tpsi

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 Go to latest Published: Feb 2, 2021 License: GPL-3.0 Imports: 9 Imported by: 0

README

Threshold Private Set Intersection

This projects provides implementations of FTPSI-diff using AHE and FTPSI-int described in Multi-Party Threshold Private Set Intersection with Sublinear Communication by Badrinarayanan, Miao and Rindal. However FTPSI-int is slightly modified as bootstrapping was not enable in the cryptosystem used. Threshold Private Set Intersection allows multiple distrustful parties find the intersection of the respective sets, if this intersection exceeds a given threshold, without revealing what is not in the intersection.

Cryptosystems

The protocol used Paillier Threshold Encryption Scheme Implementation for the additive homomorphic part and Lattigo for the fully homomorphic part. However the implementations builds on the interfaces AHE_Cryptosystem and FHE_Cryptosystem which allows the use of any implementation satisfying the homomorphic properties.

Setting

The setting is described by the interfaces AHE_setting and FHE_setting which contains the number of parties, the threshold value and means of communication. This implementation has only been run on a single machine with parties modelled as goroutines. However by creating a new setting, network communication should be easily achieved.

Usage

The basic functionalities are implemented in TPSIdiffWorker and TPSIintWorker.

A simple example application is provided and can be run as go run main/main.go diff dj 7 main/elements, which runs FTPSI-diff using the Damgård-Jurik cryptosystem provided in Paillier Threshold Encryption Scheme Implementation, with a threshold value of 7.

Documentation

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func CPComputeHankelMatrix 

func CPComputeHankelMatrix(items []*big.Int, u *big.Int, setting AHE_setting) (H gm.Matrix, err error)

compute the encrypted Hankel Matrix for central party

func CentralASSWorker 

func CentralASSWorker(a Ciphertext, sk Secret_key, setting AHE_setting) *big.Int

func CentralBFVEncryptionGenerator 

func CentralBFVEncryptionGenerator(channels []chan interface{}) (BFV_encryption, BFV_secret_key)

func CentralCardinalityTestWorker 

func CentralCardinalityTestWorker(items []*big.Int, sk Secret_key, setting AHE_setting) bool

returns true if number of elements not shared by all is <= setting.Threshold()

func CentralDecryptionWorker 

func CentralDecryptionWorker(cipher Ciphertext, sk Secret_key, setting AHE_setting) *big.Int

func CentralFHECardinalityTestWorker 

func CentralFHECardinalityTestWorker(items []*big.Int, sk Secret_key, setting FHE_setting) bool

returns true if cardinality test passes

func CentralHankelMatrix 

func CentralHankelMatrix(items []*big.Int, sk Secret_key, setting AHE_setting) gm.Matrix

func CentralIntersectionPolyWorker 

func CentralIntersectionPolyWorker(root_poly gm.Matrix, sk Secret_key, setting AHE_setting) (gm.Matrix, gm.Matrix)

step 3 of TPSI-diff

func CentralMatrixMultiplicationWorker 

func CentralMatrixMultiplicationWorker(a, b gm.Matrix, sk Secret_key, setting AHE_setting) gm.Matrix

func CentralMinPolyWorker 

func CentralMinPolyWorker(seq gm.Matrix, rec_ord int, sk Secret_key, setting AHE_setting) (gm.Matrix, gm.Matrix)

func CentralSingularityTestWorker 

func CentralSingularityTestWorker(m gm.Matrix, sk Secret_key, setting AHE_setting) bool

returns true if m is singular

func CentralZeroTestWorker 

func CentralZeroTestWorker(a Ciphertext, sk Secret_key, setting AHE_setting) bool

func CombineMatrixMultiplication 

func CombineMatrixMultiplication(MA_enc, MB_enc gm.Matrix, MAis, MBis []gm.Matrix, ctis []gm.Matrix, setting AHE_setting) (AB gm.Matrix, err error)

step 4 of MMult

func CombineMatrixShares 

func CombineMatrixShares(part_mat []gm.Matrix, enc_mat gm.Matrix, setting AHE_setting) (decrypted gm.Matrix, err error)

combine partial matrix decryptions to receive plaintext matrix

func ComputeHankelMatrix 

func ComputeHankelMatrix(items []*big.Int, u *big.Int, setting AHE_setting) (gm.Matrix, error)

compute and encrypt the Hankel Matrix for items and (random) u.

