Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves

Reo YOSHIDA  Katsuyuki TAKASHIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.1   pp.158-165
Publication Date: 2013/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.158
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Foundations
Keyword: 
isogeny,  supersingular elliptic curves,  post-quantum cryptography,  

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Summary: 
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.