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Strategies in Filtering in the Number Field Sieve
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Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three
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Designs, Codes and Cryptography
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IEEE Transactions on Information Theory
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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 ηT pairing over GF(397). The extension degree 97 has been intensively used in benchmarking tests for the implementation of the ηT 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.