Complexity Reduction of Constant Matrix Computations over the Binary Field

Authors:
Oscar Gustafsson;Mikael Olofsson
Affiliations:
Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden;Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden
Venue:
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Year:
2007

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Abstract

In this work an algorithm for realizing a multiplication of a vector by a constant matrix over the binary field with few two-input XOR-gates is proposed. This type of problem occurs in, e.g., Galois field computations, syndrome computation for linear error correcting codes, cyclic redundancy checks (CRCs), linear feedback shift-registers (LFSRs), and implementations of the Advanced Encryption Standard (AES) algorithm. As the proposed algorithm can utilize cancellation of terms it outperforms in general previously proposed algorithms based on sub-expression sharing.