On Feedback Functions of Maximum Length Nonlinear Feedback Shift Registers

Feedback shift registers are basic building blocks for many cryptographic primitives. Due to the insecurities of Linear Feedback Shift Register (LFSR) based systems, the use of Nonlinear Feedback Shift Registers (NFSRs) became more popular. In this work, we study the feedback functions of NFSRs with period 2^n. First, we provide two new necessary conditions for feedback functions to be maximum length. Then, we consider NFSRs with k-monomial feedback functions and focus on two extreme cases where k = 4 and k = 2^(n-1). We study construction methods for these special cases.