Binomial Characterization of Cryptographic Sequences

Abstract

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.