J. Korean Math. Soc. 2015; 52(4): 797-819
Printed July 1, 2015
https://doi.org/10.4134/JKMS.2015.52.4.797
Copyright © The Korean Mathematical Society.
Jin Hong and Hyeonmi Lee
Seoul National University, Hanyang University
A trapdoor discrete logarithm group is a cryptographic primitive with many applications, and an algorithm that allows discrete logarithm problems to be solved faster using a pre-computed table increases the practicality of using this primitive. Currently, the distinguished point method and one extension to this algorithm are the only pre-computation aided discrete logarithm problem solving algorithms appearing in the related literature. This work investigates the possibility of adopting other pre-computation matrix structures that were originally designed for used with cryptanalytic time memory tradeoff algorithms to work as pre-computation aided discrete logarithm problem solving algorithms. We find that the classical Hellman matrix structure leads to an algorithm that has performance advantages over the two existing algorithms.
Keywords: discrete logarithm problem, pre-computation, distinguished point, time memory tradeoff
MSC numbers: Primary 11T71, 94A60; Secondary 68R99
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