Clock-Controlled Generators

A stream cipher generator can not be considered as suitable for stream ciphers applications unless its output sequences have large periods, large linear complexities and possess certain randomness properties. The use of clock-controlled shift registers in keystream generators appears to be a good way of achieving sequences with these properties. In this thesis we look at clock-controlled generators, these are built up from two registers, one controlling the clock of a second register from which the output is taken. Examples that have appeared in the literature include the stop and go generator, the binary rate multiplier, the (a, b) clock-controlled generator, the cascade generator, and the shrinking generator. The binary rate multiplier and the (a, b) clock-controlled generator may be seen as generalizations for the stop and go generator. Similarly we introduce generalizations of the cascade generator and the shrinking generator that allows us, by using the same initial states and feedback functions, to produce many more sequences with the same desirable properties as those produced by the original generator. We establish some general properties of the output sequences of the generalized versions of these generators. We investigate these properties further when the registers that make up these generators generate msequences, or de Bruijn sequences, or a combination of an m-sequence and a de Bruijn sequence. These cases are of particular interest as they may be generated efficiently and we identify among these special cases, those in which the generators perform best. We introduce a new self-shrinking generator that is built up from one single linear feedback shift register and is more efficient than other generators of this type. We establish some general properties of the output sequences of this generator when it is built up from a primitive linear feedback shift register. We also introduce a generator that may be seen as a generalization of the new self-shrinking generator. The generalized version provides a larger family of good sequences and we establish some general properties of these sequences. Finally we look at the alternating step generator and we introduce two techniques that provide generalization of this generator. We establish some general properties of the output sequences of the generalized versions, and we move on to consider the properties of the output sequences for the particular cases when the control register of the generator generates an m-sequence, or a de Bruijn sequence, and the generating registers generate m-sequences. !