摘要:
在椭圆曲线密码体制(ECC)中, 无论是最终性能或是存储需求, 最优扩域都具有明显优势。但由于ECC要求有限域Fp是素域, 而伪Mesernne素数却难以选取, 且难以满足p恰好可由目标处理机的一个寄存器表示的要求。该文利用广义Mersenne数代替伪Mesernne数, 提出了广义最优扩域的概念, 研究了其上的快速乘法运算和模约简运算, 为乘法运算给出了通用的计算量公式, 为模约简运算给出了具体的运算公式。推广了Bailey, Mihǎilescu和Woodbury等在最优扩域上的相应结果。
Abstract:
In Elliptic Curves Cryptosystems (ECC), the optimal extension fields is preferable to others method, whether concerns performance or memory request. But, it is very difficult to choose pseudo-Mersenne prime numbers, and satisfy the condition that p just is presented by a register of processor. This paper replaces pseudo-Mersenne numbers by generalized Mersenne numbers, provides a new notation-Generalized Optimal Extension Fields(GOEFs), and studies the fast arithmetic about multiplication and modular reduction in GOEFs, finally, deduces common formulas for multiplication and some more general formulas for modular reduction in GOEFs. The results in this paper extend the corresponding work on arithmetic of Bailey, Mihǎilescu, and Woodbury in OEFs.
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