Outsourced Mutual Private Set Intersection Protocol for Edge-Assisted IoT

Algorithm 1

ElGamal threshold encryption protocol.

	Inputs:
	: The cuckoo hash table
	: The hash table
	Output: the encrypted cuckoo hash table and .
	Key generation phase
	and calculate as below:
	1. Determine a hash function .
	2. Run the KeyGen algorithm in ElGamal threshold encryption to generate the key pairs .
	3. Publish the public keys and keep the private key .
	4. Each party computes .
	Encryption phase
	1. encrypts the cuckoo hash table by bins, for all , computes as follows:
	(1) choose a random number , for all items in the k^th cuckoo hash table , using ElGamal threshold encryption algorithm to encrypt them:
	(2) sends to in shuffled order.
	2. encrypts the hash table by bins, for all , computes as follows:
	(1) choose a random number , for all items in the k^th hash table , using ElGamal threshold encryption algorithm to encrypt them:
	(2) sends to in shuffled order.
	3. re-randomizes the received by bins. For all and , computes as follows: .
	Then .
	4. re-randomizes the received by bins. For all and , computes as follows:
	Then .