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  • Abstract - Comments on "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Field"
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Comments on "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Field"
July 2010 (vol. 59 no. 7)
pp. 1007-1008
Gang Zhou, Technical University of Braunschweig, Braunschweig
Harald Michalik, Technical University of Braunschweig, Braunschweig
In this comment, we show that the gate complexity of Karatsuba polynomial multipliers presented in the above paper can be reduced by exploring the common subexpressions.

[1] C. Paar, "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields," IEEE Trans. Computers, vol. 45, no. 7, pp. 856-861, July 1996.
[2] B. Sunar, "A Generalized Method for Constructing Subquadratic Complexity $GF(2^k)$ Multipliers," IEEE Trans. Computers, vol. 53, no. 9, pp. 1097-1105, Sept. 2004.
[3] P.L. Montgomery, "Five, Six, and Seven-Term Karatsuba-Like Formulae," IEEE Trans. Computers, vol. 54, no. 3, pp. 362-369, Mar. 2005.
[4] A. Weimerskirch and C. Paar, "Generalizations of the Karatsuba Algorithm for Efficient Implementations," eprint Archive, http://eprint.iacr.org/2006224.pdf, 2006.
[5] H. Fan and M.A. Hasan, "A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields," IEEE Trans. Computers, vol. 56, no. 2, pp. 224-233, Feb. 2007.
[6] H. Fan, J. Sun, M. Gu, and K.-Y. Lam, "Overlap-Free Karatsuba-Ofman Polynomial Multiplication Algorithm," Cryptology ePrint Archive, http://eprint.iacr.org/2007393.pdf, 2007.

Index Terms:
Karatsuba algorithm, polynomial multiplication, finite field.
Citation:
Gang Zhou, Harald Michalik, "Comments on "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Field"," IEEE Transactions on Computers, vol. 59, no. 7, pp. 1007-1008, July 2010, doi:10.1109/TC.2010.46
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