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Interleaving Shifted Versions of a PN-Sequence

PN-sequence
interleaving sequence
linear complexity
period
decimation
S.D. Cardell, A. Fúster-Sabater, V. Requena
Special Issue “Algebra and Number Theory”, Mathematics, vol. 9(6), 687, March 2021
https://doi.org/10.3390/math9060687

The output sequence of the shrinking generator can be considered as an interleaving of determined shifted versions of a single PN -sequence. In this paper, we present a study of the interleaving of a PN-sequence and shifted versions of itself. We analyze some important cryptographic properties as the period and the linear complexity in terms of the shifts. Furthermore, we determine the total number of the interleaving sequences that achieve each possible value of the linear complexity.

Keywords: PN-sequence; interleaving sequence; linear complexity; period; decimation

Funding

This research is partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R. It is also supported by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), co-funded by FSE and European Union FEDER funds. Finally, the third author is partially supported by Spanish grant VIGROB-287 of the Universitat d’Alacant.

The support of D. Arroyo is gratefully acknowledged by the authors.

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