| Presentation | 1999/11/8 On the Complexity of Constructing an Elliptic Curve of a Given Order Masato YAMAMICHI, Masahiro MAMBO, Hiroki SHIZUYA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Schoof showed that the order of an elliptic curve defined over a finite field is computed in deterministic polynomial time. Then a converse problem arises: Can we find an elliptic curve of a given order in polynomial time? This is open since 1986. This paper concerns with this open question. We define the multivalued partial function f that on input a prime and an order, outputs an elliptic curve of the order, and characterize the difficulty of computing f. We show that the polynomial-time hierarchy collapses to NP if sat reduces to f with respect to the polynomial-time Turing reducibility, where sat is the multivalued partial function that on input a Boolean formula, outputs a satisfying assignment. We also give a problem that is equivalent to the open question under the Extended Riemann Hypothesis. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curve / multivalued function / polynomial-time hierarchy |
| Paper # | ISEC99-59 |
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| Conference Information | |
| Committee | ISEC |
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| Conference Date | 1999/11/8(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) | On the Complexity of Constructing an Elliptic Curve of a Given Order |
| Sub Title (in English) | |
| Keyword(1) | elliptic curve |
| Keyword(2) | multivalued function |
| Keyword(3) | polynomial-time hierarchy |
| 1st Author's Name | Masato YAMAMICHI |
| 1st Author's Affiliation | Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, TOHOKU UNIVERSITY() |
| 2nd Author's Name | Masahiro MAMBO |
| 2nd Author's Affiliation | Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, TOHOKU UNIVERSITY |
| 3rd Author's Name | Hiroki SHIZUYA |
| 3rd Author's Affiliation | Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, TOHOKU UNIVERSITY |
| Date | 1999/11/8 |
| Paper # | ISEC99-59 |
| Volume (vol) | vol.99 |
| Number (no) | 414 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |