The generalized self-shrinking generator (or generalized generator) produces binary sequences (generalized sequences) with good cryptographic properties. On the other hand, the binomial sequences can be obtained considering infinite successions of binomial coefficients modulo 2. It is possible to see that the generalized sequences can be computed as a finite binary sum of binomial sequences. Besides, 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
