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Koblitz曲线密码中倍点运算算法的改进

An Improved Method for Computing Multiplying Points on Koblitz Curve Cryptography
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摘要 针对Koblitz曲线密码中最耗时的倍点运算,提出一种新的递推算法.算法分析表明,新算法使倍点运算的效率比常规的逐点法提高55%以上,从而改善了椭圆曲线密码系统的整体运算速度. The authos analyzed the method existed and got an improved implementation curve cryptograph on computing kP. The analysis shows that the efficiency was increased 55% and this method can be used to improve the efficiency of elliptic curve cryptography method on Koblitz by a factor of over （ECC）.
作者 孙跃刚 李辉来
机构地区 吉林大学数学研究所
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2009年第2期286-288,共3页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10371050)
关键词 椭圆曲线密码 倍点 KOBLITZ曲线 elliptic curve cryptography multiplying point Koblitz curve
分类号 O157.4 [理学—基础数学]
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参考文献9

  • 1Hankerson D, Hernanclez J L, Menezes A. Software Implementation of Elliptic Curve Cryptography over Binary Fields [ C]//Proeeedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems. Berlin: Springer, 2000 : 1-24.
  • 2Lopez J, Dahab R. Improved Algorithms for Elliptic Curve Arithmetic in GF(2^n) [ C ]//Selected Areas in Cyrptography- SAC'98 LCNS 1556. Berlin: Springer, 1999: 201-212.
  • 3Solinas J A. Efficient Arithmetic on Koblitz Curves [J]. Designs, Codes, and Cyrptography, 2000, 19(2/3): 195-249.
  • 4Koblitz N. Elliptic Curve Cryptosystems [ J]. Mathematics of Computation, 1987, 48 (177) : 203-209.
  • 5Koblitz N. CM Curves with Good Cryptographic Properties [ C]//Crypto'91. London: Springer-Verlag, 1992: 279-287.
  • 6Guajardjo J, Paar C. Efficient Algorithms for Elliptic Curve Cryptosystems [ C ]//Advances in Cryptology, Proceedings of CRYPTO' 97. London: Springer-Verlag, 1997 : 342-356.
  • 7李湛.一种改进的椭圆曲线密码实现算法[J].电子科技,2004,17(7):31-33. 被引量：13
  • 8张静,辛小龙.椭圆曲线密码的快速算法[J].纯粹数学与应用数学,2008,24(1):133-135. 被引量：1
  • 9Lopez J, Dahab R. Fast Multiplication on Elliptic Curves over GF(2^m) without Precomputation: Cryptographic Hardware and Embedded Systems, Lecture Notes in Computer Science [ M ]. Berlin: Springer, 1999.

二级参考文献5

  • 1李湛.一种改进的椭圆曲线密码实现算法[J].电子科技,2004,17(7):31-33. 被引量：13
  • 2Neal Koblitz, Alfred Menezes, Scott Vanstone. The state of elliptic curve cryptography[J]. Designs, codes and cryptography, 2000,19:173-193.
  • 3Volker Muller. Fast multiplication on elliptic curves over small fields of characteristic two[J]. Journal of cryptology,1998,11:219-234.
  • 4J.Lopez,R.Dahab. Fast multiplication on elliptic curves overGF(2^m)without precomputation[J]. Crypto graphic Hardware and Embedded System,Lecture note in computer science, 1999,1717:316-327.
  • 5Neal Koblitz. CM curves with good cryptographic propertices[J]. Advance in Cryptology-CRYPTO'91,Lecture note in computer science,Springer-Verlag ,1992,576,279-287.

共引文献12

吉林大学学报（理学版）
2009年 第2期

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