Breaking pairing-based cryptosystems using ηT pairing over GF(397)

Takuya Hayashi; Takeshi Shimoyama; Naoyuki Shinohara; Tsuyoshi Takagi

doi:10.1007/978-3-642-34961-4_5

Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷)

Takuya Hayashi, Takeshi Shimoyama, Naoyuki Shinohara, Tsuyoshi Takagi

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

27 Citations (Scopus)

Abstract

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(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(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.

Original language	English
Title of host publication	Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
Pages	43-60
Number of pages	18
DOIs	https://doi.org/10.1007/978-3-642-34961-4_5
Publication status	Published - 2012
Event	18th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2012 - Beijing, China Duration: Dec 2 2012 → Dec 6 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7658 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	18th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2012
Country/Territory	China
City	Beijing
Period	12/2/12 → 12/6/12

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-34961-4_5

Cite this

Hayashi, T., Shimoyama, T., Shinohara, N., & Takagi, T. (2012). Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷). In Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings (pp. 43-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7658 LNCS). https://doi.org/10.1007/978-3-642-34961-4_5

Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷). / Hayashi, Takuya; Shimoyama, Takeshi; Shinohara, Naoyuki et al.

Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. 2012. p. 43-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7658 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hayashi, T, Shimoyama, T, Shinohara, N & Takagi, T 2012, Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷). in Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7658 LNCS, pp. 43-60, 18th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2012, Beijing, China, 12/2/12. https://doi.org/10.1007/978-3-642-34961-4_5

Hayashi T, Shimoyama T, Shinohara N, Takagi T. Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷). In Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. 2012. p. 43-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-34961-4_5

Hayashi, Takuya ; Shimoyama, Takeshi ; Shinohara, Naoyuki et al. / Breaking pairing-based cryptosystems using η_T pairing over GF(3⁹⁷). Advances in Cryptology, ASIACRYPT 2012 - 18th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings. 2012. pp. 43-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 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(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(36.97). The entire computational time requires about 148.2 days using 252 CPU cores.",

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