Improvement of Faugère et al.'s method to solve ECDLP

Yun Ju Huang, Christophe Petit, Naoyuki Shinohara, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

Solving the elliptic curve discrete logarithm problem (ECDLP) by using Gröbner basis has recently appeared as a new threat to the security of elliptic curve cryptography and pairing-based cryptosystems. At Eurocrypt 2012, Faugère, Perret, Petit and Renault proposed a new method using a multivariable polynomial system to solve ECDLP over finite fields of characteristic 2. At Asiacrypt 2012, Petit and Quisquater showed that this method may beat generic algorithms for extension degrees larger than about 2000. In this paper, we propose a variant of Faugère et al.'s attack that practically reduces the computation time and memory required. Our variant is based on the idea of symmetrization. This idea already provided practical improvements in several previous works for composite-degree extension fields, but its application to prime-degree extension fields has been more challenging. To exploit symmetries in an efficient way in that case, we specialize the definition of factor basis used in Faugère et al.'s attack to replace the original polynomial system by a new and simpler one. We provide theoretical and experimental evidence that our method is faster and requires less memory than Faugère et al.'s method when the extension degree is large enough.

Original languageEnglish
Title of host publicationAdvances in Information and Computer Security - 8th International Workshop on Security, IWSEC 2013, Proceedings
Pages115-132
Number of pages18
DOIs
Publication statusPublished - Dec 1 2013
Event8th International Workshop on Security, IWSEC 2013 - Okinawa, Japan
Duration: Nov 18 2013Nov 20 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8231 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th International Workshop on Security, IWSEC 2013
CountryJapan
CityOkinawa
Period11/18/1311/20/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Huang, Y. J., Petit, C., Shinohara, N., & Takagi, T. (2013). Improvement of Faugère et al.'s method to solve ECDLP. In Advances in Information and Computer Security - 8th International Workshop on Security, IWSEC 2013, Proceedings (pp. 115-132). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8231 LNCS). https://doi.org/10.1007/978-3-642-41383-4_8