An optimal representation for the trace zero subgroup

Elisa Gorla; Maike Massierer

Paper 2014/333

An optimal representation for the trace zero subgroup

Elisa Gorla and Maike Massierer

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 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: elliptic curve cryptosystem
Contact author(s): maike @ unsw edu au
History: 2016-06-15: last of 3 revisions; 2014-05-13: received; See all versions
Short URL: https://ia.cr/2014/333
License: CC BY

BibTeX

@misc{cryptoeprint:2014/333,
      author = {Elisa Gorla and Maike Massierer},
      title = {An optimal representation for the trace zero subgroup},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/333},
      year = {2014},
      url = {https://eprint.iacr.org/2014/333}
}