【作者】 赖晖；

【导师】 唐小虎；

【作者基本信息】 西南交通大学 ， 密码学， 2007， 硕士

【摘要】 在二十一世纪，数字通信已经成为人们生活中的重要组成部分。然而，在信息的价值不断提升的同时，信息的安全性也遭受着日益严重的威胁。因此，在信息社会中，人们强烈要求有一种技术用于保护信息以及信息系统，公钥密码势必将扮演越来越重要的角色。Miller和Koblitz在上个世纪80年代提出了椭圆曲线密码体制(ECC)。ECC作为一种新的公钥密码体制，因为有着比其他公钥体制无法替代的优点(更高的安全性、更高的实现效率、更省的实现代价)，所以从提出后到现在近二十年的时间里，得到世界各地数学家和密码学家的密切关注和快速发展，并被广泛的应用于实践中。本文围绕着椭圆曲线密码体制展开讨论和研究，回顾了椭圆曲线的发展历史和应用实现，介绍了椭圆曲线密码系统基础理论。然后较全面的分析了实现椭圆曲线快速点乘算法的几个因素，提出了一种快速不定点乘算法。经过分析，证明了该算法是一个高效可行的快速点乘算法，并且需要更少的存储空间。最后给出了在DSP芯片上建立和实现椭圆曲线密码体制的全过程，同时结合TI公司TMS320C64x系列芯片的特点对程序进行了进一步的优化，形成了一个基于有限素域的椭圆曲线加密算法的底层算法函数库，并评估了实现效率。经过对比分析，本文的域运算具有更高效的实现效率。更多还原

【Abstract】 In 21st century, digital communication has become one important part of our lives. With the rise of information value, the information security faces increasingly serious menaces. Consequently, there must be some efficient technology to protect the security of information, and public key cryptography will play a more and more important role.Miller and Koblitz proposed Elliptic curve cryptosystem (ECC) in 1980s. As a new public key system, ECC is better than other public key algorithm in terms of safety, time and cost. Thus in the last 20 years, it developed fast, attracted attention from mathematicians and cryptographists of the world, and been widely used in the society.This paper is mainly about ECC system. Firstly, the history of ECC and its application implements is reviewed, and the basic theory of ECC is introduced. Then, the key factors for realization of fast point multiplication on elliptic curve are analyzed in detail and a new fast point multiplication is proposed. After analysis, it shows that the new algorithm is high efficient, feasible, and need less storage memory. Lastly, the whole realizing process of ECC system on DSPs is given in the paper, meanwhile, combining with the characteristics of TMS320C64x chips, the program is deeply optimized. As a result, a basic functions library of ECC based on finite prime number field is formed and its efficiency is evaluated. By contrasting, the efficiency of field operations in this paper is faster than others.更多还原