

func (p Parameters) ParametersLiteral() ParametersLiteral

ParametersLiteral returns the ParametersLiteral of the target Parameters.

func (*Parameters) PiOverflowMargin 

func (p *Parameters) PiOverflowMargin(level int) int

PiOverflowMargin returns floor(2^64 / max(Pi)), i.e. the number of times elements of Z_max{Pi} can be added together before overflowing 2^64.

func (Parameters) Pow2Base 

func (p Parameters) Pow2Base() int

Pow2Base returns the base 2^x decomposition used for the key-switching keys. Returns 0 if no decomposition is used (the case where x = 0).

func (Parameters) Q 

func (p Parameters) Q() []uint64

Q returns a new slice with the factors of the ciphertext modulus q

func (Parameters) QBigInt 

func (p Parameters) QBigInt() *big.Int

QBigInt return the ciphertext-space modulus Q in big.Integer, reconstructed, representation.

func (Parameters) QCount 

func (p Parameters) QCount() int

QCount returns the number of factors of the ciphertext modulus Q

func (Parameters) QP 

func (p Parameters) QP() []uint64

QP return the extended ciphertext-space modulus QP in RNS representation.

func (Parameters) QPBigInt 

func (p Parameters) QPBigInt() *big.Int

QPBigInt return the extended ciphertext-space modulus QP in big.Integer, reconstructed, representation.

func (Parameters) QPCount 

func (p Parameters) QPCount() int

QPCount returns the number of factors of the ciphertext modulus + the modulus extension P

func (Parameters) QiFloat64 

func (p Parameters) QiFloat64(level int) float64

QiFloat64 returns the float64 value of the Qi at position level in the modulus chain.

func (*Parameters) QiOverflowMargin 

func (p *Parameters) QiOverflowMargin(level int) int

QiOverflowMargin returns floor(2^64 / max(Qi)), i.e. the number of times elements of Z_max{Qi} can be added together before overflowing 2^64.

func (Parameters) RingP 

func (p Parameters) RingP() *ring.Ring

RingP returns a pointer to ringP

func (Parameters) RingQ 

func (p Parameters) RingQ() *ring.Ring

RingQ returns a pointer to ringQ

func (Parameters) RingQP 

func (p Parameters) RingQP() *ringqp.Ring

RingQP returns a pointer to ringQP

func (Parameters) RingType 

func (p Parameters) RingType() ring.Type

RingType returns the type of the underlying ring.

func (Parameters) Sigma 

func (p Parameters) Sigma() float64

Sigma returns standard deviation of the noise distribution

func (Parameters) StandardParameters 

func (p Parameters) StandardParameters() (pci Parameters, err error)

StandardParameters returns a RLWE parameter set that corresponds to the standard dual of a conjugate invariant parameter set. If the receiver is already a standard set, then the method returns the receiver.

func (*Parameters) UnmarshalBinary 

func (p *Parameters) UnmarshalBinary(data []byte) error

UnmarshalBinary decodes a []byte into a parameter set struct.

func (*Parameters) UnmarshalJSON 

func (p *Parameters) UnmarshalJSON(data []byte) (err error)

UnmarshalJSON reads a JSON representation of a parameter set into the receiver Parameter. See `Unmarshal` from the `encoding/json` package.

type ParametersLiteral 

type ParametersLiteral struct {
	LogN     int
	Q        []uint64
	P        []uint64
	LogQ     []int `json:",omitempty"`
	LogP     []int `json:",omitempty"`
	Pow2Base int
	Sigma    float64
	H        int
	RingType ring.Type
}

ParametersLiteral is a literal representation of BFV parameters. It has public fields and is used to express unchecked user-defined parameters literally into Go programs. The NewParametersFromLiteral function is used to generate the actual checked parameters from the literal representation.

Users must set the polynomial degree (LogN) and the coefficient modulus, by either setting the Q and P fields to the desired moduli chain, or by setting the LogQ and LogP fields to the desired moduli sizes.

