Design And Analysis Of Three-party Oblivious Polynomial Evaluation Protocols

Secure multi-party computation(SMC)protocols complete the computation tasks without leaking secrets of participants when the third trusted party is not available.With significant values in both application and theory,SMC protocols have been a hot area of cryptography research for several years.Oblivious transfer(OT)protocol is an important primitive which could be used in many advanced cryptographic protocols.It is extensively studied in recent decades.Aiming at privacy protection in the multi-party computation,two three-party oblivious polynomial evaluation(OPE)protocols are proposed.There are three parties in the protocols,a sender who has a bivariate polynomial P(x,y),and two receivers who have the values of ? and ?,respectively.The protocols are to achieve the goal: the receivers can only get the value of P(?,?)but nothing else about the polynomial P;and the sender can't access any information about ? and ?.This paper firstly proposes a three-party oblivious polynomial evaluation protocol which is secure against the semi-honest participants.On the basis of the first protocol,an improved protocol which is secure against the malicious participants is proposed.The first one is more efficient but the second one is more secure.Both of the protocols are useful in practice.Through theoretical analysis,the protocols are proved to be correct and secure for both the sender and receivers.Then,the paper proposes the application scenarios of the protocols.And a privacy preserving two-party Hamming distance protocol via OPE protocol is illustrated.Last but not least,the efficiency of the protocols is carefully analyzed.And an experiment is carried out to show the correctness and the feasibility.The protocols can be implemented by any secure oblivious transfer protocols and the Diffie-Hellman key exchange protocol.The protocols expand the use of oblivious transfer protocols,provide a new way for secure multi-party computation,and have wide application.