R-ate配对的Fqm域扩展
doi: 10.3724/SP.J.1146.2008.00699
R-ate Extended to Fqm
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摘要: 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。Abstract: 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.
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