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.
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Gustafsson, O., Olofsson, M. (2007). Complexity Reduction of Constant Matrix Computations over the Binary Field. In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_9
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DOI: https://doi.org/10.1007/978-3-540-73074-3_9
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