Simple Algorithms for Computing a Sequence of 2-Isogenies

Authors:
Reo Yoshida;Katsuyuki Takashima
Affiliations:
Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501 and Mitsubishi Electric, Kanagawa, Japan 247-8501
Venue:
Information Security and Cryptology --- ICISC 2008
Year:
2009

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Abstract

Recently, some cryptographic primitives have been described that are based on the supposed hardness of finding an isogeny between two (supersingular) elliptic curves. As a part of such a primitive, Charles et al. proposed an algorithm for computing sequences of 2-isogenies.However, their method involves several redundant computations. We construct simple algorithms without such redundancy, based on very compact descriptions of the 2-isogenies. For that, we use some observations on 2-torsion points.