计算机工程 ›› 2010, Vol. 36 ›› Issue (7): 153-155,.doi: 10.3969/j.issn.1000-3428.2010.07.052

• 安全技术 • 上一篇    下一篇

基于完全平方数的RSA密码分析算法机理

孙克泉   

  1. (南开社区学院计算机系,天津 300100)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2010-04-05 发布日期:2010-04-05

RSA Cryptanalysis Algorithm Mechanism Based on Complete Square Number

SUN Ke-quan   

  1. (Department of Computer, Nankai Community College, Tianjin 300100)
  • Received:1900-01-01 Revised:1900-01-01 Online:2010-04-05 Published:2010-04-05

摘要: 给出基于完全平方数的RSA密码分析算法的机理,分析满足同余式x2≡y2 (mod n)的完全平方数x和y的数域选择与算法效率的关系。通过数学证明和相关分析方法,定义RSA公钥n的素因子特征c,证明当c>2时,如果数域范围选择和构造的算法得当,则分解n的效率较高,当c<2时,使算法的运算数域增大,可以降低分解n的效率和有效性,即构造的RSA密码是安全的。

关键词: RSA密码分析, 平方数, 筛法, 特征, 数论

Abstract: Cryptanalysis on RSA algorithm method based on the complete square numbers is presented, which concludes the number field selection and arithmetic efficiency relationship of x and y that congruence for x2≡y2. Through theoretical proof and related research to its mechanism, and c that is called the characteristic of n prime factor of public key is constituted. The result shows: the efficiency of n-decomposition is high with right number field range and algorithm while c>2, and which is low because of the large number field range while c<2, so the tectonic RSA key is safe.

Key words: RSA cryptanalysis, square number, sieve method, characteristic, number theory

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