func ComputePlainHankelMatrix 

func ComputePlainHankelMatrix(items []*big.Int, u *big.Int, setting AHE_setting) gm.Matrix

compute the Hankel Matrix for items and (random) u.

func DecodeElements 

func DecodeElements(elements []*big.Int) []*big.Int

func EncodeElements 

func EncodeElements(elements []*big.Int) []*big.Int

func EncryptMatrix 

func EncryptMatrix(a gm.Matrix, setting AHE_setting) (b gm.Matrix, err error)

encrypt matrix item-wise

func EncryptedOneMatrix 

func EncryptedOneMatrix(rows, cols int, setting AHE_setting) (m gm.Matrix, err error)

func EncryptedZeroMatrix 

func EncryptedZeroMatrix(rows, cols int, setting AHE_setting) (m gm.Matrix, err error)

func EvalIntPolys 

func EvalIntPolys(root_poly gm.Matrix, sample_max int, setting AHE_setting) (R_values_enc, R_tilde_values, p_values gm.Matrix)

func EvalPoly 

func EvalPoly(p gm.Matrix, x, mod *big.Int) *big.Int

evaluate polynomial p at point x

func GenCRP 

func GenCRP(params *bfv.Parameters) (*ring.Poly, []*ring.Poly)

func GetCti 

func GetCti(MA, MB, RA, RAi, RBi gm.Matrix, setting AHE_setting, Secret_key Secret_key) (cti gm.Matrix, MA_part, MB_part gm.Matrix, err error)

step 3 of MMult

func GetMulMatrices 

func GetMulMatrices(A, B gm.Matrix, RAs, RBs []gm.Matrix, setting AHE_setting) (RA, MA, MB gm.Matrix, err error)

step 2 of MMult

func HSeq 

func HSeq(Hvs gm.Matrix, mat_size int, setting AHE_setting) (h_seq gm.Matrix, err error)

step 3e of CTest-diff

func Interpolation 

func Interpolation(vs, ps gm.Matrix, setting AHE_setting) gm.Matrix

step 4 of TPSI-diff

func IntersectionWorker 

func IntersectionWorker(items []*big.Int, sk Secret_key, setting AHE_setting) ([]*big.Int, []*big.Int)

returns two slices, shared elements & unique elements

func IsRoot 

func IsRoot(poly gm.Matrix, x *big.Int, mod *big.Int) bool

func MaskH 

func MaskH(Hs gm.Matrix, HMasks []gm.Matrix, setting AHE_setting) (diff gm.Matrix, err error)

step 3g of CTest-diff

func MaskRootPoly 

func MaskRootPoly(p_values, party_values, R_tilde_values gm.Matrix, sample_max int, setting AHE_setting) gm.Matrix

func MultPoly 

func MultPoly(p1, p2 gm.Matrix) gm.Matrix

polynomial multiplication

func NbrMMultInstances 

func NbrMMultInstances(m gm.Matrix) int

calculates how many instances of MMult is needed to get all H, according to: n = ceil( log(matrix size) ) H^2^n being the highest order needed

func NegateValue 

func NegateValue(d *big.Int, setting AHE_setting) *big.Int

ASS, step 7

func NewCustomDJCryptosystem 

func NewCustomDJCryptosystem(n, bitSize, s int) (cryptosystem DJ_encryption, secret_keys []DJ_secret_key, err error)

func NewDJCryptosystem 

func NewDJCryptosystem(n int) (cryptosystem DJ_encryption, secret_keys []DJ_secret_key, err error)

func OuterASSWorker 

func OuterASSWorker(a Ciphertext, sk Secret_key, setting AHE_setting) *big.Int

func OuterBFVEncryptionGenerator 

func OuterBFVEncryptionGenerator(channel chan interface{}) (BFV_encryption, BFV_secret_key)

func OuterCardinalityTestWorker 

func OuterCardinalityTestWorker(items []*big.Int, sk Secret_key, setting AHE_setting) bool

returns true if number of elements not shared by all is <= setting.Threshold()

func OuterDecryptionWorker 

func OuterDecryptionWorker(cipher Ciphertext, sk Secret_key, setting AHE_setting) *big.Int

func OuterFHECardinalityTestWorker 

func OuterFHECardinalityTestWorker(items []*big.Int, sk Secret_key, setting FHE_setting) bool

