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计算机工程 ›› 2006, Vol. 32 ›› Issue (23): 143-144,. doi: 10.3969/j.issn.1000-3428.2006.23.051

• 安全技术 • 上一篇    下一篇

两类超奇异椭圆曲线的快速标量乘法

张 宁1,陈志雄1,2,肖国镇1   

  1. (1. 西安电子科技大学ISN国家重点实验室信息保密研究所,西安710071 2;2. 莆田学院数学系,莆田 351100)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2006-12-05 发布日期:2006-12-05

Fast Scalar Multiplication on Two Family of Supersingular Elliptic Curve

ZHANG Ning1, CHEN Zhixiong1,2, XIAO Guozhen1   

  1. (1. Information Security & Privacy Institute in ISN, Xidian University, Xi’an 710071; 2. Department of Mathematics, Putian College, Putian 351100)
  • Received:1900-01-01 Revised:1900-01-01 Online:2006-12-05 Published:2006-12-05

摘要: 研究了特征为2和3的域上的超奇异椭圆曲线的快速标量乘法。该两类曲线适合建立可证明安全的密码体制,利用这两类曲线的复乘性质,结合Frobenius自同态和可以简单计算的自同态,给出了一种不用预计算的快速算法,相较IEEE1363标准算法,计算效率分别提高了4倍和3倍。

关键词: 密码学, 椭圆曲线, 标量乘法

Abstract: Fast scalar multiplication on two family of supersingular elliptic curves in characteristic 2 and 3 is discussed. Provable secure cryptographic scheme can be obtained on these curves. With the complex multiplication property of these curves, a fast algorithm without precomputation is derived from Frobenius endomorphism and another fast endomorphism, which is 4 times and 3 times faster than IEEE1363 standard method.

Key words: Cryptography, Elliptic curve, Scalar multiplication