High quality resource sharing

threshold PSI

If the number of intersections exceeds a given threshold , Allow the distributed participants to find the intersection in their own set , Besides the intersection , No additional information is available .

Realize the thesis ： Multi-Party Threshold Private Set Intersection with Sublinear Communication

Source code address ：https://github.com/ontanj/tpsi

among FTPSI−intFTPSI−intF_{TPSI-int} Make some modifications , Because it is based on TFHE Unable to bootstrap （bootstrapping） technology .

The encryption algorithm used ：

TAHETAHETAHE：Paillier-https://github.com/niclabs/tcpaillier

TFHETFHETFHE：BFV-https://github.com/ldsec/lattigo

Interface ：

（1）AHE_Cryptosystem and FHE_Cryptosystem Realize homomorphic operation

type AHE_Cryptosystem interface {

    //  Ciphertext + Ciphertext 
    Add(Ciphertext, Ciphertext) (sum Ciphertext, err error)

    //  Ciphertext ^{ Plaintext }
    Scale(cipher Ciphertext, factor *big.Int) (product Ciphertext, err error)
    
    //  encryption 
    Encrypt(*big.Int) (Ciphertext, error)

    //  Aggregate plaintext 
    CombinePartials([]Partial_decryption) (*big.Int, error)

    //  Calculate the encryption matrix 
    EvaluationSpace() gm.Space

    //  Clear text space size 
    N() *big.Int
}
type FHE_Cryptosystem interface {
    AHE_Cryptosystem

    //  Ciphertext * Ciphertext 
    Multiply(Ciphertext, Ciphertext) (Ciphertext, error)
}

（2）AHE_setting and FHE_setting Include the number of participants 、 Threshold size and communication mode

type AHE_setting interface {
	//  threshold 
	Threshold() int

	//  Participant 
	Parties() int

	// AHE
	AHE\_cryptosystem() AHE_Cryptosystem

	// central Party releases information to others 
	Distribute(interface{})

	//  Others give central Party delivers messages 
	Send(interface{})

	// central Party sends a message to the designated party 
	SendTo(int, interface{})

	// central We are waiting for news from others , And its （ According to the order ） grouping 
	ReceiveAll() []interface{}

	//  To take over central Party's message 
	Receive() interface{}

	//  Judge whether it is central Fang 
	IsCentral() bool
}
type FHE_setting interface {
	AHE_setting

	// FHE
	FHE\_cryptosystem() FHE_Cryptosystem
}

This experiment simulates multi-party communication on a machine , adopt goroutine Realization .

goroutine： stay go In language , Each concurrent execution unit is called goroutine, If a program contains multiple goroutine, Calls to two functions may occur at the same time .

function ：

go run main/main.go diff dj 7 main/elements

among FTPSI-diff It uses TAHE, The threshold for 7.

function ：

（1）TPSIdiffWorker, Find the intersection and difference set under the intersection test

（2）TPSIintWorker： Find the intersection and difference set under the difference set test

test ：

P1：0,3,6,9,13,16
P2：0,3,6,9,14,17
P3：0,3,6,9,14,15
P4：0,3,6,9,12,17
P5：0,3,6,9,13,15

T=7

// When the intersection is large TFHE seek 
go run main/main.go int bfv 7 main/elements
// The difference set hour is used TAHE seek 
go run main/main.go diff dj 7 main/elements
// The difference set hour is used TFHE seek 
go run main/main.go diff bfv 7 main/elements

summary ：
use FHE Realization , Efficiency is obvious ！