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实现k=18的Brezing-Weng曲线的最优配对

Implementing Optimal Pairings over Brezing-Weng Elliptic Curves with k=18
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摘要 研究了嵌入次数为18的Brezing-Weng椭圆曲线上的最优配对的构造与实现。给出配对的Miller算法的循环长度为log2r/6,达到了Miller算法循环长度的猜想下界log2r/φ(18)。使用6次扭转映射实现了点的压缩表示,并减少了Miller算法中的除法运算,从而使得配对中的大多数计算只需要在Fq或Fq3上进行。给出了一个有效计算最优配对的算法。最后使用有限域上的Frobenius映射简化了配对算法中最终的幂运算。 The authors consider the construction and implementation of optimal pairings over Brezing-Weng elliptic curves with embedding degree 18.The loop length in the optimal pairing is log2r/φ（18）,which is the theoretical lower bound.A twisted map of degree 6 is used to realize the point compression and reduce the division operations in Miller algorithm,then most of operations can be implemented in Fq or Fq3.An efficient algorithm for the optimal pairing is given accordingly.Frobenius map in finite Frobenius map in finite fields is used to reduce the computation in the final power operation of the optimal pairing computation.
作者 唐春明 亓延峰 徐茂智
机构地区 北京大学数学科学学院 网络与软件安全保障教育部重点实验室
出处 《北京大学学报（自然科学版）》 EI CAS CSCD 北大核心 2010年第5期743-748,共6页 Acta Scientiarum Naturalium Universitatis Pekinensis
基金 国家自然科学基金资助项目(10990011 60763009)
关键词 Brezing-Weng椭圆曲线 配对友好曲线 Tare配对 Ate配对 配对的密码学 Brezing-Weng elliptic curves pairing friendly elliptic curves Tate pairing Ate pairing pairing-based cryptography
分类号 TN918.1 [电子电信—通信与信息系统]
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北京大学学报（自然科学版）
2010年 第5期

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