导　　师： 裴定一

学科专业： G0104

授予学位： 硕士

作　　者： ;

机构地区： 广州大学

摘　　要： 信息技术的不断发展，对信息安全提出了更高的要求。密码技术是保障信息安全的核心技术。在应用公钥密码体制的时候，对密钥长度要求越来越大，处理速度要求越来越快。现在广泛使用的rsa公钥密码体制已很难满足未来人们对信息高安全性的需求。而基于椭圆曲线离散对数问题的椭圆曲线密码体制，因其每比特最高的安全性，受到越来越广泛的注意。此外，椭圆曲线密码体制还具用计算负载小，密码尺寸短，占用带宽少等优点。因而特别适用于计算能力受限、空间受限、带宽受限和要求高速实现的情况。椭圆曲线密码体制的硬件快速实现成为一个倍受关注的课题。 本文从实际应用出发，研究了椭圆曲线密码体制算法的fpga的实现；以基本的数学理论，密码学理论为依据，结合一些具体的相关算法和fpga的特点，确定了密码体制的硬件实现方案。采用p1363推荐的gf(2163)上的koblitz曲线，采用微处理器模式，在fpga上实现了抵抗自主选择密文攻击的可证明安全的椭圆曲线密码体制。文章按照有限域、椭圆曲线、密码体制三方面的内容依次进行书写，每一部分分别介绍了相应的理论基础及硬件实现。 具体实现中，采用硬件描述语言vhdl，在altera公司出品的quartusⅡ5.0平台上进行电路设计。设计选用了altera公司的stratixⅡ系列器件ep2s130f1508c4。为了硬件实现上的方便高效，有限域gf(2163)上的元素利用正规基表示，其关键运算——乘法运算采用w-smpoⅡ的算法，利用状态机模式实现；椭圆曲线上的关键运算——标量乘法运算采用montgomery算法，利用微处理器模式实现；加密体制采用可证明安全opt-psec-3方案实现。程序的每一部分都结合软件编程验证以保证程序的正确性。 本设计获得了良好的性能指标：最终标量乘法的实现需要8,830个alut和5,5 With the development of information technology, the advanced information security is eagerly desired. The cryptography is the key technology. Public key cryptosystem is adopted, but larger scale keys are required with the computing arts enhanced. RSA cryptosystem, a public-key cryptosystem being used widely today, seems to have difficulty in meeting the users’need of high security. However, the elliptic curve cryptosystem /(ECC thereafter/) is widely concerned due to the highest security of the same lengthbit. In addition, ECC also has many other merits such as less computation overheads, shorter key size, considerable bandwidth savings, and so on. So the ECC is, especially, suitable for situations which are limited by capability of calculation, space, bandwidth and requirement of high implementation. The rapid implementation of the ECC hardware has been a popular topic. In this paper, we study the implementation of the ECC algorithm by the FPGA from practical aspect. Based on mathematics and cryptography theory, integrated some specific relevant algorithm and FPGA, we ascertain the implementation of ECC for hardware project. The paper, which adopts Koblitz curve on GF/(2163/) recommended by P1363 and module of microprocessor, proves security of the ECC at FPGA. The article, whose every part introduces relevant basic theory and hardware implementation respectively, is achieved by three aspects as Finity Field, the ECC and Encryption Schemes. The circuit design is achieved at the Quartus II 5.0 produced by the Altera adopted the VHDL, and choose the EP2S130F1508C4 of StratixⅡproduced by the Altera. In order to high efficiency of hardware, elements of the GF/(2163/) are showed by the Normal Basis, and its key calculation, multiplication calculation, is introduced by the w-SMPOⅡthrough implementation of module of predicament. The ECC’s key calculation----scalar quantity calculation adopts Montgomery’s algorithms and is achieved by microprocessor module. Cryptography is acheved by th

关 键 词： 信息安全 密码技术 椭圆曲线密码体制 标量乘法

领　　域： [电子电信] [电子电信]