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Breaking Pairing-Based Cryptosystems Using ηT Pairing over GF(397)

  • Takuya Hayashi
  • Takeshi Shimoyama
  • Naoyuki Shinohara
  • Tsuyoshi Takagi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7658)

Abstract

In this paper, we discuss solving the DLP over GF(36·97) by using the function field sieve (FFS) for breaking paring-based cryptosystems using the η T pairing over GF(397). The extension degree 97 has been intensively used in benchmarking tests for the implementation of the η T pairing, and the order (923-bit) of GF(36·97) is substantially larger than the previous world record (676-bit) of solving the DLP by using the FFS. We implemented the FFS for the medium prime case, and proposed several improvements of the FFS. Finally, we succeeded in solving the DLP over GF(36·97). The entire computational time requires about 148.2 days using 252 CPU cores.

Keywords

pairing-based cryptosystems ηT pairing discrete logarithm problems function filed sieve 

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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Takuya Hayashi
    • 1
  • Takeshi Shimoyama
    • 2
  • Naoyuki Shinohara
    • 3
  • Tsuyoshi Takagi
    • 1
  1. 1.Kyushu UniversityJapan
  2. 2.FUJITSU LABORATORIES Ltd.Japan
  3. 3.National Institute of Information and Communications TechnologyJapan

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