Investigations in the Design and Analysis of Key-Stream Generators

The work is focused on several important problems in §the design and analysis of key-stream generators for §stream ciphers. We look at common building blocks §that are used in key-stream generators. These are §nonlinear logical functions and clock-controlled §linear feedback shift registers (LFSR). We introduce §tensor transform which gives new tools for analyzing §security of the functions. We also study correlation §properties of Boolean functions. A newly introduced §probabilistic function of a Boolean function §estimates the probabilistic distribution of its §output bits if the distribution of the arguments, §the function depends on, is known. For a clock-§controlled LFSR, we estimate the period of its §output sequence when the feedback polynomial is §irreducible and the structure of the control §sequence is arbitrary. Away from building blocks, we §construct a key-stream generator based on the one §suggested by Geffe. Unlike the Geffe generator that §has three binary input m-sequences, this generator §runs over the extension field and combines multiple §inputs having arbitrary periods. Finally, we develop §several statistical attacks on stream ciphers.