| Presentation | 2010-09-10 Elliptic Net Based Ate Pairing And Its Variants Naoki OGURA, Naoki KANAYAMA, Shigenori UCHIYAMA, Eiji OKAMOTO, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In 2007, Stange 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. A feature of computing elliptic nets is to use the recurrence sequence and the running time of the algorithm would be independent of the Hamming weight of r. That is, elliptic net based Tate pairing is expected to be resistant against side channel attacks. Since the efficiency of the algorithm is comparable to that of Miller's algorithm, by using further improvement and optimization, we would expect that elliptic net algorithm provides an efficient alternative to Miller's algorithm. Therefore, from both theoretical and practical points of view, it would be important for us to investigate explicit formulae for computing some variants of the Tate pairing based on elliptic nets. In this paper, we explicitly give formulae for computing some variants of the Tate pairing: Ate, Ate_i, R-Ate and Optimal pairings, based on elliptic nets. We also discuss their efficiency by using some experimental results. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Tate pairing / Ate pairing / R-Ate pairing / Optimal pairing / elliptic net |
| Paper # | ISEC2010-40 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2010/9/3(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| 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) | Elliptic Net Based Ate Pairing And Its Variants |
| Sub Title (in English) | |
| Keyword(1) | Tate pairing |
| Keyword(2) | Ate pairing |
| Keyword(3) | R-Ate pairing |
| Keyword(4) | Optimal pairing |
| Keyword(5) | elliptic net |
| 1st Author's Name | Naoki OGURA |
| 1st Author's Affiliation | Graduate School of Science and Engineering, Tokyo Metropolitan University() |
| 2nd Author's Name | Naoki KANAYAMA |
| 2nd Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba |
| 3rd Author's Name | Shigenori UCHIYAMA |
| 3rd Author's Affiliation | Graduate School of Science and Engineering, Tokyo Metropolitan University |
| 4th Author's Name | Eiji OKAMOTO |
| 4th Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba |
| Date | 2010-09-10 |
| Paper # | ISEC2010-40 |
| Volume (vol) | vol.110 |
| Number (no) | 200 |
| Page | pp.pp.- |
| #Pages | 7 |
| Date of Issue | |