Attacking a Binary GLS Elliptic Curve with Magma

Conference paper

DOI: 10.1007/978-3-319-22174-8_17

Volume 9230 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Chi JJ., Oliveira T. (2015) Attacking a Binary GLS Elliptic Curve with Magma. In: Lauter K., Rodríguez-Henríquez F. (eds) Progress in Cryptology -- LATINCRYPT 2015. LATINCRYPT 2015. Lecture Notes in Computer Science, vol 9230. Springer, Cham

Abstract

In this paper we present a complete Magma implementation for solving the discrete logarithm problem (DLP) on a binary GLS curve defined over the field \(\mathbb {F}_{2^{62}}\). For this purpose, we constructed a curve vulnerable against the gGHS Weil descent attack and adapted the algorithm proposed by Enge and Gaudry to solve the DLP on the Jacobian of a genus-32 hyperelliptic curve. Furthermore, we describe a mechanism to check whether a randomly selected binary GLS curve is vulnerable against the gGHS attack. Such method works with all curves defined over binary fields and can be applied to each element of the isogeny class.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico CityMexico