We propose feedback-limited NFSRs (nonlinear feedback shift registers) which can generate periodic sequences of period 2k-1, where k is the length of the register. We investigate some characteristics of such periodic sequences. It is also shown that the scale of such NFSRs can be reduced by the feedback limitation. Some simulation and experimental results are shown including comparison with LFSRs (linear feedback shift registers) for conventional M-sequences and Gold sequences.

Since substitution boxes (S-boxes) are the only nonlinear portion of most block ciphers, the design of cryptographically strong and low-complexity S-boxes is of great importance in cryptosystems. In this paper, a new kind of S-boxes obtained by iterating a discretized piecewise linear map is proposed. The S-box has an implementation efficiency both in software and hardware. Moreover, the results of performance test show that the proposed S-box has good cryptographic properties.

This paper deals with the method for generation of maximal-period sequences which are designed by properly quantizing the variable state of a class of one-dimensional piecewise-linear onto maps. We confirmed that the proposed method enables us to generate many maximal-period sequences from such maps including De-Bruijn cases.

This paper presents design of spreading codes for asynchronous DS-CDMA systems. We generate maximal-period sequences with negative auto-correlations based on one-dimensional maps with finite bits whose shapes are similar to piecewise linear chaotic maps. We propose an efficient search algorithm to find such maximal-period sequences. This algorithm makes it possible to find many kinds of maximal-period sequences with sufficiently long period for practical CDMA applications. We also report that maximal-period sequences can outperform conventional Gold sequences in terms of bit error rate (BER) in asynchronous DS-CDMA systems.

In this paper, it is proved that there is a transformation between two types of nonlinear feedback shift register which can be regarded as implementation of the Bernoulli and tent maps with finite precision. This transformation can be interpreted as a sort of finite dimension version of topological conjugation between the Bernoulli and tent maps on continuous phase space. Several properties of periodic sequences generated from extended NFSRs are derived from the relation.

In this paper, we define a discretized chaotic map as a digital realization of a one-dimensional chaos map. As a concrete example, we consider a family of pseudochaotic sequences with maximum length, referred to as maximum length pseudochaotic sequences, obtained from a class of discretized piecewise linear map. A theoretical framework for designing maximum length pseudochaotic sequences of the discretized chaotic maps is obtained. These discretized piecewise linear chaotic maps can be used in the design of binary sequences with constant autocorrelation values for several time delays.