How to Prove That a Committed Number Is Prime

The problem of proving a number is of a given arithmetic format with some prime elements, is raised in RSA undeniable signature, group signature and many other cryptographic protocols. So far, there have been several studies in literature on this topic. However, except the scheme of Camenisch and Michels, other works are only limited to some special forms of arithmetic format with prime elements. In Camenisch and Michels’s scheme, the main building block is a protocol to prove a committed number to be prime based on algebraic primality testing algorithms. In this paper, we propose a new protocol to prove a committed number to be prime. Our protocol is O(t) times more efficient than Camenisch and Michels’s protocol, where t is the security parameter. This results in O(t) time improvement for the overall scheme.