Modelling the shrinking generator in terms of linear CA

Abstract

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.