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.
