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祝贺我们的论文被Asiacrypt2024接收！
Authors: Yu Dai, Debiao He, Cong Peng, Zhijian Yang, Changan Zhao
Title: Revisiting PairingFriendly Curves with Embedding Degrees 10 and 14
Conference: The 30th Asian Cryptography Conference
Abstract: Since 2015, there has been a significant decrease in the asymptotic complexity of computing discrete logarithms in finite fields. As a result, the key sizes of many mainstream pairingfriendly curves have to be updated to maintain the desired security level. In PKC'20, Guillevic conducted a comprehensive assessment of the security of a series of pairingfriendly curves with embedding degrees ranging from $9$ to $17$. In this paper, we focus on five pairingfriendly curves with embedding degrees 10 and 14 at the 128bit security level, with BW14351 emerging as the most competitive candidate. First, we extend the optimized formula for the optimal pairing on BW13310, a 128bit secure curve with a prime $p$ in 310 bits and embedding degree $13$, to our target curves. This generalization allows us to compute the optimal pairing in approximately $\log r/(2\varphi(k))$ Miller iterations, where $r$ and $k$ are the order of pairing groups and the embedding degree respectively. Second, we develop optimized algorithms for cofactor multiplication for $\G_1$ and $\G_2$, as well as subgroup membership testing for $\G_2$ on these curves. Finally, we provide detailed performance comparisons between BW14351 and other popular curves on a 64bit platform in terms of pairing computation, hashing to $\G_1$ and $\G_2$, group exponentiations, and subgroup membership testings. Our results demonstrate that BW14351 is a strong candidate for building pairingbased cryptographic protocols.

Fax： Email：cpeng@whu.edu.cn (彭聪）