Research of Second-Order Properties of NLFSR. Comparative Analysis of M-NLFSR and M-LFSR

Abstract

The linear complexity (Li) of PRS is the shortest shift register, which generates a given periodic sequence, provided that the first L values of the sequence are the initial filling of the register [1][2][3][4][5][6][7][8].Estimation of linear complexity is one of the main parameters of the system. Any sequence that can be generated automatically (linear or nonlinear) over a finite field has finite linear complexity. Thus, it is possible to build an algorithm that will determine the linear complexity of any sequence, regardless of the method of its generation. To calculate Li, we use the Burleckamp-Messi algorithm, the essence of which is described in detail in [9][10][11].Linear complexity is a measure of the complexity of the generated sequence [12]. Considering a certain segment of the sequence, it is possible to build a sequence of identical source on the basis of the existing sequence and with the help of an equivalent system. Finding the linear complexity of PRS makes it possible to build a circuit that generates a sequence similar to the original, while knowledge of the structure of the circuit that generated the original sequence is unnecessary. Thus, the high linear complexity of PRS is a necessary but not sufficient condition for the practical stability of PRS generators. Li was calculated for the complete set of

A New Self-Shrinking Generator

“…Thus, NLFSR sequences can be more cryptographically secure than LFSR sequences. The security of NLFSRs was examined in [8]. An important result is that with high probability, the linear complexity of a randomly chosen maximum period NLFSR will be very close to 2 n .…”

“…None of the existing self-shrinking generators employ a nonlinear feedback shift register (NLFSR). This is despite the fact that NLFSRs can provide greater security than LFSRS [8]. Thus, in this paper the concept of shrinking is combined with NLFSRs to get the benefits of both.…”