Cohabitation of Fibonacci and Galois Modes in One Linear Feedback Shift Register

A linear feedback shift register (LFSR) is the basic element of the pseudo-random generators used to generate a sequence of pseudo-random values for a stream cipher. It consists of several cells; each cell is a flip-flop and a feedback function. The feedback function is a linear polynomial function; this function has a degree equal to the number of cells in the register. The basic elements of the register are connected to each other in two different ways, either in Fibonacci mode or in Galois mode. In this work, we propose the realization of a specific register which is cohabitation of these two modes (Fibonacci and Galois) in the same register and for the same feedback function, and which will be controlled by a random function for the selection of mode, which will be based on the chaotic logistics map. This specific register gave better results compared to registers with separate modes.