The discrete logarithm problem arises from various areas, including counting the number of points of certain curves and diverse cryptographic schemes. The Gaudry–Schost algorithm and its variants are state-of-the-art low-memory methods solving the multi-dimensional discrete logarithm problem through finding collisions between pseudorandom tame walks and wild walks. In this work, we explore the impact on the choice of tame and wild sets of the Gaudry–Schost algorithm, and give two variants with improved average case time complexity for the multidimensional case under certain heuristic assumptions. We explain why the second method is asymptotically optimal.

离散对数问题来自各个领域，包括计算某些曲线的点数和不同的密码方案。Gaudry–Schost 算法及其变体是最先进的低内存方法，通过查找伪随机驯服游走和狂野游走之间的碰撞来解决多维离散对数问题。在这项工作中，我们探讨了 Gaudry-Schost 算法对驯服和野生集选择的影响，并在某些启发式假设下给出了两个具有改进的多维案例平均案例时间复杂度的变体。我们解释了为什么第二种方法是渐近最优的。