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

Gorla, Elisa ; Massierer, Maike

In: Designs, Codes and Cryptography, 2015, vol. 75, no. 2, p. 335-357

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    Title
    • Point compression for the trace zero subgroup over a small degree extension field
    Author
    • Gorla, Elisa. Institut de mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000, Neuchâtel, Switzerland
    • Massierer, Maike. Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051, Basel, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Designs, Codes and Cryptography, 2015, vol. 75, no. 2, p. 335-357. Springer US; http://www.springer-ny.com
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:331981
    Summary
    Using Semaev's summation polynomials, we derive a new equation for the $${\mathbb {F}_q}$$ F q -rational points of the trace zero variety of an elliptic curve defined over $${\mathbb {F}_q}$$ 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.