Some conditions for absence of affine functions in NFSR output stream

Nonlinear feedback shift registers (NFSR) are widely used in cryptography as the source of pseudo-random sequences used in ciphers. The nature of the feedback in a given NFSR affects its output sequence and its statistical quality. The complexity of the problem of restoring the initial state of an NFSR by partially known values of the output is one of the signs of a "good" NFSR. In this regard, we note that the presence of the output affine functions lowers the quality of an NFSR since the corresponding problem is reduced to the solution of a system of linear equations. This paper is concerned with the conditions providing the absence of nontrivial affine functions among NFSR output functions. The obtained theoretical results can be used to improve the effectiveness of experimental methods of finding NFSRs with no affine output functions.