Abstract: The authors consider pairings on binary Edwards curves and give two approaches to construct pairings and implement them. One is based on the birational equivalence between a binary Edwards curve and an elliptic curve in Weierstrass form, the other is based on a 2-isogeny from a binary Edwards curve to an elliptic curve. For both approaches, the authors give the computation of their Miller functions and present two algorithms for their pairing computation. Especially in the second algorithm, more field squaring operations are included, which is more efficient.

Key words: binary Edwards curves, Tate pairings, Miller functions, 2-isogeny

摘要： 研究了二元域上 Edwards 型椭圆曲线的配对计算问题, 并且给出了两种计算配对的方法。一种是基于Edwards型曲线与Weierstrass型曲线的双有理等价; 另一种是基.LNCS 1403 于它们之间的二次可分同源。在两种情况下, 都给出了具体的Miller 型函数计算和相应的配对计算算法, 特别是基于二次同源的配对计算, 由于其更多地采用平方运算而非一般乘法运算, 因此计算将会更为有效。

关键词: 二元域上的Edwards型曲线, Tate配对, Miller函数, 二次同源