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
Acknowledgments
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 CYNAMON (P2018/TCS-4566), also co-funded by FSE and European Union FEDER funds. The first author was supported by CAPES (Brazil). The second author was partially supported by Spanish grant VIGROB-287 of the Universitat d’Alacant. We would like to thank Fausto Montoya for his help with the analysis of the sequences.
