| Presentation | 2020-05-20 [Invited Talk] How to Construct CSIDH on Edwards Curves (from CT-RSA 2020) Tomoki Moriya, Hiroshi Onuki, Tsuyoshi Takagi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | CSIDH is an isogeny-based key-exchange protocol, that is one of the candidates for post-quantum cryptography. It is based on an ideal class group action on $mathbb{F}_p$-isomorphism classes of supersingular elliptic curves. In order to calculate the class group action, we need to take points defined over $mathbb{F}_{p^2}$. The original CSIDH algorithm only requires a calculation over $mathbb{F}_p$ by using Montgomery curves. If we try to do a similar calculation by using a $w$-coordinate on Edwards curves, we have to consider points defined over $mathbb{F}_{p^4}$. Therefore, it is not a trivial task to calculate the class group action on Edwards curves. In this presentation, I propose a new method to construct CSIDH by using the $w$-coordinate on Edwards curves, and give the computational complexity of this new algorithm. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Isogeny-based cryptography / Montgomery curves / Edwards curves / CSIDH / Post-quantum cryptography |
| Paper # | ISEC2020-8 |
| Date of Issue | 2020-05-13 (ISEC) |
| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2020/5/20(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Shiho Moriai(NICT) |
| Vice Chair | Shoichi Hirose(Univ. of Fukui) / Tetsuya Izu(Fujitsu Labs.) |
| Secretary | Shoichi Hirose(NICT) / Tetsuya Izu(Tsukuba Univ.) |
| Assistant | Dai Yamamoto(Fujitsu Labs.) / Yuuji Suga(IIJ) |
| 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) | [Invited Talk] How to Construct CSIDH on Edwards Curves (from CT-RSA 2020) |
| Sub Title (in English) | |
| Keyword(1) | Isogeny-based cryptography |
| Keyword(2) | Montgomery curves |
| Keyword(3) | Edwards curves |
| Keyword(4) | CSIDH |
| Keyword(5) | Post-quantum cryptography |
| 1st Author's Name | Tomoki Moriya |
| 1st Author's Affiliation | The University of Tokyo(UTokyo) |
| 2nd Author's Name | Hiroshi Onuki |
| 2nd Author's Affiliation | The University of Tokyo(UTokyo) |
| 3rd Author's Name | Tsuyoshi Takagi |
| 3rd Author's Affiliation | The University of Tokyo(UTokyo) |
| Date | 2020-05-20 |
| Paper # | ISEC2020-8 |
| Volume (vol) | vol.120 |
| Number (no) | ISEC-28 |
| Page | pp.pp.31-31(ISEC), |
| #Pages | 1 |
| Date of Issue | 2020-05-13 (ISEC) |