An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve

Yuki Kono; Yasuyuki Nogami

doi:10.1109/CANDAR.2014.60

An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve

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

Abstract

This paper considers the discrete logarithm problem (DLP) appeared in the context of pairing - based cryptography with Barreto - Naehrig (BN) curve. Since the embedding degree of BN curve is 12, the DLP is defined in the extension field Fp12, where p is the characteristic. This paper first points out that efficient and compact subgroup trace representation (ECSTR:XTR) is available for representing the DLP. Then, XTR-based rho method for solving the DLP is proposed. After that, its efficiency with and without tag tracing technique is evaluated by a small experiment.

Original language	English
Title of host publication	Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	519-524
Number of pages	6
ISBN (Electronic)	9781479941520
DOIs	https://doi.org/10.1109/CANDAR.2014.60
Publication status	Published - Feb 27 2015
Event	2nd International Symposium on Computing and Networking, CANDAR 2014 - Shizuoka, Japan Duration: Dec 10 2014 → Dec 12 2014

Publication series

Name	Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014

Other

Other	2nd International Symposium on Computing and Networking, CANDAR 2014
Country/Territory	Japan
City	Shizuoka
Period	12/10/14 → 12/12/14

Keywords

BarretoNaehrig curve
Discrete logarithm
Elliptic curve
Pairing
Tagtracing
XTR

ASJC Scopus subject areas

Computer Networks and Communications

Access to Document

10.1109/CANDAR.2014.60

Cite this

Kono, Y., & Nogami, Y. (2015). An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. In Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014 (pp. 519-524). [7052239] (Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CANDAR.2014.60

An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. / Kono, Yuki; Nogami, Yasuyuki.

Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014. Institute of Electrical and Electronics Engineers Inc., 2015. p. 519-524 7052239 (Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014).

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

Kono, Y & Nogami, Y 2015, An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. in Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014., 7052239, Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014, Institute of Electrical and Electronics Engineers Inc., pp. 519-524, 2nd International Symposium on Computing and Networking, CANDAR 2014, Shizuoka, Japan, 12/10/14. https://doi.org/10.1109/CANDAR.2014.60

Kono Y, Nogami Y. An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. In Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014. Institute of Electrical and Electronics Engineers Inc. 2015. p. 519-524. 7052239. (Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014). doi: 10.1109/CANDAR.2014.60

Kono, Yuki ; Nogami, Yasuyuki. / An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve. Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 519-524 (Proceedings - 2014 2nd International Symposium on Computing and Networking, CANDAR 2014).

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abstract = "This paper considers the discrete logarithm problem (DLP) appeared in the context of pairing - based cryptography with Barreto - Naehrig (BN) curve. Since the embedding degree of BN curve is 12, the DLP is defined in the extension field Fp12, where p is the characteristic. This paper first points out that efficient and compact subgroup trace representation (ECSTR:XTR) is available for representing the DLP. Then, XTR-based rho method for solving the DLP is proposed. After that, its efficiency with and without tag tracing technique is evaluated by a small experiment.",

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An application of XTR for the discrete logarithm problem on Barreto - Naehrig curve

Abstract

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Keywords

ASJC Scopus subject areas

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