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Computing the linear complexity in a class of cryptographic sequences

generalized self-shrinking generator
linear complexity
linear recurrence relationship
Sierpinski triangle
Amparo Fúster-Sabater; Sara Díaz Cardell
Lecture Notes in Computer Science, vol. 10960, pp. 110-122, n.º 1, Springer Verlag
http://dx.doi.org/10.1007/978-3-319-95162-1_8

In this work, we present a method of computing the linear complexity of the sequences produced by the cryptographic sequence generator known as generalized self-shrinking generator. This approach is based on the comparison of different shifted versions of a single PN-sequence. Just the analysis of binary digits in these shifted sequences allows one to determine the linear complexity of those generalized sequences. The method is simple, direct and efficient. Furthermore, the concept of linear recurrence relationship and the rows of the Sierpinski’s triangle are the basic tools in this computation.

Acknowledgements

This research has been 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, and by Comunidad de Madrid (Spain) under project reference S2013/ICE-3095-CIBERDINE-CM, also co-funded by European Union FEDER funds. The second author was supported by FAPESP with number of process 2015/07246-0 and CAPES.

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