Paper 2010/090

Solving a 676-bit Discrete Logarithm Problem in GF(3^{6n})

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


Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The \eta_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(3^{6n}) becomes a concern for the security of cryptosystems using \eta_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(3^{6n}). Therefore, we first fulfilled such an implementation and we successfully set a new record for solving the DLP in GF(3^{6n}), the DLP in GF(3^{6 \cdot 71}) of 676-bit size. In addition, we also compared 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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. This is a full version of PKC 2010 paper.
function field sievediscrete logarithm problempairing-based cryptosystems
Contact author(s)
takagi @ fun ac jp
2010-02-22: received
Short URL
Creative Commons Attribution


      author = {Takuya Hayashi and Naoyuki Shinohara and Lihua Wang and Shin'ichiro Matsuo and Masaaki Shirase and Tsuyoshi Takagi},
      title = {Solving a 676-bit Discrete Logarithm Problem in GF(3^{6n})},
      howpublished = {Cryptology ePrint Archive, Paper 2010/090},
      year = {2010},
      note = {\url{}},
      url = {}
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