| 椭圆曲线素阶群上的离散对数求解 |
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| 引用本文： | 李俊全,刘木兰.椭圆曲线素阶群上的离散对数求解[J].系统科学与数学,2004,24(4):443-450. |
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| 作者姓名： | 李俊全 刘木兰 |
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| 作者单位： | 中国科学院数学与系统科学研究院系统科学研究所信息安全中心,北京,100080 |
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| 基金项目： | 国家自然科学基金(60083002,90304012)资助课题. |
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| 摘 要： | 该文对解椭圆曲线上离散对数的Pollard ρ算法和并行碰撞搜索算法分别建立了它 们的图论模型和分析了碰撞技巧,比较了两个算法,进而提出了设计迭代函数的准则并 给出一个改进的并行碰撞算法.
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| 关 键 词： | 椭圆曲线离散对数 Pollardρ算法 并行碰撞搜索 迭代函数 |
| 修稿时间： | 2003年5月8日 |
SOLVING DISCRETE LOGARITHN PROBLEMS OVER A GROUP OF ELLIPTIC CURVE WITH PRIME ORDER |
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| Jun Quan LI,Mu Lan LIU.SOLVING DISCRETE LOGARITHN PROBLEMS OVER A GROUP OF ELLIPTIC CURVE WITH PRIME ORDER[J].Journal of Systems Science and Mathematical Sciences,2004,24(4):443-450. |
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| Authors: | Jun Quan LI Mu Lan LIU |
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| Institution: | Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences, Beijing 100080 |
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| Abstract: | In this paper, the graph models of Pollard p algorithm and parallel collision search algorithm for solving discrete logarithm problem over a group of elliptic curves with prime order are established. The collision technic is analyzed, and these two algorithms are compared. Furthermore, a criterion designing iteration functions is proposed and an improved parallel collision algorithm is given. |
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| Keywords: | Elliptic curve discrete logarithm pollard $\rho$ algorithm parallel collision search algorithm it |
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