Optionally, users may specify - the base 2 decomposition for the gadget ciphertexts - the error variance (Sigma) and secrets' density (H) and the ring type (RingType). If left unset, standard default values for these field are substituted at parameter creation (see NewParametersFromLiteral).

type Plaintext 

type Plaintext struct {
	Value *ring.Poly
}

Plaintext is a common base type for RLWE plaintexts.

func NewPlaintext 

func NewPlaintext(params Parameters, level int) *Plaintext

NewPlaintext creates a new Plaintext at level `level` from the parameters.

func NewPlaintextAtLevelFromPoly 

func NewPlaintextAtLevelFromPoly(level int, poly *ring.Poly) *Plaintext

NewPlaintextAtLevelFromPoly constructs a new Plaintext at a specific level where the message is set to the passed poly. No checks are performed on poly and the returned Plaintext will share its backing array of coefficients.

func (*Plaintext) Copy 

func (pt *Plaintext) Copy(other *Plaintext)

Copy copies the `other` plaintext value into the reciever plaintext.

func (Plaintext) Degree 

func (pt Plaintext) Degree() int

Degree returns the degree of the target element.

func (Plaintext) El 

func (pt Plaintext) El() *Ciphertext

El returns the plaintext as a new `Element` for which the value points to the receiver `Value` field.

func (Plaintext) Level 

func (pt Plaintext) Level() int

Level returns the level of the target element.

type PublicKey 

type PublicKey struct {
	Value [2]ringqp.Poly
}

PublicKey is a type for generic RLWE public keys.

func NewPublicKey 

func NewPublicKey(params Parameters) (pk *PublicKey)

NewPublicKey returns a new PublicKey with zero values.

func (*PublicKey) CopyNew 

func (pk *PublicKey) CopyNew() *PublicKey

CopyNew creates a deep copy of the receiver PublicKey and returns it.

func (*PublicKey) Equals 

func (pk *PublicKey) Equals(other *PublicKey) bool

Equals checks two PublicKey struct for equality.

func (*PublicKey) GetDataLen64 

func (pk *PublicKey) GetDataLen64(WithMetadata bool) (dataLen int)

GetDataLen64 returns the length in bytes of the target PublicKey.

func (*PublicKey) LevelP 

func (pk *PublicKey) LevelP() int

LevelP returns the level of the modulus P of the target. Returns -1 if P is absent.

func (*PublicKey) LevelQ 

func (pk *PublicKey) LevelQ() int

LevelQ returns the level of the modulus Q of the target.

func (*PublicKey) MarshalBinary 

func (pk *PublicKey) MarshalBinary() (data []byte, err error)

MarshalBinary encodes a PublicKey in a byte slice.

func (*PublicKey) UnmarshalBinary 

func (pk *PublicKey) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a previously marshaled PublicKey in the target PublicKey.

type RelinearizationKey 

type RelinearizationKey struct {
	Keys []*SwitchingKey
}

RelinearizationKey is a type for generic RLWE public relinearization keys. It stores a slice with a switching key per relinearizable degree. The switching key at index i is used to relinearize a degree i+2 ciphertexts back to a degree i + 1 one.

func NewRelinKey 

func NewRelinKey(params Parameters, maxRelinDegree int) (evakey *RelinearizationKey)

NewRelinKey creates a new EvaluationKey with zero values.

func (*RelinearizationKey) CopyNew 

func (rlk *RelinearizationKey) CopyNew() *RelinearizationKey

CopyNew creates a deep copy of the receiver RelinearizationKey and returns it.

func (*RelinearizationKey) Equals 

func (rlk *RelinearizationKey) Equals(other *RelinearizationKey) bool

Equals checks two RelinearizationKeys for equality.

func (*RelinearizationKey) GetDataLen 

func (rlk *RelinearizationKey) GetDataLen(WithMetadata bool) (dataLen int)

GetDataLen returns the length in bytes of the target EvaluationKey.

func (*RelinearizationKey) MarshalBinary 

func (rlk *RelinearizationKey) MarshalBinary() (data []byte, err error)

MarshalBinary encodes an EvaluationKey key in a byte slice.

func (*RelinearizationKey) UnmarshalBinary 

func (rlk *RelinearizationKey) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a previously marshaled EvaluationKey in the target EvaluationKey.

