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

中图分类号: 

• TP309