Computing Discrete Logarithms in  F_{3^{6*137}} and  F_{3^{6*163}}  using Magma

Gora Adj; Alfred Menezes; Thomaz Oliveira; Francisco Rodríguez-Henríquez

Paper 2014/057 Original: eprint.iacr.org/2014/057 ↗

Computing Discrete Logarithms in F_{3^{6137}} and F_{3^{6163}} using Magma

Gora Adj

Alfred Menezes

Thomaz Oliveira

Francisco Rodríguez-Henríquez

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 F_{3^{6*137}} and the 1551-bit finite field F_{3^{6*163}} with very modest computational resources. Our F_{3^{6*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.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2014-11-12: last updated; 2014-01-26: published
Short URL: https://ia.cr/2014/057
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2014/057,
      author = {Gora Adj and Alfred Menezes and Thomaz Oliveira and Francisco Rodríguez-Henríquez},
      title = {Computing Discrete Logarithms in  F_{3^{6*137}} and  F_{3^{6*163}}  using Magma},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/057},
      year = {2014},
      url = {https://eprint.iacr.org/2014/057}
}