Experimantal analysis of cheon's algorithm against pairing-friendly curves

Tetsuya Izu; Masahiko Takenaka; Masaya Yasuda

doi:10.1109/AINA.2011.37

Experimantal analysis of cheon's algorithm against pairing-friendly curves

Tetsuya Izu, Masahiko Takenaka, Masaya Yasuda

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

2 Citations (Scopus)

Abstract

The discrete logarithm problem (DLP) is one of the familiar problem on which some cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms. In this paper, we show our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3¹²⁷). It is shown that the algorithm combined with the kangaroo method has an advantage over that combined with the baby-step giant-step method in the sense that the required time and space are smaller. Then, for the algorithm combined with the kangaroo-method, speeding-up techniques are introduced. Based on our experimental results and the speeding-up techniques, we evaluate the required time and space for some pairing-friendly elliptic curves curves. As results, a portion of pairing-friendly elliptic curves can be analyzed by Cheon's algorithm at reasonable cost.

Original language	English
Title of host publication	Proceedings - 25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011
Pages	90-96
Number of pages	7
DOIs	https://doi.org/10.1109/AINA.2011.37
Publication status	Published - Jun 3 2011
Externally published	Yes
Event	25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011 - Biopolis, Singapore Duration: Mar 22 2011 → Mar 25 2011

Other

Other	25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011
Country	Singapore
City	Biopolis
Period	3/22/11 → 3/25/11

All Science Journal Classification (ASJC) codes

Engineering(all)

Access to Document

10.1109/AINA.2011.37

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Izu, T., Takenaka, M., & Yasuda, M. (2011). Experimantal analysis of cheon's algorithm against pairing-friendly curves. In Proceedings - 25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011 (pp. 90-96). [5763374] https://doi.org/10.1109/AINA.2011.37

Izu, T, Takenaka, M & Yasuda, M 2011, Experimantal analysis of cheon's algorithm against pairing-friendly curves. in Proceedings - 25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011., 5763374, pp. 90-96, 25th IEEE International Conference on Advanced Information Networking and Applications, AINA 2011, Biopolis, Singapore, 3/22/11. https://doi.org/10.1109/AINA.2011.37

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abstract = "The discrete logarithm problem (DLP) is one of the familiar problem on which some cryptographic schemes rely. In 2006, Cheon proposed an algorithm for solving DLP with auxiliary input which works better than conventional algorithms. In this paper, we show our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3127). It is shown that the algorithm combined with the kangaroo method has an advantage over that combined with the baby-step giant-step method in the sense that the required time and space are smaller. Then, for the algorithm combined with the kangaroo-method, speeding-up techniques are introduced. Based on our experimental results and the speeding-up techniques, we evaluate the required time and space for some pairing-friendly elliptic curves curves. As results, a portion of pairing-friendly elliptic curves can be analyzed by Cheon's algorithm at reasonable cost.",

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