On the Implementation of Unified Arithmetic on Binary Huff Curves

Santosh Ghosh; Amit Kumar; Amitabh Das; Ingrid Verbauwhede

Paper 2015/423

On the Implementation of Unified Arithmetic on Binary Huff Curves

Santosh Ghosh, Amit Kumar, Amitabh Das, and Ingrid Verbauwhede

Abstract

Unified formula for computing elliptic curve point addition and doubling are considered to be resistant against simple power-analysis attack. A new elliptic curve formula known as unified binary Huff curve in this regard has appeared into the literature in 2011. This paper is devoted to analyzing the applicability of this elliptic curve in practice. Our paper has two contributions.We provide an efficient implementation of the unified Huff formula in projective coordinates on FPGA. Secondly, we point out its side-channel vulnerability and show the results of an actual attack. It is claimed that the formula is unified and there will be no power consumption difference when computing point addition and point doubling operations, observable with simple power analysis (SPA). In this paper, we contradict their claim showing actual SPA results on a FPGA platform and propose a modified arithmetic and its suitable implementation technique to overcome the vulnerability.

Metadata

Available format(s): PDF
Publication info: Published by the IACR in CHES 2013
Keywords: Elliptic curves Binary fields Side-channel FPGA Karatsuba multiplier Power analysis SPA.
Contact author(s): santosh ghosh @ gmail com
History: 2015-05-12: revised; 2015-05-05: received; See all versions
Short URL: https://ia.cr/2015/423
License: CC BY

BibTeX

@misc{cryptoeprint:2015/423,
      author = {Santosh Ghosh and Amit Kumar and Amitabh Das and Ingrid Verbauwhede},
      title = {On the Implementation of Unified Arithmetic on Binary Huff Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2015/423},
      year = {2015},
      url = {https://eprint.iacr.org/2015/423}
}