Knowledge-proof based versatile smart card verification protocol

We propose a zero-knowledge interactive proof based identification and signature scheme. The protocol is based on Euler's totient function and discrete logarithms over the ring Z/nZ, and can be applied to smart cards. A prover keeps a signed subgroup generator provided by a trusted center as its secret information. Our scheme has symmetricity in the sense that the same computational complexity and the same hardware both for Prover and for Verifier are required. Also, it requires minimal amount of computation and communications for secret information. The protocol is versatile enough to be applicable to digital signature scheme, multiple digital signature scheme and key exchange protocol. We outline those protocols to show the versatility of our protocol.