【作者】 于彬；

【导师】 许占文；

【作者基本信息】 沈阳工业大学 ， 计算机应用技术， 2004， 硕士

【摘要】 随着信息技术的不断发展和应用，信息的安全性变得越来越重要。现在广泛使用的RSA公钥密码系统已很难满足未来人们对信息高安全性的需求。椭圆曲线密码系统(Elliptic Curve Cryptosystem)是迄今为止每比特具有最高安全强度的密码系统。与其他公钥密码系统相比，椭圆曲线密码系统除了安全性高外，还具有计算负载小，密码尺寸短，占用带宽少等优点。因此，椭圆曲线密码系统被认为是最有希望成为下一代通用的公钥密码系统。 本文首先对密码技术的发展现状及其发展趋势进行了分析和综述，详细的介绍了私钥密码系统和公钥密码系统的发展，并给出了一些典型的加密体制的简要分析。其次，探讨了椭圆曲线密码体制的原理，包括椭圆曲线密码的数学基础、椭圆曲线的基本概念、椭圆曲线密码体制的构造思想、椭圆曲线上点的运算等问题，同时分析了椭圆曲线密码系统的安全性和有效性，给出了安全椭圆曲线应该符合的三个标准。第三，给出了一个基于CM算法的安全椭圆曲线产生算法，利用这个算法产生的椭圆曲线的阶是两个大素数的乘积，并对其的正确性进行了理论上证明。第四，实现了椭圆曲线密码系统中的一些关键性算法，包括椭圆曲线生成算法、椭圆曲线密码中的KP运算、素性检测算法以及大整数间的运算。第五，提出了一种基于ECC的ElGamal数字签名方案，将经典的ElGamal数字签名方案移植到椭圆曲线密码系统之上，并验证了该方案的正确性。最后，对ECC的发展趋势和研究方向进行了探讨。更多还原

【Abstract】 With the development and application of information technology, the problem of information security becomes more and more important. RS A cryptosystem, a public-key cryptosystem being used widely today, seems to have difficulty in meeting the users’ need of higher security. So far, the Elliptic Curve Cryptosystem (ECC) provides the highest strength-per-bit of any cryptosystem known.In addition to its high security, ECC also has many other merits over other public-key cryptosystems such as less computation overheads,shorter key size, considerable bandwidth savings,and so on. All of these merits have made it the best public-key cryptosystem that is suitable for current use in future.This paper first analyses and summarizes the ststus quo and evolution trend of encryption, and introduces in detail the development of private-key cryptosystem and public-key cryptosystem, and provides the brief analysis of a few typical schemes. Second, the principle of ECC is discussed, including the math foundation of ECC, basic conception of elliptic curve, constructing idea of ECC, operation on the elliptic curve and so on. Meanwhile, the security and efficiency of ECC are analyzed and thus three conditions required by ECC are given. Third, an efficient algorithm to generate the secure elliptic curves which bases on the CM algorithm is presented. According to this algorithm, the rank of elliptic curve constructed is the product of two large prime numbers. And its correctness is proved in theory. Fourth, some key algorithms in ECC are implemented, including algorithm of generating the elliptic curve,algorithm of computing the kP of the ECC, algorithm of detecting prime number and lgorithm of operating between the big integers. Fifth, the variation of Elgamal signature scheme based on ECC is presented and its validity is proved.And the new scheme transplates the typical Elgamal signature scheme int ECC. At last, the evolution trend and reseach direction are discussed.更多还原