In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions.

In this study, we propose a novel keyed hash algorithm based on a Boolean function and chaotic attractor. The hash algorithm called BentSign is based on two Signature attractors and XOR function and a bent Boolean function. The provided theoretical and experimental results confirm that the novel scheme can generate output hashes with a good level of security, collision resistance, and protection against most common attacks.