Clock-controlled shift registers: a review

Key-stream generators are discussed in which shift registers are clocked in a quasi-random manner under the control of other shift registers. They are a promising practical alternative to those using nonlinear combining functions on the outputs from regularly stepped shift registers and are now almost as well understood. Some World War II ciphers using stuttered rotors are briefly described as natural predecessors, including one cryptanalyzed on the Colossus machines. The algebraic theory is discussed, from which it is shown how large periods and linear equivalences can readily be obtained. The work of a number of authors on cascades is reviewed; these are linear hierarchies in which each register except the first is clock controlled by its predecessor. Other schemes are considered. Results on statistical properties and autocorrelation functions are quoted.<>