| Presentation | 2015-09-04 Improved addition algorithm for Edwards Curve Masaaki Shirase, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper introduces a new coordinate system (named ${cal P}times {cal P}$ coordinate system) in which a point $(x,y)$ in affine is represented as $[X,Y,Z,W]$ satisfying $x=X/Z,y=Y/W$ and then proposes new algorithms for computing addition and duplication on Edwards curve $x^2+y^2=1+dx^2y^2$. Given $P$ in ${cal P}times {cal P}$ and $Q$ in affine, $P+Q$ and $2P$ take 8{bf M} and 3{bf M}+4{bf S}, respectively, where $M$ and $S$ are multiplication and squaring cost. This paper also proposes algorithms for computing addtion and duplication on twisted Edwards curve $ax^2+y^2=1+dx^2y^2$. Addition takes 9{bf M}, or 7{bf M} when $a=-1$. Duplication takes 6{cal M}+3{cal S}, or 3{bf M}+4{cal S} when $a=-1$. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve cryptosystem / Edwards curve / addition algorithm / coordinate system |
| Paper # | ISEC2015-25 |
| Date of Issue | 2015-08-28 (ISEC) |
| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2015/9/4(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kikai-Shinko-Kaikan Bldg. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Yukiyasu Tsunoo(NEC) |
| Vice Chair | Masahiro Mambo(Kanazawa Univ.) / Kazuto Ogawa(NHK) |
| Secretary | Masahiro Mambo(AIST) / Kazuto Ogawa(Toshiba) |
| Assistant | Tetsuya Izu(Fujitsu Lab.) / Takaaki Mizuki(Tohoku Univ.) / Noritaka Yamashita(NEC) |
| Paper Information | |
| Registration To | Technical Committee on Information Security |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Improved addition algorithm for Edwards Curve |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve cryptosystem |
| Keyword(2) | Edwards curve |
| Keyword(3) | addition algorithm |
| Keyword(4) | coordinate system |
| 1st Author's Name | Masaaki Shirase |
| 1st Author's Affiliation | Future University Hakodate(Future Univ Hakodate) |
| Date | 2015-09-04 |
| Paper # | ISEC2015-25 |
| Volume (vol) | vol.115 |
| Number (no) | ISEC-215 |
| Page | pp.pp.1-8(ISEC), |
| #Pages | 8 |
| Date of Issue | 2015-08-28 (ISEC) |