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- Title
Design of elliptic curve cryptoprocessors over GF(2<sup>163</sup>) using the Gaussian normal basis.
- Authors
Realpe-Muñoz, P. C.; Trujillo-Olaya, V.; Velasco-Medina, J.
- Abstract
This paper presents an efficient hardware implementation of cryptoprocessors that perform the scalar multiplication kP over a finite field GF(2163) using two digit-level multipliers. The finite field arithmetic operations were implemented using the Gaussian normal basis (GNB) representation, and the scalar multiplication kP was implemented using the Lopez-Dahab algorithm, the 2-non-adjacent form (2-NAF) halve-and-add algorithm and the w-τNAF method for Koblitz curves. The processors were designed using a 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 provide a very good performance when performing the scalar multiplication kP. In this case, the computation times of the multiplication kP using the Lopez-Dahab algorithm, 2-NAF halve-and-add algorithm and 16-τNAF method for Koblitz curves were 13.37 μs, 16.90 μs and 5.05 μs, respectively.
- Subjects
ELLIPTIC curve cryptography; GAUSSIAN basis sets (Quantum mechanics); MULTIPLIERS (Mathematical analysis); MATRIX multiplications; SCALAR field theory; ALGORITHMS
- Publication
Revista Ingeniería e Investigación, 2014, Vol 34, Issue 2, p55
- ISSN
0120-5609
- Publication type
Article
- DOI
10.15446/ing.investig.v34n2.40542