RSA密码基本运算工具的设计与实现

发布时间：2018-07-01 16:22

本文选题：公钥密码 + 大整数　；参考：《华中科技大学》2014年硕士论文

【摘要】：RSA公钥密码不仅可以用于加密，也是第一个可用于数字签名和身份验证的密码体制，其安全性和抗攻击性在广泛的应用中不断得到人们的肯定，是现代密码学研究领域中一个重要的里程碑。基于对密码安全性的考虑，，RSA密码对密钥规模的要求已经达到1024比特，具有更高要求的密码体制要求密钥长度为2048比特甚至以上。 RSA密码技术讨论集中于大素数的生成、RSA密钥对生成、RSA加密解密计算与对RSA作安全分析，其包括对模数的分解问题。这些都需要大数（1024比特以上）模幂等基本计算。而考虑到安全性RSA密码还需要以Miller-Rabin检测次数不限定的方法过滤出高概率的概率素数。为适应RSA密码实现与安全分析的需要，以RSA密码相关计算技术为研究对象深入分析，设计并实现了RSA密码基本运算工具，其具有多种大整数的基本运算、大素数产生、RSA密钥对生成、RSA加密解密以及模数n分解功能，运算数据可达2048比特，满足并超过了RSA密码对现有应用的基本要求，使生成的RSA密码具有更高的安全性。除实现大数基本运算外，工具还提供了模加、模减、模乘以及乘法逆元等大整数运算功能，可用于大整数的基本计算。素数生成工具采用随机递增搜索法对素数进行探测并可根据需要设定Miller-Rabin检测次数，提高了素数产生的质量，对系统安全性有很大的影响。实现了基于中国剩余定理的解密算法，通过降低模指数提高RSA解密效率以及工具实用性。经过测试，RSA密码基本运算工具基本实现了预期功能，对RSA的进一步研究与工具的深度开发具有重要意义。
[Abstract]:RSA public key cryptography can be used not only for encryption, but also for digital signature and authentication. It is an important milestone in the field of modern cryptography. Based on the consideration of cryptographic security, the requirement of key size for RSA cryptography has reached 1024 bits. The cryptosystem with higher requirements requires the length of the key to be 2048 bits or more. The discussion of RSA cryptography technology focuses on the generation of large prime numbers and the encryption and decryption calculation of RSA encryption and decryption and the security analysis of RSA. It includes the decomposition of modulus. All of these require the basic calculation of the modular idempotent of large numbers (1024 bits or more). Considering the security of RSA cipher, we also need to filter the probabilistic prime number of high probability by Miller-Rabin detection method. In order to meet the needs of RSA cryptographic implementation and security analysis, a RSA cryptographic basic operation tool is designed and implemented with RSA cryptographic computing technology as the research object, which has a variety of basic operations of large integers. The large prime number produces RSA key pair to generate RSA encryption and decryption as well as the modulus n decomposition function. The operation data can reach 2048 bits, which satisfies and exceeds the basic requirements of the existing application of RSA cryptography, which makes the generated RSA cipher more secure. In addition to the basic operation of large numbers, the tool also provides large integer operations such as module addition, module subtraction, modular multiplication and multiplication inverse, which can be used for the basic calculation of large integers. The prime generating tool uses random incremental search method to detect prime number and can set Miller-Rabin detection times according to the need, which improves the quality of prime number generation and has a great influence on system security. The decryption algorithm based on the Chinese residue theorem is implemented. The efficiency of RSA decryption is improved by reducing the modulus index and the utility of the tool is improved. After testing, the basic cryptographic operation tool of RSA has basically realized the expected function, which is of great significance to the further study of RSA and the deep development of the tool.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

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