The generalized self-shrinking generator is a sequence generator that produces binary sequences with good cryptographic properties. On the other hand, the binomial sequences are a well-defined class of sequences that can be obtained considering infinite successions of binomial coefficients modulo 2. In this work, we see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Moreover, the cryptographic parameters of the generalized sequences can be studied in terms of the binomial sequences.
Acknowledgements
Research partially supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación, and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS (TIN2017-84844-C2-1-R) and by Comunidad de Madrid (Spain) under project CYNAMON (P2018/TCS-4566), also co-funded by European Union FEDER funds. The first author was supported by CAPES (Brazil).
