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Fast subgroup membership testings for $$\mathbb {G} 1$$, $$\mathbb {G} 2$$ and $$\mathbb {G} T$$ on pairing-friendly curves by Yu Dai; Kaizhan Lin; Chang-An Zhao; Zijian Zhou is a Computer Science article available to read on EtoBox.

What is Fast subgroup membership testings for $$\mathbb {G} 1$$, $$\mathbb {G} 2$$ and $$\mathbb {G} T$$ on pairing-friendly curves about?

Pairing-based cryptographic protocols are typically vulnerable to small-subgroup attacks in the absence of protective measures. Subgroup membership testing is one of the feasible methods to address this security weakness. However, it generally causes an expensive computational cost on many pairing-friendly curves. Recently, Scott proposed efficient methods of subgroup membership testings for G 1 , G 2 and G T on the BLS family. In this paper, we generalize these methods and show that the new techniques are applicable to a large class of pairing-friendly curves. In particular, we also confirm that our new methods lead to a significant speedup for subgroup membership testings on many popular pairing-friendly curves at high security level.

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Author

Yu Dai; Kaizhan Lin; Chang-An Zhao; Zijian Zhou

Publisher

Springer Science and Business Media LLC

Published

2023

Language

EN

Field

Computer Science (Physical Sciences)