| Presentation | 2009-05-22 Joint Sparse Forms with Twelve Precomputed Points Katsuyuki OKEYA, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The joint sparse form (JSF) is a representation of a pair of integers, which is famous for accelerating a multi-scalar multiplication in elliptic curve cryptosystems. Solinas' original paper showed three unsolved problems on the enhancement of JSF. Whereas two of them have been solved, the other still remains to be done. The remaining unsolved problem is as follows: To design a represntation of a pair of integers using a larger digit set such as a set involves ±3, while the original JSF utilizes the digit set that consists of 0, ±1 for representing a pair of integers. This paper put an end to the problem. In the case with 12 precomputed points, whereas one of the best known results achieved 0.3615 of non-zero density, this paper improves it to 0.3577. In addition, the proposed enhancement satisfies some of properties, as the original does. For example, the enhanced represetation is defined as a representation that satisfies some rules. Some other properties are the existance, the uniquness of such a representation, and the optimality of the Hamming weight. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve cryptosystem / multi-scalar multiplication / joint sparse form (JSF) |
| Paper # | ISEC2009-7 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2009/5/15(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) | Joint Sparse Forms with Twelve Precomputed Points |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve cryptosystem |
| Keyword(2) | multi-scalar multiplication |
| Keyword(3) | joint sparse form (JSF) |
| 1st Author's Name | Katsuyuki OKEYA |
| 1st Author's Affiliation | Hitachi, Ltd., Systems Development Laboratory() |
| Date | 2009-05-22 |
| Paper # | ISEC2009-7 |
| Volume (vol) | vol.109 |
| Number (no) | 42 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |