An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems

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Abstract

Gaudry and Schost gave a low-memory algorithm for solving the 2-dimensional discrete logarithm problem. We present an improvement to their algorithm and extend this improvement to the general multidimensional DLP. An important component of the algorithm is a multidimensional pseudorandom walk which we analyse thoroughly in the 1 and 2 dimensional cases as well as giving some discussion for higher dimensions.