Computing Discrete Logarithms in \({\mathbb F}_{3^{6 \cdot 137}}\) and \({\mathbb F}_{3^{6 \cdot 163}}\) Using Magma

  • Gora Adj
  • Alfred Menezes
  • Thomaz Oliveira
  • Francisco Rodríguez-Henríquez
Conference paper

DOI: 10.1007/978-3-319-16277-5_1

Volume 9061 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Adj G., Menezes A., Oliveira T., Rodríguez-Henríquez F. (2015) Computing Discrete Logarithms in \({\mathbb F}_{3^{6 \cdot 137}}\) and \({\mathbb F}_{3^{6 \cdot 163}}\) Using Magma. In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham

Abstract

We show that a Magma implementation of Joux’s \(L[1/4+o(1)]\) algorithm can be used to compute discrete logarithms in the 1303-bit finite field \({\mathbb F}_{3^{6 \cdot 137}}\) and the 1551-bit finite field \({\mathbb F}_{3^{6 \cdot 163}}\) with very modest computational resources. Our \({\mathbb F}_{3^{6 \cdot 137}}\) implementation was the first to illustrate the effectiveness of Joux’s algorithm for computing discrete logarithms in small-characteristic finite fields that are not Kummer or twisted-Kummer extensions.

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Gora Adj
    • 1
  • Alfred Menezes
    • 2
  • Thomaz Oliveira
    • 1
  • Francisco Rodríguez-Henríquez
    • 1
  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico CityMexico
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada