On the significance of the directed acyclic word graph in cryptology

Abstract

Blumer’s algorithm can be used to build a Directed Acyclic Word Graph (DAWG) in linear time and memory from a given sequence of characters. In this paper we introduce the DAWG and show that Blumer’s algorithm can be used very effectively to determine the maximum order (or nonlinear) complexity profile of a given sequence. We also show that this algorithm can be used to determine the period of a periodic sequence in linear time and memory. It also appears that the DAWG is an even more efficient means of generating the sequence, given a number of characters, than e.g. the nonlinear feedback shift register equivalent of that sequence, as it always needs the least amount of characters to generate the remainder of the sequence.