| Presentation | 2011-11-15 On Definition Fields of Pairing-Friendly Curves With Embedding Degree 4, 6, 8 Masaaki SHIRASE, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The BN prime p, which is required for constructing the BN curve, is given by p = 36z^4 + 36z^3 + 24z^2 + 6z + 1. By the way, the p has a representation as p = (6z^2 + 3z + 1)^2 + 3z^2 and then a primary resolution of p is given as p = -(6z^2 + 4z + 1) - 2zω (if z ≡ 0 (mod 3)), p = 2z - (6z^2 + 2z + 1)ω (if z ≡ 1 (mod 3)), or p = 6z^ + 2z + 1 + (6z^2 + 4z + 1)ω (if z = 2 (mod 3)), where ω satisfies ω^3 = 1, ω ≠ 1. It is known that these results help for efficiently constructing the extension field F_ |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | pairing-friendly curve / primary / 4th residue / embedding degree / CM discriminant |
| Paper # | ISEC2011-58,LOIS2011-52 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2011/11/7(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
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| Vice Chair | |
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| Assistant | |
| 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) | On Definition Fields of Pairing-Friendly Curves With Embedding Degree 4, 6, 8 |
| Sub Title (in English) | |
| Keyword(1) | pairing-friendly curve |
| Keyword(2) | primary |
| Keyword(3) | 4th residue |
| Keyword(4) | embedding degree |
| Keyword(5) | CM discriminant |
| 1st Author's Name | Masaaki SHIRASE |
| 1st Author's Affiliation | Future University Hakodate() |
| Date | 2011-11-15 |
| Paper # | ISEC2011-58,LOIS2011-52 |
| Volume (vol) | vol.111 |
| Number (no) | 285 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |