R-ate Extended to Fqm

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 Fqm , 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.