Presentation | 2010-03-04 Improved Method for Constructing Pairing-friendly Elliptic Curves with Fixed Coefficients Masaaki SHIRASE, |
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Abstract(in Japanese) | (See Japanese page) |
Abstract(in English) | This paper shows that the number of points of elliptic curves y^2=x^3±2 and y^2=x^3±16 over F_ is given by 6 polynomials in z classified by the value of z mod 12 for a prime p(z)=36z^4+36z^3+24z^2+6z+1 with z an integer. Elliptic curves y^2=x^3+2 with z≡2,11 (mod 12), y^2=x^3-2 with z≡2,5 (mod 12) and y^2=x^3-16 with z≡5 (mod 6) become Barreto-Naehrig (BN) curves, and above curves with other zs become twists of BN curve. Due to the results of this paper, we have a method for constructing pairing-friendly elliptic curves with small coefficients using just primality tests to find a prime p(z) and a prime order without use of CM method. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | Pairing-friendly elliptic curve / BN curve / twist / Gauss' theorem / Euler's conjecture |
Paper # | IT2009-78,ISEC2009-86,WBS2009-57 |
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Conference Information | |
Committee | ISEC |
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Conference Date | 2010/2/25(1days) |
Place (in Japanese) | (See Japanese page) |
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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) | Improved Method for Constructing Pairing-friendly Elliptic Curves with Fixed Coefficients |
Sub Title (in English) | |
Keyword(1) | Pairing-friendly elliptic curve |
Keyword(2) | BN curve |
Keyword(3) | twist |
Keyword(4) | Gauss' theorem |
Keyword(5) | Euler's conjecture |
1st Author's Name | Masaaki SHIRASE |
1st Author's Affiliation | Future University Hakodate() |
Date | 2010-03-04 |
Paper # | IT2009-78,ISEC2009-86,WBS2009-57 |
Volume (vol) | vol.109 |
Number (no) | 445 |
Page | pp.pp.- |
#Pages | 8 |
Date of Issue |