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An optimal representation for the trace zero variety

Abstract : We give an optimal-size representation for the elements of the trace zero subgroup of the Picard group of an elliptic or hyperelliptic curve of any genus, with respect to a base field extension of any prime degree. The representation is via the coefficients of a rational function, and it is compatible with scalar multiplication of points. We provide efficient compression and decompression algorithms, and complement them with implementation results. We discuss in detail the practically relevant cases of small genus and extension degree, and compare with the other known compression methods.
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Contributor : Maike Massierer <>
Submitted on : Saturday, December 26, 2015 - 3:31:13 PM
Last modification on : Wednesday, November 28, 2018 - 2:48:22 PM
Long-term archiving on: : Sunday, March 27, 2016 - 10:40:55 AM


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  • HAL Id : hal-01097405, version 2
  • ARXIV : 1405.2733



Elisa Gorla, Maike Massierer. An optimal representation for the trace zero variety. 2014. ⟨hal-01097405v2⟩



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