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Block Recombination Approach for Subquadratic Space Complexity Binary Field Multiplication Based on Toeplitz Matrix-Vector Product
February 2012 (vol. 61 no. 2)
pp. 151-163
M. Anwar Hasan, University of Waterloo, Waterloo
Nicolas Méloni, Université de Toulon-Var, Toulon
Ashkan Hosseinzadeh Namin, University of Waterloo, Waterloo
Christophe Negre, University of Waterloo, Waterloo and Université de Perpignan, Perpignan
In this paper, we present a new method for parallel binary finite field multiplication which results in subquadratic space complexity. The method is based on decomposing the building blocks of the Fan-Hasan subquadratic Toeplitz matrix-vector multiplier. We reduce the space complexity of their architecture by recombining the building blocks. In comparison to other similar schemes available in the literature, our proposal presents a better space complexity while having the same time complexity. We also show that block recombination can be used for efficient implementation of the GHASH function of Galois Counter Mode (GCM).

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Index Terms:
Binary field, subquadratic space complexity multiplier, Toeplitz matrix, block recombination.
M. Anwar Hasan, Nicolas Méloni, Ashkan Hosseinzadeh Namin, Christophe Negre, "Block Recombination Approach for Subquadratic Space Complexity Binary Field Multiplication Based on Toeplitz Matrix-Vector Product," IEEE Transactions on Computers, vol. 61, no. 2, pp. 151-163, Feb. 2012, doi:10.1109/TC.2010.276
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