基于FPGA的椭圆曲线点乘算法设计与实现

Improvement and implementation of the algorithm design of elliptic curve dot product based on GF （2^n）

椭圆曲线密码体制的核心是椭圆曲线点乘算法,点乘算法决定了密码体制的速度和需要的硬件资源,所以本文对点乘算法进行研究.在对经典的点乘算法及其底层二进制乘法算法进行分析基础上,重点对椭圆曲线加密点乘算法和底层有限域乘法进行了改进,并利用VHDL对点乘算法各核心模块进行设计,最后利用FPGA实现了整个点乘运算.本文对改进后的椭圆曲线加密系统进行了实验仿真测试,主要对设计进行仿真验证和综合,结果证明改进后的算法能够使整个点乘运算速度得到提高,可应用于信息安全与保密通信领域.

Point multiplication algorithm is a key issue in Elliptic Curve Cryptography （ECC）, as it determines the speed and the required hardware resources of the cipher system, so this paper carries out a research on this algorithm. Based on the analysis of classical point multiplication algorithm and its binary multiplication, this paper emphatically makes an improvement on the encrypted point multiplication algorithm and the subjacent multiplication operations of elliptic curve encryption. Then, we use VHDL to design each core module, and finally realize the whole point multiplication algorithm. At last, the concerned experimental simulation of ECC system, especially the simulation and synthesis of the design is carried out and the results show that the improved algorithm can perfectly speed up the point multiplication algorithm, thus, can be applied to the information security and secure communication fields.