Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This work analyses the output sequence from a cryptographic non-linear generator, the so-called shrinking generator. This sequence, known as the shrunken sequence, can be built by interleaving a unique PN-sequence whose characteristic polynomial serves as basis for the shrunken sequence's characteristic polynomial. In addition, the shrunken sequence can be also generated from a linear model based on cellular automata. The cellular automata here proposed generate a family of sequences with the same properties, period and characteristic polynomial, as those of the shrunken sequence. Moreover, such sequences appear several times along the cellular automata shifted a fixed number. The use of discrete logarithms allows the computation of such a number. The linearity of these cellular automata can be advantageously employed to launch a cryptanalysis against the shrinking generator and recover its output sequence.104797809Generalitat Valenciana [APOSTD/2013/081]FAPESP [2015/07246-0]Ministerio de Economia y Competitividad, Spain [TIN2014-55325-C2-1-R]Comunidad de Madrid, Spain [S2013/ICE-3095-CM]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)