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    National Tsing Hua University Institutional Repository > 理學院 > 數學系 > 博碩士論文  >  改良在有限體上的橢圓曲線群的乘法運算


    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86515


    Title: 改良在有限體上的橢圓曲線群的乘法運算
    Authors: 許仁傑
    Hsu, Jen-Chieh
    Description: GH02100021507
    碩士
    數學系
    Date: 2014
    Keywords: 橢圓曲線;蒙哥馬利演算法
    elliptic curves;montgomery method
    Abstract: 在西元1999年時,Lo ?pez and Dahab 想出一種基於蒙哥馬利演算法的演算法,用來計算在特徵值為2上的橢圓曲線群的乘法運算。這套演算法不需預先計算所需的數值,並且在某些特定的條件下,運算速度會比傳統的橢圓曲線群的乘法還快。這篇論文則是將這個演算法推廣到在特徵值大於3的上的橢圓曲線群上。
    In 1999,L ?opez and Dahab suggest an algorithm for non-supersingular elliptic curves y2 + xy = x3 + ax2 + b over GF(2m), and is based on an idea of Montgomery.Their algorithm is easy to implement in both hard- ware and software, works for any elliptic curved over GF(2m), requires no precomputed multiples of a point and faster on average than the tra- dition addition method. This paper describe an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves defined over GF(p), and is based on an idea of algorithm of L ?opez and Dahab.
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/86515
    Source: http://thesis.nthu.edu.tw/cgi-bin/gs/hugsweb.cgi?o=dnthucdr&i=sGH02100021507.id
    Appears in Collections:[數學系] 博碩士論文

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