Construction Method for Infinite Families of Bent Sequences

Abstract

Bent-sequences is one of the most important classes of Boolean functions, which are widely used in modern cryptographic algorithms, and telecommunication systems that are based on CDMA and OFDM standards. The problem of synthesis of bent-sequences of large lengths is actual and widely discussed. However, in view of the high complexity and unpredictability of the class of bent-sequences, the creation of methods for their synthesis faces significant difficulties. In this paper, a recursive method for constructing infinite families of bent-sequences, based on easily synthesized bent-sequences of small length, has been developed. As the basis of this method, the operations of interleaving of elements and strings, which are widely used in the theory of synthesis of perfect binary arrays, are applied. Effective reproduction rules for bent-sequences in the time domain based on the operation of rearrangement of segments, a rotor, and dimensional changes are proposed. The method developed allows rapid acquisition of a lot of bentsequences of any predefined length. Moreover, the obtained bent-sequences belong to different classes according to Agievich classification, which is important from the cryptographic point of view.