Parallel point-addition and point-double for cryptosystem on conic curves over ring Zn

Conic curves cryptosystem is a new technology for achieving information security. Point-addition and point-double are fundamental operations in conic curves cryptosystem over ring Zn. There is no existing research about the parallel computation for conic curves cryptosystem over ring Zn. This paper proposes parallel algorithms of point-addition and point-double for cryptosystem on conic curves over ring Zn. Additionally, we present a methodology to simplify the operation of computing greatest common factor by replacing it using two reduction operations in this cryptosystem. Research in this paper is based on our previous works about parallel algorithms for conic curves cryptosystem over finite field Fp. We design the parallel algorithms by analyzing basic multiple-precision algorithms used in these operations. The performance evaluation demonstrates that our methodology could improve efficiency for conic curves cryptosystem over ring Zn.