A generalization of Verheul's theorem for some ordinary curves

Authors:
Zhi Hu;Maozhi Xu;Zhenghua Zhou
Affiliations:
LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R. China and Department of Computer Science, University of Bristol, Bristol, United Kingdom;LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R. China;LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R. China
Venue:
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Year:
2010

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Abstract

Verheul's theorem [20,21] on some certain supersingular elliptic curves is usually considered as an evidence for the difficulty of pairing inversion. Moody in [16] generalized it to some other supersingular curves. In this paper, we construct two types of ordinary elliptic curves with embedding degree k = 1, and give the corresponding distortion maps. Following their method, we generalize Verheul's theorem to our curves.