A Weil Pairing on a Family of Genus 2 Hyperelliptic Curves with Efficiently Computable Automorphisms

Masahiro ISHII
Kazutoshi FUJIKAWA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A    No.1    pp.62-72
Publication Date: 2017/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.62
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Weil pairing,  pairing-friendly hyperelliptic curves,  automorphism,  twist,  miller function,  

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In this paper, we provided a new variant of Weil pairing on a family of genus 2 curves with the efficiently computable automorphism. Our pairing can be considered as a generalization of the omega pairing given by Zhao et al. We also report the algebraic cost estimation of our pairing. We then show that our pairing is more efficient than the variant of Tate pairing with the automorphism given by Fan et al. Furthermore, we show that our pairing is slightly better than the twisted Ate pairing on Kawazoe-Takahashi curve at the 192-bit security level.