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Open AccessArticle

Randomness Analysis for the Generalized Self-Shrinking Sequences

1
Instituto de Matemática, Estatística e Computação Científica, UNICAMP, Campinas-SP, 13083-859, Brazil
2
Departamento de Matemáticas, Universidad de Alicante, Alicante 03690, Spain
3
Instituto de Tecnologías Físicas y de la Información, CSIC, Madrid 28006, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1460; https://doi.org/10.3390/sym11121460
Received: 30 September 2019 / Revised: 21 November 2019 / Accepted: 23 November 2019 / Published: 28 November 2019
(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)
In cryptography, the property of randomness in pseudo-random generators is very important to avoid any pattern in output sequences, to provide security against attacks, privacy and anonymity. In this article, the randomness of the family of sequences obtained from the generalized self-shrinking generator is analyzed. Moreover, the characteristics, generalities and relationship between the t-modified self-shrinking generator and the generalized self-shrinking generator are presented. We find that the t-modified self-shrunken sequences can be generated from a generalized self-shrinking generator. Then, an in-depth analysis of randomness focused on the generalized sequences by means of complete and powerful batteries of statistical tests and graphical tools is done, providing a useful vision of the behaviour of these sequences and proving that they are suitable to be used in cryptography.
Keywords: generalized self-shrinking generator; t-modified self-shrinking generator; pseudo-random number generator; statistical randomness tests; cryptography. generalized self-shrinking generator; t-modified self-shrinking generator; pseudo-random number generator; statistical randomness tests; cryptography.
MDPI and ACS Style

Cardell, S.D.; Requena, V.; Fúster-Sabater, A.; Orúe, A.B. Randomness Analysis for the Generalized Self-Shrinking Sequences. Symmetry 2019, 11, 1460.

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