| Presentation | 1998/3/18 Construction of CM hyperelliptic curves using RM family Hiroto KAWASHIRO, Osamu NAKAMURA, Jinhui CHAO, Fumiyuki MOMOSE, Shigeo TSUJII, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Construction of hyperellptic curves is of most important yet most difficult problem in design of cryptosystems based on the discrete logarithm problems on hyperelliptic curves. The extension of so-called "CM field algorithm" sufured from both difficulties to calculate the Siegel modular function and to solve the model of the curve from its invariant. This paper presents new algorithms to find explicit models of hyperelliptic curves of genus two with CM. Algorithms for CM test of jacobiant varieties of algebraic curves by using various properties of redution and algorithms to lift from finite field both the models and the invariants of CM curves with CM are presented. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | hyperellptic curves / hyperelliptic cryptosystems / discrete logarithm problems / complex multiplication / RM family / invariants |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 1998/3/18(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| 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) | Construction of CM hyperelliptic curves using RM family |
| Sub Title (in English) | |
| Keyword(1) | hyperellptic curves |
| Keyword(2) | hyperelliptic cryptosystems |
| Keyword(3) | discrete logarithm problems |
| Keyword(4) | complex multiplication |
| Keyword(5) | RM family |
| Keyword(6) | invariants |
| 1st Author's Name | Hiroto KAWASHIRO |
| 1st Author's Affiliation | Dept.of Information System Eng.Chuo Univ.() |
| 2nd Author's Name | Osamu NAKAMURA |
| 2nd Author's Affiliation | Dept.of Information System Eng.Chuo Univ. |
| 3rd Author's Name | Jinhui CHAO |
| 3rd Author's Affiliation | Dept.of Electrical and Electronics Eng.Chuo Univ. |
| 4th Author's Name | Fumiyuki MOMOSE |
| 4th Author's Affiliation | Dept.of Mathematics Chuo Univ. |
| 5th Author's Name | Shigeo TSUJII |
| 5th Author's Affiliation | Dept.of Information System Eng.Chuo Univ. |
| Date | 1998/3/18 |
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| Volume (vol) | vol.97 |
| Number (no) | 611 |
| Page | pp.pp.- |
| #Pages | 7 |
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