域椭圆曲线点乘的VLSI实现方法研究

Research and Implementation of Point Multiplication Over Elliptic Curve F2 m Based on VLSI

摘要:

为了实现椭圆曲线密码算法的高效性,提出了基于优化的底层有限域算法的点乘设计方法;基于对二进制有限域运算的研究,提出并行模乘算法和基于欧几里得算法的右移求逆算法,并在实现中进行优化,在此基础上采用蒙哥马利算法实现点乘的快速运算；根据该算法,提出了ECC硬件电路实现方法,并用Verilog RTL进行逻辑设计,最终在Xilinx的XC7A100T FPGA硬件平台上验证实现;通过仿真测试、综合验证和时序后仿真的结果分析,所设计电路的时钟频率可以达到110 MHz,运算速度可达2.92 ms,证明了设计的有效性和可行性。

Abstract:

To realize the elliptic curve cryptography (ECC) effectively, the design method of modular multiplication based on optimized binary finite filed algorithm was presented. By the study of the binary finite fields, paralleled modular multiplication algorithm and inversion algorithm which was based on Euclidean algorithm were presented. The two algorithms were optimized during the process and then realized the fast evaluation of point multiplication by adopting Montgomery algorithm. ECC hardware implementation design was proposed based on the algorithm, and converted to logic designs using Verilog RTL, finally it worked on the XC7A100T FPGA platform of Xilinx. By pre-simulation, synthetical verification and analyzing the results of post simulation, the clock frequency of the designed circuit could reach up to 110MHz and the operating rate attained to 2.92 ms which demonstrated the feasibility and effectiveness of the project.