Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

Yumi Sakemi; Goichiro Hanaoka; Tetsuya Izu; Masahiko Takenaka; Masaya Yasuda

doi:10.1007/978-3-642-30057-8_35

Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

Yumi Sakemi, Goichiro Hanaoka, Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda

Laboratory of Mathematical Design for Advanced Cryptography

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

14 Citations (Scopus)

Abstract

A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, α ^dG in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r - 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon's algorithm). This paper reports our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.

Original language	English
Title of host publication	Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
Pages	595-608
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-642-30057-8_35
Publication status	Published - 2012
Event	15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012 - Darmstadt, Germany Duration: May 21 2012 → May 23 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7293 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012
Country/Territory	Germany
City	Darmstadt
Period	5/21/12 → 5/23/12

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-30057-8_35

Cite this

Sakemi, Y., Hanaoka, G., Izu, T., Takenaka, M., & Yasuda, M. (2012). Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve. In Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings (pp. 595-608). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7293 LNCS). https://doi.org/10.1007/978-3-642-30057-8_35

Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve. / Sakemi, Yumi; Hanaoka, Goichiro; Izu, Tetsuya et al.
Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings. 2012. p. 595-608 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7293 LNCS).

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

Sakemi, Y, Hanaoka, G, Izu, T, Takenaka, M & Yasuda, M 2012, Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve. in Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7293 LNCS, pp. 595-608, 15th International Conference on Practice and Theory in Public Key Cryptography, PKC 2012, Darmstadt, Germany, 5/21/12. https://doi.org/10.1007/978-3-642-30057-8_35

Sakemi Y, Hanaoka G, Izu T, Takenaka M, Yasuda M. Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve. In Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings. 2012. p. 595-608. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-30057-8_35

Sakemi, Yumi ; Hanaoka, Goichiro ; Izu, Tetsuya et al. / Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve. Public Key Cryptography, PKC 2012 - 15th International Conference on Practice and Theory in Public Key Cryptography, Proceedings. 2012. pp. 595-608 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve

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