Ingeniería e Investigación (May 2014)

Design of elliptic curve cryptoprocessors over GF(2^163) using the Gaussian normal basis

  • Paulo Cesar Realpe,
  • Vladimir Trujillo-Olaya,
  • Jaime Velasco-Medina

DOI
https://doi.org/10.15446/ing.investig.v34n2.40542
Journal volume & issue
Vol. 34, no. 2
pp. 55 – 65

Abstract

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This paper presents the efficient hardware implementation of cryptoprocessors that carry out the scalar multiplication kP over finite field GF(2163) using two digit-level multipliers. The finite field arithmetic operations were implemented using Gaussian normal basis (GNB) representation, and the scalar multiplication kP was implemented using Lopez-Dahab algorithm, 2-NAF halve-and-add algorithm and w-tNAF method for Koblitz curves. The processors were designed using VHDL description, synthesized on the Stratix-IV FPGA using Quartus II 12.0 and verified using SignalTAP II and Matlab. The simulation results show that the cryptoprocessors present a very good performance to carry out the scalar multiplication kP. In this case, the computation times of the multiplication kP using Lopez-Dahab, 2-NAF halve-and-add and 16-tNAF for Koblitz curves were 13.37 µs, 16.90 µs and 5.05 µs, respectively.

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