returns true if cardinality test passes

func OuterHankelMatrix 

func OuterHankelMatrix(items []*big.Int, sk Secret_key, setting AHE_setting) gm.Matrix

func OuterIntersectionPolyWorker 

func OuterIntersectionPolyWorker(root_poly gm.Matrix, sk Secret_key, setting AHE_setting) (gm.Matrix, gm.Matrix)

step 3 of TPSI-diff

func OuterMatrixMultiplicationWorker 

func OuterMatrixMultiplicationWorker(a, b gm.Matrix, sk Secret_key, setting AHE_setting) gm.Matrix

func OuterMinPolyWorker 

func OuterMinPolyWorker(seq gm.Matrix, rec_ord int, sk Secret_key, setting AHE_setting) (gm.Matrix, gm.Matrix)

func OuterSingularityTestWorker 

func OuterSingularityTestWorker(m gm.Matrix, sk Secret_key, setting AHE_setting) bool

returns true if m is singular

func OuterZeroTestWorker 

func OuterZeroTestWorker(a Ciphertext, sk Secret_key, setting AHE_setting) bool

func PartialDecryptMatrix 

func PartialDecryptMatrix(cipher gm.Matrix, Secret_key Secret_key) (part_mat gm.Matrix, err error)

perform partial decryption for key share Secret_key

func PolyFromRoots 

func PolyFromRoots(roots []*big.Int, mod *big.Int) gm.Matrix

func PolyMult 

func PolyMult(a_num, a_den, b_num, b_den gm.Matrix, sk Secret_key, setting AHE_setting) (prod_num, prod_den gm.Matrix, err error)

func PolySub 

func PolySub(a_num, a_den, b_num, b_den gm.Matrix, sk Secret_key, setting AHE_setting) (diff_num, diff_den gm.Matrix, err error)

func RootMask 

func RootMask(root_poly gm.Matrix, setting AHE_setting) gm.Matrix

func SampleHMasks 

func SampleHMasks(setting AHE_setting)

step 3f of CTest-diff

func SampleInt 

func SampleInt(q *big.Int) (*big.Int, error)

sample a uniform random integer smaller than q

func SampleMatrix 

func SampleMatrix(rows, cols int, q *big.Int) (a gm.Matrix, err error)

sample a matrix with size rows x cols, with elements from field defined by q

func SampleRMatrices 

func SampleRMatrices(a, b gm.Matrix, setting AHE_setting) (RAi_plain, RAi_enc, RBi_plain, RBi_enc gm.Matrix, err error)

step 1 of MMult

func SampleSlice 

func SampleSlice(l int, q *big.Int) (a []*big.Int, err error)

func SampleUVector 

func SampleUVector(m gm.Matrix, setting AHE_setting) (u gm.Matrix, err error)

sample u from step 3e of CTest-diff

func SampleVVector 

func SampleVVector(m gm.Matrix, setting AHE_setting) (v gm.Matrix, err error)

step 3b of CTest-diff

func SecretShare 

func SecretShare(d, e *big.Int, setting AHE_setting) *big.Int

ASS, step 7

func SetupBFV 

func SetupBFV(n int) ([]BFV_encryption, []BFV_secret_key)

func TPSIdiffWorker 

func TPSIdiffWorker(items []*big.Int, sk Secret_key, setting AHE_setting) ([]*big.Int, []*big.Int)

returns two slices: shared elements & unique elements if cardinality test passes, otherwise nil, nil

func TPSIintWorker 

func TPSIintWorker(items []*big.Int, sk Secret_key, setting FHE_setting) ([]*big.Int, []*big.Int)

returns two slices: shared elements & unique elements if cardinality test passes, otherwise nil, nil

Types

type AHESetting 

type AHESetting struct {
	T int // threshold
	// contains filtered or unexported fields
}

func SetupAHE 

func SetupAHE(n, T int, cs AHE_Cryptosystem) []AHESetting

func (AHESetting) AHE_cryptosystem 

func (s AHESetting) AHE_cryptosystem() AHE_Cryptosystem

func (AHESetting) Distribute 

func (s AHESetting) Distribute(any interface{})

func (AHESetting) IsCentral 

func (s AHESetting) IsCentral() bool

func (AHESetting) Parties 

func (s AHESetting) Parties() int

func (AHESetting) Receive 

func (s AHESetting) Receive() interface{}

func (AHESetting) ReceiveAll 

func (s AHESetting) ReceiveAll() []interface{}

func (AHESetting) Send 

func (s AHESetting) Send(any interface{})

func (AHESetting) SendTo 

func (s AHESetting) SendTo(i int, any interface{})

func (AHESetting) Threshold 

func (s AHESetting) Threshold() int

type AHE_Cryptosystem 

type AHE_Cryptosystem interface {

	// addition of two elements
	Add(Ciphertext, Ciphertext) (sum Ciphertext, err error)

