Solving discrete logarithm problems faster with the aid of pre-computation

Abstract

A trapdoor discrete logarithm group is an algebraic structure in which the feasibility of solving discrete logarithm problems depends on the possession of some trapdoor information, and this primitive has been used in many cryptographic schemes. The current designs and applications of this primitive are such that the practicality of its use is greatly increased by methods that allow for discrete logarithm problems of sizes that are barely solvable to be solved faster. In this article, we propose an algorithm that can reduce the time taken to solve discrete logarithm problems through a one-time pre-computation process. We also provide a careful complexity analysis of the algorithm and compare its performance with those of existing algorithms for solving discrete logarithm problems with the aid of pre-computation. Our new method performs much better than the most widely known algorithm and is advantageous over a more recently proposed method in view of pre-computation cost.