Volume 37 Issue 11
Nov.  2011
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Zhang Xiaoqiang, Zhu Guiliang, Wang Weiping, et al. Scalar multiplication algorithm of ECC based on precomputation and periodicity[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(11): 1451-1455. (in Chinese)
Citation: Zhang Xiaoqiang, Zhu Guiliang, Wang Weiping, et al. Scalar multiplication algorithm of ECC based on precomputation and periodicity[J]. Journal of Beijing University of Aeronautics and Astronautics, 2011, 37(11): 1451-1455. (in Chinese)

Scalar multiplication algorithm of ECC based on precomputation and periodicity

  • Received Date: 02 Jul 2010
  • Publish Date: 30 Nov 2011
  • Based on the binary method, non-adjacent form (NAF) method, etc., a new scalar multiplication algorithm was proposed, which uses the periodicity of based point and the precomputation mean. Meanwhile, the steps of new algorithm were given. The periodicity of based point and the coefficient of scalar multiplication determine performing the operation of scalar multiplication directly or computing its inverse element. The precomputation mean can void a quantity of repeat computation during the encryption and decryption processes of elliptic curve cryptosystem (ECC). To verify the correctness of new algorithm, a concrete experiment was offered with an elliptic curve, whose key length is 192 bit. The experimental results and algorithm analyses show that comparing with binary and NAF methods, although the new algorithm requires a little extra space to store precomputed points, it does not need the operation of point doublings and reduces the operation times of point addition. Therefore, the new algorithm can improve the efficiency of scalar multiplication sharply. The research achievement is significant for completing the theory of ECC and accelerating its application in practice.

     

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  • [1] Yang Feng,Zhong Cheng,Yin Mengxiao,et al.Teaching cryptology course based on theory-algorithm-practice-application mode//Proceedings of the 1st International Workshop on Education Technology and Computer Science.Shanghai:Inst.of Elec and Elec Eng Computer Society,2009:468-470 [2] Koray K,Berkant U.Invalid-curve attacks on (hyper) elliptic curve cryptosystems[J].Advances in Mathematics of Communications,2010,4(3):307-321 [3] 祝跃飞,张亚娟.椭圆曲线公钥密码导引[M].北京:科学出版社,2006:129,219-223 Zhu Yuefei,Zhang Yajuan.Introduction of elliptic curve cyptosystem[M].Beijing:Science Press,2006:129,219-223(in Chinese) [4] Shah P G,Huang Xu,Sharma D.Sliding window method with flexible window size for scalar multiplication on wireless sensor network nodes//Proceedings of the 1st International Conference on Wireless Communication and Sensor Computing.New York:IEEE Computer Society,2010:1-6 [5] Katja S S,Olivier S,Tsuyoshi T.Analysis of fractional window recoding methods and their application to elliptic curve cryptosystems[J].IEEE Transactions on Computers,2006,55(1):48-57 [6] 赵佳,韩臻.自适应的椭圆曲线滑动窗口标量乘法[J].北京交通大学学报,2007,31(2):6-9 Zhao Jia,Han Zhen.Adaptive elliptic curve sliding window scalar multiplication algorithm[J].Journal of Beijing Jiaotong University,2007,31(2):6-9(in Chinese) [7] Shah P G,Huang Xu,Sharma D.lgorithm based on one's complement for fast scalar multiplication in ECC for wireless sensor network//Proceedings of the 24th International Conference on Advanced Information Networking and Applications Workshops.New York:IEEE Computer Society,2010:571-576 [8] Wu Keke,Li Dawei,Li Huiyun,et al.Partitioned computation to accelerate scalar multiplication for elliptic curve cryptosystems//Proceedings of the 15th International Conference on Parallel and Distributed Systems.New York:IEEE Computer Society,2009:551-555 [9] Miller V.Uses of elliptic curves in cryptography//Advances in Cryptology-Crypto'85.Berlin:Springer-Verlag,1985:417-426 [10] Koblitz N.Elliptic curve cryptosystems[J].Mathematics of Computation,1987,48(17):203-209 [11] Stinson D R.Cryptography theory and practice[M].3rd ed.London:Chapman & Hall/CRC Press Taylor & Francis Group,2006:257-258 [12] Diffie W,Hellman M E.New directions in cryptography[J].IEEE Transactions on Information Theory,1976,22(6):644-654 [13] 董付国,厉玉蓉.秦九韶算法思想在RSA密码算法中的应用研究[J].计算机工程与应用,2008,44(28):65-66 Dong Fuguo,Li Yurong.Study on Qin Jiushao algorithm and its application in RSA[J].Computer Engineering and Applications,2008,44(28):65-66(in Chinese)
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