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

Elisa Gorla; Maike Massierer

Paper 2014/158

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

Elisa Gorla and Maike Massierer

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Designs, Codes and Cryptography
DOI: 10.1007/s10623-014-9921-0
Keywords: elliptic curve cryptography pairing-based cryptography discrete logarithm problem trace zero variety efficient representation point compression summation polynomials
Contact author(s): maike massierer @ inria fr
History: 2014-03-03: received
Short URL: https://ia.cr/2014/158
License: CC BY

BibTeX

@misc{cryptoeprint:2014/158,
      author = {Elisa Gorla and Maike Massierer},
      title = {Point compression for the trace zero subgroup over a small degree extension field},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/158},
      year = {2014},
      doi = {10.1007/s10623-014-9921-0},
      url = {https://eprint.iacr.org/2014/158}
}