改进椭圆曲线上离散对数问题的Pollard Rho方法的新碰撞
New Collisions to Improve Pollard's Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves
摘要：
在椭圆曲线上离散对数问题的Pollard Rho方法的加速计算中，人们采用了不同的方法。然而，捕获在循环徒劳将获得使用的随机游动与波拉德的Rho。提出了一种有效的替代方法，该方法基于依赖于值ai，bi的新冲突来解决这个问题。这可能需要更少的迭代比波拉德的Rho原始达到碰撞。因此，Pollard的Rho方法的性能更有效，因为改进的方法不仅减少了数学运算的数量，而且这些碰撞也可以应用于文献中报道的先前的改进。
英文摘要：
It is true that different approaches have been utilised to accelerate the computation of discrete logarithm problem on elliptic curves with Pollard's Rho method. However, trapping in cycles fruitless will be obtained by using the random walks with Pollard's Rho. An efficient alternative approach that is based on new collisions which are reliant on the values ai , bi to solve this problem is proposed. This may requires less iterations than Pollard's Rho original in reaching collision. Thus, the performance of Pollard's Rho method is more efficiently because the improved method not only reduces the number of mathematical operations but these collisions can also applied on previous improvements which reported in the literature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
