“…The main reason of PSI cardinality has been widely studied is that it has many real applications. Such as, PSI cardinality has been used in privacy preserving data mining 3 , information-sharing 4 , human genome research 5 , national security 6 , Botnet identification 7 , medical data preserving 8 , 9 , social networks 10 , 11 , location privacy protecting 12 , 13 , searchable encryption scheme 14 and anonymous authentication 15 , 16 . In recent years more and more PSI cardinality protocols are proposed, e.g.…”