JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Articles
Constructing an efficient hash function from $3$-isogenies
Hikari TachibanaKatsuyuki TakashimaTsuyoshi Takagi
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2017 Volume 9 Pages 29-32

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Abstract

Charles et al. proposed hash functions based on the difficulty of computing isogenies between supersingular elliptic curves. Yoshida and Takashima then improved the 2-isogeny hash function computation by using some specific properties of 2-torsion points. In this paper, we extend the technique to 3-isogenies and give the efficient 3-isogeny hash computation based on a simple representation of the (backtracking) 3-torsion point. Moreover, we implement the 2- and 3-isogeny hash functions using Magma and show our 3-isogeny proposal has a comparable efficiency with the 2-isogeny one.

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© 2017, The Japan Society for Industrial and Applied Mathematics
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