| Presentation | 2012-12-12 Generating elliptic curves having efficient endomorphisms suitable for pairing computation and scalar multiplication Naoki Kanayama, Eiji Okamoto, Kazutaka Saito, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In the present paper, we proposed a method for generating elliptic curves having endomorphisms suitable for computing pairings and scalar multiplication. In 2001, Gallant et al. proposed a novel method for computing scalar multiplication over elliptic curves which have efficient computable endomorphisms. In 2005, Scott proposed an efficient method for computing pairings over such elliptic curves. Their results are very useful for construct of pairing-based cryptosystems. Takashima proposed a method for genarating elliptic curves over Fq having efficient computable endomorphisms. He uses the Cocks-Pinch method for generating elliptic curves and the p-values, defined by the ratio the size of the group order r and that of q, of elliptic curves generated by his method are larger than 2. In the present paper, we proposed a method for generating elliptic curves having endomorphisms and p-values smaller than 2. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curves / pairing cryptography / elliptic curve scalar multiplication / endomorphism / the Cocks-Pinch method / ρ-values |
| Paper # | ISEC2012-75 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2012/12/5(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) | Generating elliptic curves having efficient endomorphisms suitable for pairing computation and scalar multiplication |
| Sub Title (in English) | |
| Keyword(1) | elliptic curves |
| Keyword(2) | pairing cryptography |
| Keyword(3) | elliptic curve scalar multiplication |
| Keyword(4) | endomorphism |
| Keyword(5) | the Cocks-Pinch method |
| Keyword(6) | ρ-values |
| 1st Author's Name | Naoki Kanayama |
| 1st Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba() |
| 2nd Author's Name | Eiji Okamoto |
| 2nd Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba |
| 3rd Author's Name | Kazutaka Saito |
| 3rd Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba |
| Date | 2012-12-12 |
| Paper # | ISEC2012-75 |
| Volume (vol) | vol.112 |
| Number (no) | 342 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |