RSA算法中大素数快速生成和运算方法实现  

Implementation of Fast Generation and Operation Methods for Large Prime Numbers in RSA Algorithm

作　　者：杜俊[1] Du Jun(School of Mathematics and Information Engineering,Longdong University,Qingyang 745000)

机构地区：[1]陇东学院数学与信息工程学院,甘肃庆阳745000

出　　处：《中阿科技论坛（中英文）》2024年第9期108-112,共5页China-Arab States Science and Technology Forum

基　　金：庆阳市科技计划项目(QY2021A-S074);甘肃省教育科技创新项目(2022A-132);陇东学院青年科技创新项目(XYZK2107)。

摘　　要：RSA算法是目前应用最为广泛的公钥密码算法,其安全性是以大质数因子的分解不存在经典的多项式算法为基础,对极大整数进行因数分解的难度决定了RSA算法的可靠性。密钥的生成需要依赖于大素数,而大数的产生由于其复杂性和计算成本较高,成为影响RSA算法效率的重要因素。文章提出并实现了一种快速产生大数的方法,使用随机数生成器生成指定范围内的随机数,并利用素性测试算法对生成的随机数进行素性验证;针对不符合条件的数值进行调整和重新生成,直至得到符合要求的大素数。测试验证结果表明,文章提出的快速生成大数方法能显著提高大素数生成的效率,大幅缩短大素数的生成时间,有效保证生成数的素性和安全性。RSA algorithm is currently the most widely used public-key cryptography algorithm,and its security is based on the fact that there is no classical polynomial algorithm for factoring large prime numbers.Hence,the difficulty of factoring large integers determines the reliability of RSA algorithm.The generation of keys relies on large prime numbers,which,due to their complexity and high computational cost,become a key factor to the efficiency of RSA algorithms.To address this,the article proposes an efficient method which uses a generator to generate random numbers within a specified range,then employing an algorithm to verify the prime of the generated numbers;finally,adjusting and regenerate values that do not meet the criteria until a large prime number that meets the requirements is obtained.The verification results show that the proposed method can significantly enhance the efficiency of generating large prime numbers and ensure the prime nature and security of the generated numbers.

关 键 词：网络安全 RSA 大素数 素性测试 快速生成 

分 类 号：TP313[自动化与计算机技术—计算机软件与理论]