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Designs, Codes and Cryptography
Erschienen in: Designs, Codes and Cryptography 2/2015

01.05.2015

Point compression for the trace zero subgroup over a small degree extension field

verfasst von: Elisa Gorla, Maike Massierer

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2015

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Abstract

Using Semaev’s summation polynomials, we derive a new equation for the \({\mathbb {F}_q}\)-rational points of the trace zero variety of an elliptic curve defined over \({\mathbb {F}_q}\). Using this equation, we produce an optimal-size representation for such points. Our representation is compatible with scalar multiplication. We give a point compression algorithm to compute the representation and a decompression algorithm to recover the original point (up to some small ambiguity). The algorithms are efficient for trace zero varieties coming from small degree extension fields. We give explicit equations and discuss in detail the practically relevant cases of cubic and quintic field extensions.
Vorheriger Artikel Generalized residue and t-residue codes and their idempotent generators
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Metadaten
Titel
Point compression for the trace zero subgroup over a small degree extension field
verfasst von
Elisa Gorla
Maike Massierer
Publikationsdatum
01.05.2015
Verlag
Springer US
Erschienen in
Designs, Codes and Cryptography / Ausgabe 2/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-014-9921-0

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