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Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves
Reo YOSHIDA Katsuyuki TAKASHIMA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2013/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
isogeny, supersingular elliptic curves, post-quantum cryptography,
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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.