| Presentation | 2000/9/21 New explicit conditions of elliptic curve traces for FR-reductions Atsuko Miyaji, Masaki Nakabayashi, Shunzou Takano, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Elliptic curve cryptosystems(ECC) are based on ECDLP. If ECC avoid FR-reduction and anomalous elliptic curve, then with current knowledge we can construct ECC over a smaller definition field. ECDLP has an interesting property that the security deeply depends on elliptic curve traces rather than definition fields, which does not occur in the case of DLP. Therefore it is important to characterize elliptic curve traces explicitly from the security point of view. As for FR-reduction, supersingular elliptic curves or elliptic curves with trace 2 have been reported to be vulnerable. However unfortunately these have been only results that characterize elliptic curve traces explicitly for FR- and MOV-reductions. More importantly, the secure trace against FR-reduction has not been reported at all. Elliptic curves with the secure trace means that the reduced extension degree is always higher than a certain level. In this paper, we aim at characterizing elliptic curve traces by FR-reduction and investigate explicit conditions of traces vulnerable or secure against FR-reduction. We show new explicit conditions of elliptic curve traces for FR-reduction. We also present algorithms to construct such elliptic curves. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve cryptosystems / trace |
| Paper # | ISEC2000-67 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2000/9/21(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 | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | New explicit conditions of elliptic curve traces for FR-reductions |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve cryptosystems |
| Keyword(2) | trace |
| 1st Author's Name | Atsuko Miyaji |
| 1st Author's Affiliation | School of Information Science, Japan Advanced Institute of Science and Technology(JAIST)() |
| 2nd Author's Name | Masaki Nakabayashi |
| 2nd Author's Affiliation | School of Information Science, Japan Advanced Institute of Science and Technology(JAIST) |
| 3rd Author's Name | Shunzou Takano |
| 3rd Author's Affiliation | School of Information Science, Japan Advanced Institute of Science and Technology(JAIST) |
| Date | 2000/9/21 |
| Paper # | ISEC2000-67 |
| Volume (vol) | vol.100 |
| Number (no) | 323 |
| Page | pp.pp.- |
| #Pages | 10 |
| Date of Issue | |