Cryptology ePrint Archive: Report 2017/1262

A few more index calculus algorithms for the ECDLP

Gary McGuire and Daniela Mueller

Abstract: The introduction of summation polynomials for elliptic curves by Semaev has opened up new avenues of investigation in index calculus type algorithms for the elliptic curve discrete logarithm problem, and several recent papers have explored their use. Most papers use Grobner basis computations at some point. We question if Grobner bases are needed at all, and we propose a faster algorithm to solve the ECDLP that does not involve Grobner basis computations, and does not involve a linear algebra step either. We further propose an even faster algorithm that does not involve Grobner basis computations, or a linear algebra step, or summation polynomials. Our algorithms are aimed at prime order fields, although they are valid for any finite field. We give a complexity analysis of our algorithms and provide extensive computational data.

Category / Keywords: discrete logarithm problem, elliptic curve cryptosystem

Date: received 29 Dec 2017, last revised 31 Dec 2017

Contact author: gary mcguire at ucd ie

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Version: 20171231:195807 (All versions of this report)

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