An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences

Amparo Fúster-Sabater, Verónica Requena and Sara D. Cardell
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Amparo Fúster-Sabater: Instituto de Tecnologías Físicas y de la Información, C.S.I.C., 28006 Madrid, Spain
Verónica Requena: Departament de Matemàtiques, University of Alicante, 03690 Alicante, Spain
Sara D. Cardell: Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Santo André 09210-580, Brazil

Mathematics, 2022, vol. 10, issue 5, 1-23

Abstract: Binary sequences are algebraic structures currently used as security elements in Internet of Things devices, sensor networks, e-commerce, and cryptography. In this work, a contribution to the evaluation of such sequences is introduced. In fact, we present a novel algorithm to compute a fundamental parameter for this kind of structure: the linear complexity, which is related to the predictability (or non-predictability) of the binary sequences. Our algorithm reduced the computation of the linear complexity to just the addition modulo two (XOR logic operation) of distinct terms of the sequence. The performance of this procedure was better than that of other algorithms found in the literature. In addition, the amount of required sequence to perform this computation was more realistic than in the rest of the algorithms analysed. Tables, figures, and numerical results complete the work.

Keywords: Hadamard matrix; generalized sequence; linear complexity; Sierpinski’s triangle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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