Presentation 2010-03-04
Improved Method for Constructing Pairing-friendly Elliptic Curves with Fixed Coefficients
Masaaki SHIRASE,
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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
Conference Date 2010/2/25(1days)
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Paper Information
Registration To Information Security (ISEC)
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