大整数取模的快速运算

大整数取模运算是密码学应用的一种基本运算，尤其是在基于因子分解假设的公钥密码学中占有极其重要的地位。提出的m位和n位两个大整数快速取模算法，是利用分治法思想，将n位的大整数分解为n个独立十进制整数的组合，通过八次大整数乘法建立一个预处理表，能够有效地将大整数取模的计算复杂度降为O(n(m-n))]，经大量实验数据验证该算法的合理性和高效性。

Fast algorithm for modular operation

Modular operation is a basic operation in modern cryptography. It plays an important role in public key cryp-tography based on factorization assumption. This paper proposes a fast modular operation algorithm for the m-bit and n-bit integers. This algorithm, utilizing divide and conquer thought, transfers modular operation into subtractions, and then establishes a preprocessing table to further reduce the computational complexity to O（n（m-n）） . Experiments show that this algorithm outperforms existing algorithms.