Outsourced Mutual Private Set Intersection Protocol for Edge-Assisted IoT

Table 3

Simulation of the queries in O-mPSI protocol.

Number	Queries
(1)	Hash (or ): If there is a record existing in list , return . Otherwise, select a random number to return, and add the record to the list (or list ).
(2)	Send (, , start): For each of the hash bins, if , choose a random number , compute , and then return ; if , choose a random number , compute , and then return .
(3)	Send (): For , if , compute , and then return ; if , compute , and then return .
(4)	Send (, (, )): For each of the hash bins, compute and . Then return .
(5)	Execute (): According to the successive simulations of the send-queries, return send-query (, start), send-query (, start), send-query (, ), send-query (, ), and send-query (, (, )).
(6)	Corrupt (): Return and if ; return and if .
(7)	Collude (): Return , , and of .
(8)	Reveal (): Compute and return the private key of and .
(9)	Challenge (): The instance randomly selects , then computes , and returns the .
(10)	Test-query (): According to the obtained from challenge-query, outputs a guess bit . If , return 1; otherwise return 0.