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Published in:
2012 | OriginalPaper | Chapter
Breaking Pairing-Based Cryptosystems Using η T Pairing over GF(397)
Authors : Takuya Hayashi, Takeshi Shimoyama, Naoyuki Shinohara, Tsuyoshi Takagi
Published in: Advances in Cryptology – ASIACRYPT 2012
Publisher: Springer Berlin Heidelberg
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In this paper, we discuss solving the DLP over
GF
(3
6·97
) by using the function field sieve (FFS) for breaking paring-based cryptosystems using the
η
T
pairing over
GF
(3
97
). 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
(3
6·97
) 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
(3
6·97
). The entire computational time requires about 148.2 days using 252 CPU cores.