Implementing optimized pairings with elliptic nets  

作　　者：TANG ChunMing NI DongMei XU MaoZhi GUO BaoAn QI YanFeng 

机构地区：[1]School of Mathematics and Information, China West Normal University [2]LMAM, Chinese Ministry of Education, Peking University [3]School of Mathematical Sciences, Peking University [4]Aisino Corporation Inc.

出　　处：《Science China(Information Sciences)》2014年第5期133-142,共10页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61272499,10990011);Science and Technology on Information Assurance Laboratory(Grant No.KJ-11-02)

摘　　要：In this paper, we use elliptic nets to implement the optimized Ate pairings and optimal pairings on the Barreto-Naehrig curves with embedding degree 12. In order to do the arithmetic of elliptic curves over finite fields with elliptic nets, we first give some basic properties of elliptic nets associated to elliptic curves over finite fields and the expression of Miller function in terms of elliptic nets. Then we give formulae to compute some optimized pairings with elliptic nets, which is a new method to implement pairings. This method with elliptic nets has time complexity comparable to Miller＇s algorithm and it can be optimized.In this paper, we use elliptic nets to implement the optimized Ate pairings and optimal pairings on the Barreto-Naehrig curves with embedding degree 12. In order to do the arithmetic of elliptic curves over finite fields with elliptic nets, we first give some basic properties of elliptic nets associated to elliptic curves over finite fields and the expression of Miller function in terms of elliptic nets. Then we give formulae to compute some optimized pairings with elliptic nets, which is a new method to implement pairings. This method with elliptic nets has time complexity comparable to Miller＇s algorithm and it can be optimized.

关 键 词：elliptic curves elliptic nets PAIRINGS Miller＇s algorithm pairing-based cryptography 

分 类 号：TN918.4[电子电信—通信与信息系统]