XOR-metrics measure the efficiency of certain arithmetic operations in binary finite fields. We prove some new results about two different XOR-metrics that have been used in the past. In particular, we disprove a conjecture from [10]. We consider implementations of multiplication with one fixed element in a binary finite field. Here we achieve a complete characterization of all elements whose multiplication matrix can be implemented using exactly 2 XOR-operations, confirming a conjecture from [2]. Further, we provide new results and examples in more general cases, showing that significant improvements in implementations are possible.
CITATION STYLE
Kölsch, L. (2019). XOR-counts and lightweight multiplication with fixed elements in binary finite fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11476 LNCS, pp. 285–312). Springer Verlag. https://doi.org/10.1007/978-3-030-17653-2_10
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