MQ*-IP: An Identity-based Identification Scheme without Number-theoretic Assumptions

In this article, we propose an identification scheme which is based on the two combinatorial problems Multivariate Quadratic equations (MQ) and Isomorphism of Polynomials (IP). We show that this scheme is statistical zero-knowledge. Using a trapdoor for the MQ-problem, it is possible to make it also identity-based, i.e., there is no need for distributing public keys or for certificates within this scheme. The size of the public keys and the communication complexity are within the range of other non-number-theoretic identification schemes. In contrast toMQ∗-IP, these schemes do usually no permit identity-based public keys.