椭圆曲线密码的优化设计方法  

Optimized design method on elliptic curve cryptography

作　　者：崔西宁[1,2] 杨经纬[3] 叶宏[2] 戴小氐[2] 

机构地区：[1]西安电子科技大学计算机学院,陕西西安710071 [2]中国航空计算技术研究所,陕西西安710068 [3]北京航空航天大学计算机科学与工程学院,北京100191

出　　处：《西安电子科技大学学报》2015年第1期69-74,共6页Journal of Xidian University

基　　金：国家重大科技专项资助项目(2012ZX01041-006);航空科学基金资助项目(2013ZC31003;2011ZC31006)

摘　　要：椭圆曲线密码算法依赖于离散对数问题的困难性,具有安全强度高、计算复杂度小的特点.椭圆曲线密码系统的主要操作为点乘运算,是加解密过程中最为耗时的部分.文中对点乘运算进行优化,提出了椭圆曲线密码算法实现的硬件体系结构,设计了基于FPGA/ASIC的加解密系统.通过对有限二进制域的乘法优化、平方优化和除法优化,提高了加解密算法的实现效率.分析和测试表明,所设计的硬件体系结构具有硬件资源消耗小、模块接口复杂度低和可扩展性强的特点,且支持113、163、193等多种密钥长度,相对于椭圆曲线密码算法的软件实现,文中的椭圆曲线密码处理器加速比最高可达到上千倍.Elliptic Curve Cryptography algorithm, which depends on the difficulty of the discrete logarithm problem, has some characteristics of low computational overhead and high security. The main operation of Elliptic Curve Cryptography is point multiplication which is the most time-consuming part in the encryption and decryption process. This paper optimizes the point multiplication, proposes a hardware architecture to implement Elliptic Curve Cryptography algorithm and designs encryption and decryption system basing on FGPA. The proposed method improves the encryption and decryption efficiency by the multiplication, squaring and division optimization in the finite binary field. Analysis and testing show that the proposed architecture has some advantages with low hard resource consumption, low complexity of module interface and scalability, the designed encryption and decryption system supports key length of ll3bit, 163 bit, 193 bit and so on, and relative to the software Elliptic Curve Cryptography system running on embedded processor, this encryption and decryption processor can achieve thousands of times faster.

关 键 词：现场可编程门阵列 椭圆曲线密码算法 椭圆曲线 点乘 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]