Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.1 pp.158-165
- Publication Date
- 2013/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.158
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
- Foundations
Authors
Keyword
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Reo YOSHIDA, Katsuyuki TAKASHIMA, "Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 1, pp. 158-165, January 2013, doi: 10.1587/transfun.E96.A.158.
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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.158/_p
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@ARTICLE{e96-a_1_158,
author={Reo YOSHIDA, Katsuyuki TAKASHIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves},
year={2013},
volume={E96-A},
number={1},
pages={158-165},
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.},
keywords={},
doi={10.1587/transfun.E96.A.158},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - Computing a Sequence of 2-Isogenies on Supersingular Elliptic Curves
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 158
EP - 165
AU - Reo YOSHIDA
AU - Katsuyuki TAKASHIMA
PY - 2013
DO - 10.1587/transfun.E96.A.158
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2013
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.
ER -
English
