The linear complexity and autocorrelation values are very important measures for evaluating the randomness of sequences. The engineering interpretation of linear complexity (LC) is as the length of the shortest linear feedback shift register (LFSR) that generates the sequence. By BerlekampMassey algorithm, if the linear complexity of a key stream is L, then 2L consecutive characters of the sequ...

The linear complexity and the k-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, the k-error linear complexity distribution of 2-periodic binary sequences is investigated based on Games-Chan algorithm. First, for k = 2, 3, the complete countin...

The linear complexity and the k-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By studying the linear complexity of binary sequences with period 2n, one could convert the computation of kerror linear complexity into finding error sequences with minimal Hamming weight. Based on Games-C...

In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field (ZN ,+,×), where N > 3 is a prime. The sequences generated by the IPRNGs are transformed to 2-dimensional linear feedback shift register (LFSR) sequences. By employing the generating function method and the finite field theory, the period distribution is obtain...

Linear feedback shift registers (LFSR’s) are fundamental primitives in the theory and practice of pseudorandom number generation and coding theory (see, e.g., [1], [2], [3], [4], [6], [7], and references therein). Figure 1 describes a typical LFSR over the two-element field F2 = {0, 1}, where each step consists of adding some of the state bits (we follow the convention that the elements of F2 a...

Utilisation of input compatibilities alleviates test costs inmany applications such as reducing linear feedback shift register (LFSR) size, and scan tree construction among others. Correlation among inputs, identified based on a test set analysis, can be exploited by driving the circuit inputs through fewer channels. The reduction in the number of channels, which is dictated by the number of co...

The recently developed algebraic attacks apply to all keystream generators whose internal state is updated by a linear transition function, including LFSR-based generators. Here, we describe this type of attacks and we present some open problems related to their complexity. We also investigate the design criteria which may guarantee a high resistance to algebraic attacks for keystream generator...

Non-Linear Feedback Shift Registers (NLFSRs) are a generalization of Linear Feedback Shift Registers (LFSRs) in which a current state is a nonlinear function of the previous state. While the theory behind LFSRs is wellunderstood, many fundamental problems related to NLFSRs remain open. Probably the most important one is finding a systematic procedure for constructing NLFSRs with a guaranteed lo...

Grain and Trivium are the hardware-oriented finalists of the eSTREAM. They are both based on nonlinear feedback shift registers. In this paper, we study their generalized classes of nonlinear feedback shift registers with time varying feedback functions, namely, Grain-like and Trivium-like structures. Some interesting results regarding their periods are obtained.

1 One of the main drawbacks of the conventional reseeding architecture is the limited seed efficiency due to the variance in the number of specified bits per vector. This paper proposes a new LFSR reseeding architecture that essentially solves this problem, resulting in a significant compression ratio. The compression ratio is very close to the entropy in terms of #total bits / #specified bits....