Cardell, Sara D., Climent, Joan-Josep, Fúster Sabater, Amparo, Requena Arévalo, Verónica
Representations of Generalized Self-Shrunken Sequences
Cardell SD, Climent J-J, Fúster-Sabater A, Requena V. Representations of Generalized Self-Shrunken Sequences. Mathematics. 2020; 8(6):1006. doi:10.3390/math8061006
URI: http://hdl.handle.net/10045/107613
DOI: 10.3390/math8061006
ISSN: 2227-7390
Abstract: 
Output sequences of the cryptographic pseudo-random number generator, known as the generalized self-shrinking generator, are obtained self-decimating Pseudo-Noise (PN)-sequences with shifted versions of themselves. In this paper, we present three different representations of this family of sequences. Two of them, the p and G-representations, are based on the parameters p and G corresponding to shifts and binary vectors, respectively, used to compute the shifted versions of the original PN-sequence. In addition, such sequences can be also computed as the binary sum of diagonals of the Sierpinski’s triangle. This is called the B-representation. Characteristics and generalities of the three representations are analyzed in detail. Under such representations, we determine some properties of these cryptographic sequences. Furthermore, these sequences form a family that has a group structure with the bit-wise XOR operation.
Keywords:Generalized self-shrinking generator, PN-sequence, Binomial sequence, Additive group, Coset
MDPI
info:eu-repo/semantics/article