	// scaling of an element by scalar factor
	Scale(cipher Ciphertext, factor *big.Int) (product Ciphertext, err error)

	// encrypt a plaintext message
	Encrypt(*big.Int) (Ciphertext, error)

	// combine partial decryptions to plaintext
	CombinePartials([]Partial_decryption) (*big.Int, error)

	// encrypted matrix evaluation
	EvaluationSpace() gm.Space

	// size of plaintext space
	N() *big.Int
}

type AHE_setting 

type AHE_setting interface {
	// threshold value
	Threshold() int

	// numer of parties
	Parties() int

	// ahe cryptosystem
	AHE_cryptosystem() AHE_Cryptosystem

	// used by central party to send a value to all
	Distribute(interface{})

	// used by outer parties to send to central party
	Send(interface{})

	// used by central party to send
	// a message to given party
	SendTo(int, interface{})

	// for central to await messages from all
	// and get them (ordered) in a slice
	ReceiveAll() []interface{}

	// receive a message from central party
	Receive() interface{}

	// true if this party is central
	IsCentral() bool
}

type BFV_ciphertext 

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

func CentralRefresh 

func CentralRefresh(cipher BFV_ciphertext, pk BFV_encryption) BFV_ciphertext

func OuterRefresh 

func OuterRefresh(cipher BFV_ciphertext, pk BFV_encryption) BFV_ciphertext

type BFV_encryption 

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

func CentralKeyGenerator 

func CentralKeyGenerator(init BFV_init, channels []chan interface{}) (BFV_encryption, *bfv.SecretKey)

func OuterKeyGenerator 

func OuterKeyGenerator(init BFV_init, channel chan interface{}) (BFV_encryption, *bfv.SecretKey)

func (BFV_encryption) Add 

func (pk BFV_encryption) Add(a, b Ciphertext) (sum Ciphertext, err error)

func (BFV_encryption) CombinePartials 

func (pk BFV_encryption) CombinePartials(parts []Partial_decryption) (*big.Int, error)

func (BFV_encryption) Encrypt 

func (pk BFV_encryption) Encrypt(a *big.Int) (Ciphertext, error)

func (BFV_encryption) EvaluationSpace 

func (pk BFV_encryption) EvaluationSpace() gm.Space

func (BFV_encryption) Multiply 

func (pk BFV_encryption) Multiply(a, b Ciphertext) (product Ciphertext, err error)

func (BFV_encryption) N 

func (pk BFV_encryption) N() *big.Int

func (BFV_encryption) Scale 

func (pk BFV_encryption) Scale(cipher Ciphertext, factor *big.Int) (product Ciphertext, err error)

type BFV_eval_space 

type BFV_eval_space struct {
	BFV_encryption
}

func (BFV_eval_space) Add 

func (pk BFV_eval_space) Add(a, b interface{}) (interface{}, error)

func (BFV_eval_space) Multiply 

func (pk BFV_eval_space) Multiply(a, b interface{}) (product interface{}, err error)

func (BFV_eval_space) Scalarspace 

func (pk BFV_eval_space) Scalarspace() bool

func (BFV_eval_space) Scale 

func (pk BFV_eval_space) Scale(ciphertext interface{}, factor interface{}) (product interface{}, err error)

func (BFV_eval_space) Subtract 

func (pk BFV_eval_space) Subtract(a, b interface{}) (diff interface{}, err error)

type BFV_init 

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

type BFV_partial 

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

type BFV_secret_key 

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

func (BFV_secret_key) PartialDecrypt 

func (sk BFV_secret_key) PartialDecrypt(ciphertext Ciphertext) (Partial_decryption, error)

type Ciphertext 

type Ciphertext interface{}

func CentralInverseWorker 

func CentralInverseWorker(a Ciphertext, sk Secret_key, setting FHE_setting) Ciphertext

