On the Linearity of Cryptographic Sequence Generators

Abstract

<p>In this paper we show that the output sequences of the generalized self-shrinking generator are particular solutions of a binary homogeneous linear difference equation. In fact, all these sequences are just linear combinations of primary sequences weighted by binary coefficients. We show that in addition to the output sequences of the generalized selfshrinking generator, the complete class of solutions of the corresponding binary homogeneous linear difference equation also includes other balanced sequences that are very suitable for cryptographic applications, as they have the same period and even greater linear complexity than the generalized self-shrinking sequences. Cryptographic parameters of all the above mentioned sequences can be analyzed in terms of linear equation solutions.</p>