Analysis of the generalized self-shrinking generator

This work shows that the output sequences of a well-known cryptographic generator, the so-called generalized self-shrinking generator, are particular solutions of homogeneous linear difference equations with binary coefficients. In particular, all those generated sequences are just linear combinations of primary sequences weighted by binary values. Furthermore, the complete class of solutions of these difference equations includes other balanced sequences with the same period and even greater linear complexity than that of the generalized self-shrinking sequences. Cryptographic parameters of all above mentioned sequences are here analyzed in terms of linear equation solutions. In addition, this work describes an efficient algorithm to synthesize the component primary sequences as well as to compute the linear complexity and period of any generalized self-shrinking sequence.