# Alternating Step Generators Controlled by De Bruijn Sequences

## Abstract

The alternating step generator (ASG) is a new generator of pseudorandom sequences which is closely related to the stop-and-go generator. It shares all the good properties of this latter generator without Posessing its weaknesses. The ASG consists of three subgenerators *k, m*, and Open image in new window . The main characteristic of its structure is that the output of one of the subgenerators, *k*, controls the clock of the two others, *m* and Open image in new window . In the present contribution, we determine the period, the distribution of short patterns and a lower bound for the linear complexity of the sequences generated by an ASG. The proof of the lower bound is greatly simplified by assuming that *k* generates a de Bruijn sequence. Under this and other not very restrictive assumptions the period and the linear complexity are found to be proportional to the period of the de Bruijn sequence. Furthermore the frequency of all short patterns as well as the autocorrelations turn out to be ideal. This means that the sequences generated by the ASG are provably secure against the standard attacks.

## Keywords

Linear Complexity Pseudorandom Sequence Short Pattern Cascade Sequence Linear Recurrence Relation## Selected References

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