| Presentation | 2012-09-21 Computation of pairings and scalar multiplication by using elliptic nets over small characteristic finite fields Naoki KANAYAMA, Yang LIU, Eiji OKAMOTO, Kazutaka SAITO, Tadanori TERUYA, Shigenori UCHIYAMA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In 2007, Stange [25] proposed a novel method of computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps that satisfy a certain recurrence relation related to elliptic functions. Ogura et al. [20] gave formulae for computing of the Ate and other pairings, based on ellipticn ets. Elliptic net can be used for scalar multiplication on elliptic curves(see [11]). In these results, the characteristic of the ground field is greater than 3. In this paper, we use results of Stange [26], we explicitly give algorithms for computing pairings and scalar multiplication on elliptic curves over finite fields of characteristic 2, 3. We also discusstheir efficiency by using some experimental results. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve / elliptic net / pairing / scalar multiplication |
| Paper # | ISEC2012-44 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2012/9/14(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Information Security (ISEC) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Computation of pairings and scalar multiplication by using elliptic nets over small characteristic finite fields |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve |
| Keyword(2) | elliptic net |
| Keyword(3) | pairing |
| Keyword(4) | scalar multiplication |
| 1st Author's Name | Naoki KANAYAMA |
| 1st Author's Affiliation | Graduate School of Systems and Information Engineering University of Tsukuba() |
| 2nd Author's Name | Yang LIU |
| 2nd Author's Affiliation | Graduate School of Systems and Information Engineering University of Tsukuba |
| 3rd Author's Name | Eiji OKAMOTO |
| 3rd Author's Affiliation | Graduate School of Systems and Information Engineering University of Tsukuba |
| 4th Author's Name | Kazutaka SAITO |
| 4th Author's Affiliation | Graduate School of Systems and Information Engineering University of Tsukuba |
| 5th Author's Name | Tadanori TERUYA |
| 5th Author's Affiliation | Graduate School of Systems and Information Engineering University of Tsukuba |
| 6th Author's Name | Shigenori UCHIYAMA |
| 6th Author's Affiliation | Graduate School of Science and Engineering Tokyo Metropolitan University |
| Date | 2012-09-21 |
| Paper # | ISEC2012-44 |
| Volume (vol) | vol.112 |
| Number (no) | 211 |
| Page | pp.pp.- |
| #Pages | 7 |
| Date of Issue | |