Cryptology ePrint Archive: Report 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.

Category / Keywords: Elliptic curves, Binary fields, Side-channel, FPGA, Karatsuba multiplier, Power analysis, SPA.

Original Publication (in the same form): IACR-CHES-2013

Date: received 4 May 2015, last revised 12 May 2015

Contact author: santosh ghosh at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20150512:171028 (All versions of this report)

Short URL: ia.cr/2015/423