Oblivious Polynomial Evaluation

The problem of two-party oblivious polynomial evaluation (OPE) isstudied, where one party (Alice) has a polynomial P(x)and the other party (Bob) with an input x wants to learn P(x)in such an oblivious way that Bob obtains P(x) without learningany additional information about P except what is implied byP(x) and Alice does not know Bob's input x. The former OPEprotocols are based on an intractability assumption except for OTprotocols. In fact, evaluating P(x) is equivalent to computingthe product of the coefficient vectors (a0,……, an) and(1,……, x^n). Using this idea, an efficientscale product protocol of two vectors is proposed first and then two OPEprotocols are presented which do not need any other cryptographic assumptionexcept for OT protocol. Compared with the existing OPE protocol,another characteristic of the proposed protocols is the degree of thepolynomial is private. Another OPE protocol works in case of existenceof untrusted third party.