基于改进<i<x</i<<sup<2<sup<<i<n</i<</sup<</sup<次方器的二进制域快速模逆

A Fast Modular Inversion Architecture over GF(2<sup<<i<m</i<</sup<) Based Modified <i<x</i<<sup<2<sup<<i<n</i<</sup<</sup< Units

  • 摘要: 研究椭圆曲线加密算法(ECC)中模逆运算的硬件结构.实现了2个基于Itoh-Tsujii算法(ITA)的模逆硬件结构,最小时钟周期模逆结构(LCC)和高速模逆结构(HS),两种结构均使用简化为非迭代逻辑的二进制域2<sup<<i<n</i<</sup<次方器和模乘器,并在Xilinx Virtex-5上实现.综合结果表明,本算法提高了时钟频率,两种结构分别达到了不同场景的最小延迟.LCC结构在GF (2<sup<163</sup<)上用9周期完成运算,频率达到126.1 MHz,性能比以往工作提高56%;HS结构在GF (2<sup<193</sup<)上用20周期完成两次运算,频率达到177.6 MHz,性能比以往工作提高134%.

     

    Abstract: A high-speed hardware architecture was presented to implement modular inversion operations for the field of elliptic curve cryptograph (ECC) in the paper. Two hardware architectures based on Itoh-Tsujii algorithm (ITA), Least-Cock-Cycle-ITA (LCC-ITA) architecture and high-speed-ITA (HS-ITA) architecture, were built and implemented on Xilinx Virtex-5. In the architectures, power operations and multiplications were simplified into non-iterative logic to speed up modular inversion operations. The test results show that the operating frequencies of both architectures are higher than the work before. LCC-ITA architecture takes nine clock cycles to complete a modular inversion operation with the operating frequency 126.1 MHz over GF(2<sup<163</sup<), while HS-ITA architecture takes 20 cycles with the operating frequency 177.6 MHz over GF(2<sup<193</sup<).

     

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