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On the Possibility of Transformation of Multidimensional ECDLP into 1-Dimensional ECDLP

Conference paper
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Part of the Lecture Notes in Computer Science book series (LNCS, volume 10737)

Abstract

In this article the attack on elliptic curve discrete logarithm problem (ECDLP) with partial information is considered. If unknown bits of discrete logarithm are continuous then 1-dimensional algorithms for ECDLP may be used. One of these algorithms is improved Gaudry-Schost using equivalence classes which requires \(O(1.47\sqrt{n}) \) operations. It will be showed that if unknown bits are not continuous and are given in \(c>1\) partitions and also two most significant bits are known, transformation of this partitions into one partition to use 1-dimensional algorithm without increasing size of the problem is impossible. It is also showed that in some situations it is better to “forget” some of known bits to transform the problem to 1-dimensional ECDLP.

Keywords

Elliptic curve ECDLP Partial information Multidimensional Gaudry-Schost algorithm 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Cybernetics, Institute of Mathematics and CryptologyMilitary University of Technology in WarsawWarsawPoland

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