| Presentation | 2001/7/18 A Remark on Jacobian Group Arithmetic on Nonsingular Algebraic Curves Ryuichi HARASAWA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The aim of this paper is to describe a method that gives an efficient algorithm for performing Jacobian group arithmetic on the most general algebraic curves over finite fields.When we consider algebraic curve cryptosystems, an efficient Jacobian group arithmetic is required.For elliptic and hyperelliptic curve cryptosystems, there exist algorithms for performing the Jacobian group arithmetic in O(g^2) operations in the base field, where g is the genus of a curve.Furthermore, for more general curves so-called C_ab curves, R.Harasawa and J.Suzuki proposed a method for performing the Jacobian group arithmetic in O(g^2) operations in the base field.We generalize the method to C_a1, _…, _at curves.Furthermore, it turns out that the generalization gives an efficient algorithm for performing Jacobian group arithmetic in O(g^2) operations in the base field for all algebraic curves that we consider from an algebraic curve cryptographical point of view. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | algebraic curve cryptography / Jacobian group arithmetic / ideal class group / C_a1, _…, _at curves |
| Paper # | ISEC2001-30 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2001/7/18(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 | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Remark on Jacobian Group Arithmetic on Nonsingular Algebraic Curves |
| Sub Title (in English) | |
| Keyword(1) | algebraic curve cryptography |
| Keyword(2) | Jacobian group arithmetic |
| Keyword(3) | ideal class group |
| Keyword(4) | C_a1, _…, _at curves |
| 1st Author's Name | Ryuichi HARASAWA |
| 1st Author's Affiliation | Oasaka University() |
| Date | 2001/7/18 |
| Paper # | ISEC2001-30 |
| Volume (vol) | vol.101 |
| Number (no) | 214 |
| Page | pp.pp.- |
| #Pages | 8 |
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