摘要
椭圆曲线密码系统(ECC)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，密钥尺寸短，占用带宽少等优点。因此，椭圆曲线密码系统被认为是下一代通用的公钥密码系统。
本课题先介绍了ECC的数学基础与相关理论，描述了素域Fp上椭圆曲线点群的几种运算，给出点乘，点加运算的理论基础；其次探讨了ECC的原理以及参数的选择，分析比较了ECC的安全性和有效性和kp的快速标量乘算法；第三，介绍了在VC++6.0环境下设计和实现一个素域Fp上的椭圆曲线加密算法；最后，对椭圆曲线加密算法进行了总结与展望，对ECC的发展趋势和研究方向进行了探讨。
ABSTRACT
Elliptic curve cryptosystems (ECC) is by far the highest every bit of strength of security password system.Compared with other public-key cryptosystem, elliptic curve cryptosystem besides high security, still has a little short, key dimensions load, bandwidth etc. Therefore, the elliptic curve cryptosystem is believed to be the next general public key cryptography.
This subject introduces the mathematical basis and related ecc theory, describes the elliptic curve meal Fp domain of several points of computing, give point by point and operation of the theoretical basis, Then discusses the principle and parameters of.ecc choice, analyses and compares the efficacy and safety of ECC KP mohan and rapid scalar multiply algorithm, Third, introduced in vc ++ 6.0 environment design and realization of a meal domain of Fp elliptic curve encryption algorithm, Finally, the elliptic curve encryption algorithms are summarized and the prospects of the development trend of the ECC, and research direction is discussed.
Keywords: Elliptic curve encryption, Vc + + 6.0, Algorithm
