| Presentation | 2002/9/17 A Systematic Generation of Irreducible Polynomials of Degree 3 for Use in Elliptic Curve Cryptosystem Masato OKAMURA, Yasuyuki NOGAMI, Yoshitaka MORIKAWA, |
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| PDF Download Page | PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | The order of elliptic curve which is adopted in the elliptic curve cryptosystem is prefered to be a prime except for the characteristic of the definition field. Accordingly, some algorithms for generating such a prime-order elliptic curve has been proposed. Among these algorithms, there is an algorithm using irreducible polynomials of degree 3 effectively in order to generate no-two torsion elliptic curves in which all prime-order elliptic curves are contained. In this paper, let us consider that an irreducible polynomial of degree 3 is given, an algorithm to generate a lot of irreducible polynomials of degree 3 is proposed by use of a relation between the zeros and the coefficients of the given irreducible polynomial. And then, it is experimentally shown that the preceding algorithm can quickly generate prime order elliptic curves by using this algorithm and some properties between an elliptic curve and its twisted version. In the case of the characteristic p = 2^<24> - 3, for example, the number of possible prime-order elliptic curves for this algorithm is 164, and all kinds of these prime-order elliptic curves are generated within 3 minutes by using 10 processors, such as Pentium4 (1.7GHz). |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | No - Two Torsion Elliptic Curve / Irreducible Polynomial of Degree 3 / twist |
| Paper # | IT2002-35 |
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| Conference Information | |
| Committee | IT |
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| Conference Date | 2002/9/17(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 Theory (IT) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Systematic Generation of Irreducible Polynomials of Degree 3 for Use in Elliptic Curve Cryptosystem |
| Sub Title (in English) | |
| Keyword(1) | No - Two Torsion Elliptic Curve |
| Keyword(2) | Irreducible Polynomial of Degree 3 |
| Keyword(3) | twist |
| 1st Author's Name | Masato OKAMURA |
| 1st Author's Affiliation | Faculty of Engineering, Okayama University() |
| 2nd Author's Name | Yasuyuki NOGAMI |
| 2nd Author's Affiliation | Faculty of Engineering, Okayama University |
| 3rd Author's Name | Yoshitaka MORIKAWA |
| 3rd Author's Affiliation | Faculty of Engineering, Okayama University |
| Date | 2002/9/17 |
| Paper # | IT2002-35 |
| Volume (vol) | vol.102 |
| Number (no) | 331 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |