Comparison of Three Parallel Point-Multiplication Algorithms on Conic Curves

Abstract

This paper makes a comparison of three parallel point-multiplication algorithms on conic curves over ring Zn. We propose one algorithm for paralleling point-multiplication by utilizing Chinese Remainder Theorem to divide point-multiplication over ring Zn into two different point-multiplications over finite field and to compute them respectively. Time complexity and speedup ratio of this parallel algorithm are computed on the basis of our previous research about the basic parallel algorithms in conic curves cryptosystem. A quantitative performance analysis is made to compare this algorithm with two other algorithms we designed before. The performance comparison demonstrates that the algorithm presented in this paper can reduce time complexity of pointmultiplication on conic curves over ring Zn and it is more efficient than the preceding ones.