Comparison of Three Parallel Point-Multiplication Algorithms on Conic Curves
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 point-multiplication on conic curves over ring Zn and it is more efficient than the preceding ones.
Keywordsconic curves ring Zn finite field Fp point-addition point-double point-multiplication Chinese Remainder Theorem
Unable to display preview. Download preview PDF.
- 1.Cao, Z.: A public key cryptosystem based on a conic over finite fields Fp. In: Advances in Cryptology: Chinacrypt 1998, pp. 45–49. Science Press, Beijing (1998) (in Chinese)Google Scholar
- 2.Cao, Z.: Conic analog of RSA cryptosystem and some improved RSA cryptosystems. Natural Science Journal of Heilongjiang University 16(4), 5–18 (1999)Google Scholar
- 3.Chen, Z., Song, X.: A public-key cryptosystem scheme on conic curves over the ring Zn. In: 6th International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2183–2187. IEEE Press, Hong Kong (2007)Google Scholar
- 5.Wang, B., Zhu, W., Sun, Q.: Public key cryptosystem based on the conic curves over Zn. J. Sichuan Univ. (Engin. Sci. Ed.) 37(5), 112–117 (2005) (in Chinese)Google Scholar
- 6.Li, Y.: Research of Conic Curve Cryptosystems and the Construction of CC-CSP. Thesis for the degree of master in computer application technology, Northestern University, pp. 25–27 (2008) (in Chinese) Google Scholar
- 7.Li, Y., Xiao, L., Hu, Y., Liang, A., Tian, L.: Parallel algorithms for cryptosystem on conic curves over finite field Fp. In: 9th International Conference on Grid and Cloud Computing, pp. 163–167. IEEE Press, Nanjing (2010)Google Scholar
- 8.Li, Y., Xiao, L., Liang, A., Wang, Z.: Parallel point-addition and point-double for cryptosystem on conic curves over ring Zn. In: 11th International Conference on Parallel and Distributed Computing, Applications and Technologies, pp. 317–322. IEEE Press, Wuhan (2010)Google Scholar
- 9.Li, Y., Xiao, L.: Parallel point-multiplication for conic curves cryptosystem. In: 3rd International Symposium on Parallel Architectures, Algorithms and Programming, pp. 116–120. IEEE Press, Dalian (2010)Google Scholar
- 10.Li, Y., Xiao, L., Chen, S., Tian, H., Ruan, L., Yu, B.: Parallel Extended Basic Operations for Conic Curves Cryptography over Ring Zn. In: 9th IEEE International Symposium on Parallel and Distributed Processing with Applications Workshops, pp. 203–209. IEEE Press, Busan (2011)Google Scholar
- 11.Li, Y., Xiao, L., Wang, Z., Tian, H.: High Performance Point-Multiplication for Conic Curves Cryptosystem based on Standard NAF Algorithm and Chinese Remainder Theorem. In: 2011 International Conference on Information Science and Applications. IEEE Press, Jeju (2011)Google Scholar