The self-shrinking generator is a non-linear cryptographic sequence generator designed to be used in stream cipher applications. In this work, its output sequence, the self-shrunken sequence, is computed as one of the output sequences of a linear model based on Cellular Automata. Such Automata are uniform, null, one-dimensional and use rules 102 or 60 for their computations. The linearity of these structures can be advantageous exploited to recover the complete selfshrunken sequence from a number of intercepted bits. Indeed, a Cellular Automata-based reconstruction procedure that is deterministic, does not need the knowledge of the LFSR characteristic polynomial and is performed exclusively by means of XOR operations has been proposed. © 2016 Old City Publishing, Inc.11 195211