基于三类代数曲线上的双线性对实现

Bilinear Pairing Implementation Based on Three Type Algebraic Curves

双线性对中,最常见的是Tate对,Eta对和Ate对是Tate对的变种.针对椭圆曲线y2+y=x3+x+b,其中b∈F2,通过分类讨论,给出了4种情况下的Tate对和Eta对实现算法.同时,还提出了基于超椭圆曲线y2+y=x5+ax+b(其中a,b∈F2)上的Tate对和Ate对实现算法,以及基于超椭圆曲线y2=xp-ax-b(其中a,b∈Fp)上的Ate对实现算法.为基于双线性对密码体制的研究和应用提供了一定的参考.

In pairings,the most common is the Tate pairing,Eta pairing and Ate pairing are the variations of the Tate pairing.For the elliptic curve y^2＋y =x^3＋x ＋b where b∈ F2,the implementation algorithms of Tate pairing and Eta pairing in four cases are given by discussing respectively.Meanwhile,the implementation algorithms of Tate pairing and Ate pairing based on the hyperelliptic curve y^2＋y=x^5＋ax＋b where a,b∈F2and the implementation algorithms of Ate pairing based on the hyperelliptic curve y^2=x^p-ax-b where a,b∈Fpare proposed.It provides a reference for the research and application of the pairing-based cryptosystem.