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
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


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.


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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

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