Pseudo-random sequences exhibit interesting properties with applications in many and distinct areas ranging from reliable communications to number generation or cryptography. Inside the family of decimation-based sequence generators, the modified self-shrinking generator (an improved version of the self-shrinking generator) is one of its best-known elements. In fact, such a generator divides the PN-sequence produced by a maximum-length LFSR into groups of three bits. When the sum of the first two bits in a group is one, then the generator returns the third bit, otherwise the bit is discarded. In this work, we introduce a generalization of this generator, where the PN-sequence is divided into groups of t bits, t≥2. It is possible to check that the properties of the output sequences produced by this family of generators have the same or better properties than those of the classic modified self-shrunken sequences. Moreover, the number of sequences generated by this new family with application in stream cipher cryptography increases dramatically.
The first author was supported by FAPESP with number of process 2015/07246-0 and CAPES. 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.