摘要:
在橢圓曲線密碼體制(ECC)中, 無論是最終性能或是存儲需求, 最優(yōu)擴域都具有明顯優(yōu)勢。但由于ECC要求有限域Fp是素域, 而偽Mesernne素數(shù)卻難以選取, 且難以滿足p恰好可由目標處理機的一個寄存器表示的要求。該文利用廣義Mersenne數(shù)代替?zhèn)蜯esernne數(shù), 提出了廣義最優(yōu)擴域的概念, 研究了其上的快速乘法運算和模約簡運算, 為乘法運算給出了通用的計算量公式, 為模約簡運算給出了具體的運算公式。推廣了Bailey, Mihǎilescu和Woodbury等在最優(yōu)擴域上的相應(yīng)結(jié)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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