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.
Supported by the Natural Science Foundation of China (Grants No.10990011 and No.60763009). The author Zhi Hu was also supported by China Scholarship Council (Grant No.2009601236).
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Hu, Z., Xu, M., Zhou, Z. (2011). A Generalization of Verheul’s Theorem for Some Ordinary Curves. In: Lai, X., Yung, M., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2010. Lecture Notes in Computer Science, vol 6584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21518-6_8
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