R-ate配对的F_(q^m)域扩展

R-ate Extended to F_(q^m)

为解决R-ate对实现中的不完全约减问题,提高计算效率,该文提出一种方法m-R-ate,将R-ate对的实现由Fq扩展至Fqm域中。此外,通过用特征q代替qm的方法对R-ate的公式进行化简,可大大提高R-ate算法效率。实验表明,消除整数不完全约减问题可至少提高7.8%的效率,粒度更细的(A,B)选择方式可有效的减少Miller循环次数,效率高于Atei算法。

In order to solve the troubles of incomplete reduction tumbled in the realization of R-ate and efficient compute the R-ate,a new technique named m-R-ate,which extend R-ate from Fq to Fq m,is proposed.Furthermore,in m-R-ate a very efficient algorithm of R-ate is obtained by replacing qm with the field character q in the formula.That overcoming incomplete reduction will improve the efficiency of R-ate 7.8% at least,and the Miller loop will be reduced by selecting of smaller granularity of（A,B）,which is much better than Atei.