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-HenríquezEmail author
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.


Discrete Logarithm Discrete Logarithm Problem Bilinear Pairing Irreducible Factor Descent Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material


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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
    Email author
  1. 1.Computer Science DepartmentCINVESTAV-IPNMexico CityMexico
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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