公开密钥密码体制RSA算法的一种实现

摘要

Through the analysis about RSA algorithm and comparison with several realization methods, aiming to the problem of huge calculation, a series of methods are adopted in order to create the secret key couple. It includes test through small prime numbers aggregate, optimized Miner-Rabit test, solution to the biggest common divisor by Stein algorithm and arithmetical compliment equation. After the discussion, a higher speed realization method is presented. In the test environment of AMD266 CPU, 64MB memory and Windows98 OS, the encryption intensity, the method length of RSA algorithm, is selected to be 1 024 bit. The average running time to extract the secret key couple of RSA algorithm is 3. 622 seconds by 100 times and satisfies the need of practicalities.%通过对RSA算法的分析和对其几种实现方法的研究比较，针对该算法巨大的计算量开销问题，对生成密钥对的全过程采用了小素数集测试、优化的Miner-Rabit测试、Stein算法、求解同余方程等一系列方法，给出了该算法运行速度较高的一种实现，在AMD266 CPU、64 MB内存、Windows98操作系统的测试环境下，选取加密强度(即RSA算法的模长)为1 024 bit时，生成RSA算法密钥对的运行时间取100次运算的平均值为3．662 s，达到了实用化要求。