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High-Performance Implementation of Point Multiplication on Koblitz Curves

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2 Author(s)
Reza Azarderakhsh ; Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada ; Arash Reyhani-Masoleh

Fast and high-performance computation of finite-field arithmetic is crucial for elliptic curve cryptography (ECC) over binary extension fields. In this brief, we propose a highly parallel scheme to speed up the point multiplication for high-speed hardware implementation of ECC cryptoprocessor on Koblitz curves. We slightly modify the addition formulation in order to employ four parallel finite-field multipliers in the data flow. This reduces the latency of performing point addition and speeds up the overall point multiplication. To the best of our knowledge, the proposed data flow of point addition has the lowest latency in comparison to the counterparts available in the literature. To make the cryptoprocessor more efficient, we employ a low-complexity and efficient digit-level Gaussian normal basis multiplier to perform lower level finite-field multiplications. Finally, we have implemented our proposed architecture for point multiplication on an Altera Stratix II field-programmable gate array and obtained the results of timing and area.

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IEEE Transactions on Circuits and Systems II: Express Briefs  (Volume:60 ,  Issue: 1 )