Clock-controlled shift registers in binary sequence generators

Cryptographic binary sequence generators are discussed in which a linear feedback shift register is clock controlled in a pseudorandom manner by another register. Huge values of the linear equivalence are readily achieved. To illustrate the possibilities three types of generator are described: First, the output from a clock-controlled shift register is scrambled by a MacLaren-Marsaglia shuffler. Secondly, the output sequence is generated as the scalar product of the state-vector of a clock-controlled shift register with a pseudorandom sequence of vectors and thirdly, a cascade of clock-controlled shift registers is set up in which several bits are passed in parallel from stage to stage through invertible s-boxes. A new version of the theorem which guarantees large values of the linear equivalence is given, together with a proof along novel lines.