Simple algorithms for computing a sequence of 2-isogenies

Reo Yoshida; Katsuyuki Takashima

doi:10.1007/978-3-642-00730-9_4

Simple algorithms for computing a sequence of 2-isogenies

Reo Yoshida^*, Katsuyuki Takashima

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

3 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)	52-65
Number of pages	14
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5461
DOIs	https://doi.org/10.1007/978-3-642-00730-9_4
Publication status	Published - 2009
Externally published	Yes
Event	11th International Conference on Information Security and Cryptology, ICISC 2008 - Seoul, Korea, Republic of Duration: 2008 Dec 3 → 2008 Dec 5

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-642-00730-9_4

Cite this

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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.",

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AU - Takashima, Katsuyuki

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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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JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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T2 - 11th International Conference on Information Security and Cryptology, ICISC 2008

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ER -

Simple algorithms for computing a sequence of 2-isogenies

Abstract

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