基于GF（2^m）的椭圆曲线求逆算法的改进研究

Improvement and research of inversion algorithm of elliptic curve based on GF （2m）

针对二进制域上现有求逆算法计算量大、并行度小、速度慢的缺点进行改进,基于二元Euclidean算法提出了改进,设计了相应的乘法器硬件结构,并且分析了其运算效能和资源占用情况。将此求逆计算器的并行改进算法使用Verilog语言编程实现,利用Xilinx ISE 12.4对整个求逆算法综合仿真(行为级),在Xilinx Virtex-5 XC5VFX70T的硬件平台上验证求逆算法的运算效率,结果表明对求逆算法的改进有效地提高了求逆运算的速度。

Since the existing inversion operation algorithm based on GF（2^m） has the following disadvantages： large amount of calculation, poor degree of parallelism and slow speed, an improved algorithm is proposed in this paper based on Extended Euclidean Algorithm. A corresponding multiplier hardware structure was designed. Its operation performance and the status of re- source occupancy are analyzed. This parallel improved algorithm of inversion operation calculator was realized with the program based Verilog. The comprehensive simulation of the whole inversion algorithm was conducted with Xilinx ISE 12.4. The opera- tion efficiency of the inversion algorithm was verified on hardware platform of Xilinx Virtex-5 xc5vfx70t. The experimental result and performance comparison show that the modification of the inversion algorithm has improved its speed.