南京林业大学学报(自然科学版) ›› 2004, Vol. 28 ›› Issue (06): 27-30.doi: 10.3969/j.jssn.1000-2006.2004.06.007

• 研究论文 • 上一篇    下一篇

多精度整数高效模幂运算算法的研究

吕志英   

  1. 南京林业大学;江苏 南京 210037
  • 出版日期:2004-12-18 发布日期:2004-12-18

A Study on Multiple-precision Integer Efficient Modular Exponentiation Algorithm

L Zhi-ying   

  1. Nanjing Forestry University,Nanjing 210037,China
  • Online:2004-12-18 Published:2004-12-18

摘要: <正>介绍了多精度整数求幂运算中的"滑动窗口"算法,并结合Montgomery约简算法,对"滑动窗口"算法进行了应用研究,分析了根据多精度整数的位数来确定相应的窗口大小。结果表明,采用这种组合的模幂运算算法具有十分高效的执行效率,4096位多精度整数的模幂计算大约需要1.5s,并可满足RSA的应用对密钥长度的安全需求。

Abstract: This paper introduced a method called "sliding-window" used in multiple-precision integer exponentiation arithmetic,and studied its application combined with Montgomery reduction,and how to calculate the "window size" related to the bits of the multiple-precision integer.The result indicates that the combined algorithm carries out an efficient calculation,the elapsed time of 4 096 bits multiple-precision integers modular exponentiation is about 1.5 s,and it will be the base of applied RSA public-key cryptography used in information security.

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