International Association for Cryptologic Research
The authors investigate the use of multivariate polynomials in constructing a fully homomorphic encryption. In this paper they come up with two fully homomorphic schemes. First, they propose an IND-CPA secure symmetric key homomorphic encryption scheme using multivariate polynomial ring over finite fields. This scheme gives a method of constructing a CPA secure homomorphic encryption scheme from another symmetric deterministic CPA secure scheme. They base the security of the scheme on pseudo random functions and also construct an information theoretically secure variant, rather than basing security on hard problems like ideal membership and grobner basis as seen in most polly cracker based schemes which also use multivariate polynomial rings.