Randomness Analysis for GSS-sequences Concatenated

S. D. Cardell, A. Fúster-Sabater, A. B. Orúe, V. Requena
Á. Herrero et al. (Eds.). 13th International Conference on Computational Intelligence in Security for Information Systems (CISIS 2020). Advances in Intelligent Systems and Computing (AISC), vol. 1267. Springer, Cham, pp. 350-360, 2021

Binary sequences produced by a generator should appear as random as possible, that is, have no logical pattern to be used in cryptographic applications. In this paper, we give a detailed analysis of the randomness of a family of binary sequences obtained from generalized self-shrinking generator, an element in the class of decimation-based sequence generators. We have applied the most important batteries of statistical tests to the sequence resulting from the concatenation of the family of generalized sequences obtained from a PN-sequence. This complete study provides good results and allow us to construct a new binary sequence with good cryptographic properties from a family of generalized self-shrunken sequences.

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 fourth author was partially supported by Spanish grant VIGROB-287 of the Universitat d’Alacant.