Computing a sequence of 2-isogenies on supersingular elliptic curves

Reo Yoshida; Katsuyuki Takashima

doi:10.1587/transfun.E96.A.158

Computing a sequence of 2-isogenies on supersingular elliptic curves

Reo Yoshida^*, Katsuyuki Takashima

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	158-165
Number of pages	8
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E96-A
Issue number	1
DOIs	https://doi.org/10.1587/transfun.E96.A.158
Publication status	Published - 2013 Jan
Externally published	Yes

Keywords

Isogeny
Post-quantum cryptography
Supersingular elliptic curves

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1587/transfun.E96.A.158

Cite this

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AB - 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.

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Computing a sequence of 2-isogenies on supersingular elliptic curves

Abstract

Keywords

ASJC Scopus subject areas

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