func CentralInverseWorkerWithFactor 

func CentralInverseWorkerWithFactor(a Ciphertext, factor *big.Int, sk Secret_key, setting FHE_setting) Ciphertext

func CentralMultWorker 

func CentralMultWorker(a, b Ciphertext, sk Secret_key, setting AHE_setting) Ciphertext

func FHEEvaluate 

func FHEEvaluate(x *big.Int, poly []Ciphertext, setting FHE_setting) Ciphertext

func FHEInterpolation 

func FHEInterpolation(q []Ciphertext, sk Secret_key, setting FHE_setting) []Ciphertext

func GetRandomEncrypted 

func GetRandomEncrypted(setting AHE_setting) (plain *big.Int, cipher Ciphertext, err error)

ASS, step 1

func OuterInverseWorker 

func OuterInverseWorker(a Ciphertext, sk Secret_key, setting FHE_setting) Ciphertext

func OuterInverseWorkerWithFactor 

func OuterInverseWorkerWithFactor(a Ciphertext, factor *big.Int, sk Secret_key, setting FHE_setting) Ciphertext

func OuterMultWorker 

func OuterMultWorker(a, b Ciphertext, sk Secret_key, setting AHE_setting) Ciphertext

func PolynomialDivisionWorker 

func PolynomialDivisionWorker(a, b gm.Matrix, a_den, b_den Ciphertext, sk Secret_key, setting AHE_setting) (gm.Matrix, gm.Matrix, gm.Matrix, Ciphertext)

returns:

  • q numerator
  • q denominator
  • r numerator
  • r denominator

func SumSlice 

func SumSlice(values []Ciphertext, setting AHE_setting) (sum Ciphertext, err error)

Mult, step 6

type DJ_ds 

type DJ_ds struct {
	*tcpaillier.DecryptionShare
}

type DJ_encryption 

type DJ_encryption struct {
	gm.DJ_public_key
}

func (DJ_encryption) Add 

func (pk DJ_encryption) Add(a, b Ciphertext) (sum Ciphertext, err error)

func (DJ_encryption) CombinePartials 

func (pk DJ_encryption) CombinePartials(parts []Partial_decryption) (plaintext *big.Int, err error)

func (DJ_encryption) Encrypt 

func (pk DJ_encryption) Encrypt(plaintext *big.Int) (ciphertext Ciphertext, err error)

func (DJ_encryption) EvaluationSpace 

func (pk DJ_encryption) EvaluationSpace() gm.Space

func (DJ_encryption) N 

func (pk DJ_encryption) N() *big.Int

func (DJ_encryption) Scale 

func (pk DJ_encryption) Scale(cipher Ciphertext, factor *big.Int) (Ciphertext, error)

type DJ_secret_key 

type DJ_secret_key struct {
	*tcpaillier.KeyShare
}

func (DJ_secret_key) PartialDecrypt 

func (sk DJ_secret_key) PartialDecrypt(ciphertext Ciphertext) (Partial_decryption, error)

type FHESetting 

type FHESetting struct {
	AHESetting
	// contains filtered or unexported fields
}

func SetupFHE 

func SetupFHE(n, T int, cs []FHE_Cryptosystem) []FHESetting

func (FHESetting) AHE_cryptosystem 

func (s FHESetting) AHE_cryptosystem() AHE_Cryptosystem

func (FHESetting) FHE_cryptosystem 

func (s FHESetting) FHE_cryptosystem() FHE_Cryptosystem

type FHE_Cryptosystem 

type FHE_Cryptosystem interface {
	AHE_Cryptosystem

	// multiplication of two elements
	Multiply(Ciphertext, Ciphertext) (Ciphertext, error)
}

type FHE_setting 

type FHE_setting interface {
	AHE_setting

	// fhe cryptosystem
	FHE_cryptosystem() FHE_Cryptosystem
}

type Partial_decryption 

type Partial_decryption interface{}

func SumMasksDecrypt 

func SumMasksDecrypt(a Ciphertext, ds []Ciphertext, sk Secret_key, setting AHE_setting) (e_partial Partial_decryption, err error)

ASS, step 5 & 6

type Secret_key 

type Secret_key interface {
	PartialDecrypt(Ciphertext) (Partial_decryption, error)
}

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