Solving a 676-bit discrete logarithm problem in GF(36n)

Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'Ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi

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

15 Citations (Scopus)

Abstract

Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The η T pairing on supersingular curves over GF(3 n ) is particularly popular since it is efficiently implementable. Taking into account the Menezes-Okamoto-Vanstone (MOV) attack, the discrete logarithm problem (DLP) in GF(36n ) becomes a concern for the security of cryptosystems using η T pairings in this case. In 2006, Joux and Lercier proposed a new variant of the function field sieve in the medium prime case, named JL06-FFS. We have, however, not yet found any practical implementations on JL06-FFS over GF(36n ). Therefore, we first fulfill such an implementation and we successfully set a new record for solving the DLP in GF(36n ), the DLP in GF(36•71) of 676-bit size. In addition, we also compare JL06-FFS and an earlier version, named JL02-FFS, with practical experiments. Our results confirm that the former is several times faster than the latter under certain conditions.

Original languageEnglish
Title of host publicationPublic Key Cryptography, PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
Pages351-367
Number of pages17
DOIs
Publication statusPublished - Dec 1 2010
Event13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010 - Paris, France
Duration: May 26 2010May 28 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6056 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010
CountryFrance
CityParis
Period5/26/105/28/10

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Hayashi, T., Shinohara, N., Wang, L., Matsuo, SI., Shirase, M., & Takagi, T. (2010). Solving a 676-bit discrete logarithm problem in GF(36n). In Public Key Cryptography, PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings (pp. 351-367). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6056 LNCS). https://doi.org/10.1007/978-3-642-13013-7_21