A Public-Key Cryptosystem Scheme on Conic Curves Over Z<inf>n</inf>

Abstract

A public key cryptosystem scheme is proposed that are based on conic curves over the ring Zn. Our scheme is motivated by KMOV scheme on elliptic curves, but our scheme remove some restrictive condition from KMOV scheme and constructed on conic curves. Its security bases on the difficulty of factoring a composite number n, just like RSA. It can resist some of the known attacks on RSA. We also constructed digital signature and a proxy signature on our scheme. Since encoding and decoding over conic are easily implement, it has enabled our scheme to greatly enhance efficiency. Also, our schemes can be used in the mobile payment system with the limited bandwidth.