Zero-knowledge proofs of identity based on ELGAMAL on conic

A protocol for zero-knowledge proofs of identity based on ElGamal on conic is proposed in this paper. The solution to a hard puzzle is divided into two parts, and the P (prover) provides one of them according to the V (verifier)s random bit. The eavesdropper cannot obtain any useful knowledge about the P (prover)s identity during the process of authentication. No adversary in this protocol can cheat each other or get the privacy of each other. The security of this protocol relies on the discrete logarithm problem on conic over finite fields. Compared with those identification protocols implemented on elliptic, these kinds of identification protocols implemented on conic can be designed and implemented easier. Corresponding to the simple version, a parallel version is presented subsequently. The characteristic of ZKp and security of the simple version is proved. The trait of our identification protocol is given. We also analyzed the "soundness", the "completeness", before analyzed the amount of computation in the protocol. A simple solution considering t(timeout) is proposed to prevent a potential leak of our protocol. Some problems need to be solved in the future is brought forward at the end of this paper.