type RotationKeySet 

type RotationKeySet struct {
	Keys map[uint64]*SwitchingKey
}

RotationKeySet is a type for storing generic RLWE public rotation keys. It stores a map indexed by the galois element defining the automorphism.

func NewRotationKeySet 

func NewRotationKeySet(params Parameters, galoisElement []uint64) (rotKey *RotationKeySet)

NewRotationKeySet returns a new RotationKeySet with pre-allocated switching keys for each distinct galoisElement value.

func (*RotationKeySet) Equals 

func (rtks *RotationKeySet) Equals(other *RotationKeySet) bool

Equals checks to RotationKeySets for equality.

func (*RotationKeySet) GetDataLen 

func (rtks *RotationKeySet) GetDataLen(WithMetaData bool) (dataLen int)

GetDataLen returns the length in bytes of the target RotationKeys.

func (*RotationKeySet) GetRotationKey 

func (rtks *RotationKeySet) GetRotationKey(galoisEl uint64) (*SwitchingKey, bool)

GetRotationKey return the rotation key for the given galois element or nil if such key is not in the set. The second argument is true iff the first one is non-nil.

func (*RotationKeySet) Includes 

func (rtks *RotationKeySet) Includes(other *RotationKeySet) bool

Includes checks whether the receiver RotationKeySet includes the given other RotationKeySet.

func (*RotationKeySet) MarshalBinary 

func (rtks *RotationKeySet) MarshalBinary() (data []byte, err error)

MarshalBinary encodes a RotationKeys struct in a byte slice.

func (*RotationKeySet) UnmarshalBinary 

func (rtks *RotationKeySet) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a previously marshaled RotationKeys in the target RotationKeys.

type SecretKey 

type SecretKey struct {
	Value ringqp.Poly
}

SecretKey is a type for generic RLWE secret keys.

func NewSecretKey 

func NewSecretKey(params Parameters) *SecretKey

NewSecretKey generates a new SecretKey with zero values.

func (*SecretKey) CopyNew 

func (sk *SecretKey) CopyNew() *SecretKey

CopyNew creates a deep copy of the receiver secret key and returns it.

func (*SecretKey) GetDataLen64 

func (sk *SecretKey) GetDataLen64(WithMetadata bool) (dataLen int)

GetDataLen64 returns the length in bytes of the target SecretKey. Assumes that each coefficient uses 8 bytes.

func (*SecretKey) LevelP 

func (sk *SecretKey) LevelP() int

LevelP returns the level of the modulus P of the target. Returns -1 if P is absent.

func (*SecretKey) LevelQ 

func (sk *SecretKey) LevelQ() int

LevelQ returns the level of the modulus Q of the target.

func (*SecretKey) MarshalBinary 

func (sk *SecretKey) MarshalBinary() (data []byte, err error)

MarshalBinary encodes a secret key in a byte slice.

func (*SecretKey) UnmarshalBinary 

func (sk *SecretKey) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a previously marshaled SecretKey in the target SecretKey.

type SwitchingKey 

type SwitchingKey struct {
	GadgetCiphertext
}

SwitchingKey is a type for generic RLWE public switching keys.

func NewSwitchingKey 

func NewSwitchingKey(params Parameters, levelQ, levelP int) *SwitchingKey

NewSwitchingKey returns a new public switching key with pre-allocated zero-value

func (*SwitchingKey) CopyNew 

func (swk *SwitchingKey) CopyNew() *SwitchingKey

CopyNew creates a deep copy of the target SwitchingKey and returns it.

func (*SwitchingKey) Equals 

func (swk *SwitchingKey) Equals(other *SwitchingKey) bool

Equals checks two SwitchingKeys for equality.

func (*SwitchingKey) MarshalBinary 

func (swk *SwitchingKey) MarshalBinary() (data []byte, err error)

MarshalBinary encodes the target SwitchingKey on a slice of bytes.

func (*SwitchingKey) UnmarshalBinary 

func (swk *SwitchingKey) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a slice of bytes on the target SwitchingKey.

Source Files

View all Source files

Directories

Path Synopsis
Package ringqp is implements a wrapper for both the ringQ and ringP.
 Package ringqp is implements a wrapper for both the ringQ and ringP.

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