Solving a 676-Bit Discrete Logarithm Problem in GF(36n)

Abstract. Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The T pairing on supersingular curves over GF(3n ) 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 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

• Type: Conference
• Year: 2010
• Where: PKC
• Authors: Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shin'ichiro Matsuo, Masaaki Shirase, Tsuyoshi Takagi
• Keywords: Cryptology, Discrete Logarithm Problem, Function Field Sieve, PKC 2010, Various Cryptographic Schemes