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An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences

Author

Listed:
  • 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)

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.

Suggested Citation

  • Amparo Fúster-Sabater & Verónica Requena & Sara D. Cardell, 2022. "An Efficient Algorithm to Compute the Linear Complexity of Binary Sequences," Mathematics, MDPI, vol. 10(5), pages 1-23, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:794-:d:762507
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    References listed on IDEAS

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    1. Sara D. Cardell & Amparo Fúster-Sabater, 2019. "Binomial Representation of Cryptographic Binary Sequences and Its Relation to Cellular Automata," Complexity, Hindawi, vol. 2019, pages 1-13, March.
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