Scalar multiplication in compressed coordinates in the trace-zero subgroup

Giulia Bianco; Elisa Gorla

Paper 2017/884

Scalar multiplication in compressed coordinates in the trace-zero subgroup

Giulia Bianco and Elisa Gorla

Abstract

We consider trace-zero subgroups of elliptic curves over a degree three field extension. The elements of these groups can be represented in compressed coordinates, i.e. via the two coefficients of the line that passes through the point and its two Frobenius conjugates. In this paper we give the first algorithm to compute scalar multiplication in the degree three trace-zero subgroup using these coordinates.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: elliptic curve cryptography trace-zero subgroup
Contact author(s): elisa gorla @ unine ch
History: 2017-09-17: received
Short URL: https://ia.cr/2017/884
License: CC BY

BibTeX

@misc{cryptoeprint:2017/884,
      author = {Giulia Bianco and Elisa Gorla},
      title = {Scalar multiplication in compressed coordinates in the trace-zero subgroup},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/884},
      year = {2017},
      url = {https://eprint.iacr.org/2017/884}
}