Polygons characterizing the joint statistical properties of the input and output sequences of the binary shift register

Binary non-autonomous shift registers, which are widely used as intermediate nodes in cascade pseudo-random sequence generators, are considered. The joint statistical properties of the symbols of the input and output sequences of such registers are studied depending on the used output function. A geometric approach is proposed for description of such properties, within the framework of which the output function can be characterized by its polygon in the unit square [0, 1] × [0, 1]. The properties of such polygons and their relationship with the properties of the used output function are investigated. © 2020 ACM.