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

Abstract : Using Semaev's summation polynomials, we derive a new equation for the F_q-rational points of the trace zero variety of an elliptic curve defined over 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.
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https://hal.inria.fr/hal-01097434
Contributor : Maike Massierer <>
Submitted on : Tuesday, January 6, 2015 - 11:29:30 AM
Last modification on : Tuesday, December 17, 2019 - 10:10:03 AM
Long-term archiving on: : Wednesday, June 3, 2015 - 12:06:15 PM

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Elisa Gorla, Maike Massierer. Point compression for the trace zero subgroup over a small degree extension field. Designs, Codes and Cryptography, Springer Verlag, 2015, 75 (2), pp.335--357. ⟨10.1007/s10623-014-9921-0⟩. ⟨hal-01097434⟩

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