On the Implementation of Unified Arithmetic on Binary Huff Curves

  • Santosh Ghosh
  • Amit Kumar
  • Amitabh Das
  • Ingrid Verbauwhede
Conference paper

DOI: 10.1007/978-3-642-40349-1_20

Volume 8086 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Ghosh S., Kumar A., Das A., Verbauwhede I. (2013) On the Implementation of Unified Arithmetic on Binary Huff Curves. In: Bertoni G., Coron JS. (eds) Cryptographic Hardware and Embedded Systems - CHES 2013. CHES 2013. Lecture Notes in Computer Science, vol 8086. Springer, Berlin, Heidelberg

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.

Keywords

Elliptic curves Binary fields Side-channel FPGA Karatsuba multiplier Power analysis SPA 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Santosh Ghosh
    • 1
  • Amit Kumar
    • 2
  • Amitabh Das
    • 3
  • Ingrid Verbauwhede
    • 3
  1. 1.Security Center of Excellence (SeCoE)Intel CorporationHillsboroUSA
  2. 2.Department of Electrical EngineeringIndian Institute of Technology KharagpurIndia
  3. 3.COSIC-SCD/ESATKU Leuven & iMindsHeverleeBelgium