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A Word-Level Finite Field Multiplier Using Normal Basis
June 2011 (vol. 60 no. 6)
pp. 890-895
Ashkan Hosseinzadeh Namin, University of Waterloo, Waterloo
Huapeng Wu, University of Windsor, Windsor
Majid Ahmadi, University of Windsor, Windsor
Hardware implementations of finite field arithmetic using normal basis are advantageous due to the fact that the squaring operation can be done at almost no cost. In this paper, a new word-level finite field multiplier using normal basis is proposed. The proposed architecture takes d clock cycles to compute the product bits, where the value for d, 1\leq d \leq m, can be arbitrarily selected by the designer to set the tradeoff between area and speed. When there exists an optimal normal basis, it is shown that the proposed design has a smaller critical path delay than other word-level normal basis multipliers found in the literature, while its circuit complexities are moderate and comparable to the others. Different word size multipliers were implemented in hardware, and implementation results are also presented.

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Index Terms:
Finite field multiplier, normal basis, optimal normal basis, elliptic curve cryptography.
Citation:
Ashkan Hosseinzadeh Namin, Huapeng Wu, Majid Ahmadi, "A Word-Level Finite Field Multiplier Using Normal Basis," IEEE Transactions on Computers, vol. 60, no. 6, pp. 890-895, June 2011, doi:10.1109/TC.2010.235
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