Marsaglia (2003) has described a class of“xorshift”random number generators (RNGs) with periods 2 − 1 for n = 32, 64, etc. We show that the sequences generated by these RNGs are identical to the sequences generated by certain linear feedback shift register (LFSR) generators using “exclusive or” (xor) operations on n-bit words, with a recurrence defined by a primitive polynomial of degree n.

Abstact A new design approach is proposed for a fault coverage circuit. In this design a linear feedback shift register which is called as LT_LFSR (Low Transition Linear Feedback Shift Register) is used. Using LT_LFSR reduces the power consumption by reducing the number of transitions during test mode. Power reduction is done by implementing two new test pattern generation methods in LFSR. In b...

This paper presents a method to reduce the power consumption of the popular linear feedback shift register. The proposed scheme is based on the gated clock design approach and it can offer a significant power reduction, depending on technological characteristics of the employed gates. A modified Linear Feedback Shift Register is designed in which power consumption is reduced by deactivating the...

We present a simple construction of a small probability space on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is O(log log n + k + log ~), where e is the statistical difference between of the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recentl...

Sum-product message passing (belief propagation) was recently extended to messages/summaries with some nontrivial Markov structure. In this paper, a general update rule for Markov-structured messages is proposed, and further experimental results are presented for the synchronization of noisy linear-feedback shift register (LFSR) sequences.

We determine the imbalances of the keystreams produced by Achterbahn-80 and Achterbahn-128 in two different ways. The number of cyclically inequivalent keystreams produced by the keystream generators of Achterbahn-80 and Achterbahn-128 is determined. An abstract model for the keystream generator of a primitive NLFSR combination generator is used to justify the correlation attack introduced in [...

Linear feedback shift registers (LFSRs) and nonlinear feedback shift registers (NLFSRs) are major components of stream ciphers. It has been shown that, under certain idealized assumptions, LFSRs and LFSR-based stream ciphers are susceptible to cryptanalysis using simple power analysis (SPA). In this paper, we show that simple power analysis can be practically applied to a CMOS digital hardware ...

Non-linear feedback shift registers are widely used in lightweight cryptographic primitives. For such constructions we propose a general analysis technique based on differential cryptanalysis. The essential idea is to identify conditions on the internal state to obtain a deterministic differential characteristic for a large number of rounds. Depending on whether these conditions involve public ...

In this paper, we study sequences generated by arbitrary feedback registers (not necessarily feedback shift registers) with arbitrary feedforward functions. We generalize the definition of linear complexity of a sequence to the notions of strong and weak linear complexity of feedback registers. A technique for finding upper bounds for the strong linear complexities of such registers is develope...

Maximal length Feedback with Carry Shift Register sequences have several remarkable statistical properties. Among them is the property that the arithmetic correlations between any two cyclically distinct decimations are precisely zero. It is open, however, whether all such pairs of decimations are indeed cyclically distinct. In this paper we show that the set of distinct decimations is large an...