| Presentation | 2005-07-21 Performance of Prime Order Elliptic Curve Generation based on y-twist Mayumi OBARA, Yasuyuki NOGAMI, Yoshitaka MORIKAWA, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper proposes a new twist technique and then shows some necessary conditions for prime order curves in the form y^2=x^3+a. Then, by combining x-twist and y-twist, we consider six elliptic curves. For these six elliptic curves, when the characteristic p of the definition field F_q satisfies that p>3 and 3|(p-1), we show that it is possible for only two elliptic curves among the six curves defined over F_q, q=p^<2^i3^j> to have prime orders, where i, j are non-negative integers. Then, we show an example of prime order curve. After that, compared to the complex multiplication method, we evaluate the performance of the proposed method. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve / twist / quadratic residue/non-residue / third power residue/non-residue |
| Paper # | ISEC2005-17,SITE2005-15 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2005/7/14(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
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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) | Performance of Prime Order Elliptic Curve Generation based on y-twist |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve |
| Keyword(2) | twist |
| Keyword(3) | quadratic residue/non-residue |
| Keyword(4) | third power residue/non-residue |
| 1st Author's Name | Mayumi OBARA |
| 1st Author's Affiliation | The graduate school of natural science and technology, Okayama University() |
| 2nd Author's Name | Yasuyuki NOGAMI |
| 2nd Author's Affiliation | The graduate school of natural science and technology, Okayama University |
| 3rd Author's Name | Yoshitaka MORIKAWA |
| 3rd Author's Affiliation | The graduate school of natural science and technology, Okayama University |
| Date | 2005-07-21 |
| Paper # | ISEC2005-17,SITE2005-15 |
| Volume (vol) | vol.105 |
| Number (no) | 193 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |