554 research outputs found
On lattice profile of the elliptic curve linear congruential generators
Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order k to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG
Continued fraction for formal laurent series and the lattice structure of sequences
Besides equidistribution properties and statistical independence the lattice profile, a generalized version of Marsaglia's lattice test, provides another quality measure for pseudorandom sequences over a (finite) field. It turned out that the lattice profile is closely related with the linear complexity profile. In this article we give a survey of several features of the linear complexity profile and the lattice profile, and we utilize relationships to completely describe the lattice profile of a sequence over a finite field in terms of the continued fraction expansion of its generating function. Finally we describe and construct sequences with a certain lattice profile, and introduce a further complexity measure
On linear complexity of binary lattices
The linear complexity is an important and frequently used
measure of unpredictability and pseudorandomness of binary
sequences. In this paper our goal is to extend this notion
to two dimensions. We will define and study the linear complexity of binary lattices. The linear complexity of a truly random binary lattice will be estimated. Finally, we will analyze the connection between the linear complexity and the correlation measures, and we will utilize the inequalities obtained in this way for estimating the linear complexity of an important special binary lattice. Finally,
we will study the connection between the linear complexity of binary lattices and of the associated binary sequences
Quantifying hidden order out of equilibrium
While the equilibrium properties, states, and phase transitions of
interacting systems are well described by statistical mechanics, the lack of
suitable state parameters has hindered the understanding of non-equilibrium
phenomena in diverse settings, from glasses to driven systems to biology. The
length of a losslessly compressed data file is a direct measure of its
information content: The more ordered the data is, the lower its information
content and the shorter the length of its encoding can be made. Here, we
describe how data compression enables the quantification of order in
non-equilibrium and equilibrium many-body systems, both discrete and
continuous, even when the underlying form of order is unknown. We consider
absorbing state models on and off-lattice, as well as a system of active
Brownian particles undergoing motility-induced phase separation. The technique
reliably identifies non-equilibrium phase transitions, determines their
character, quantitatively predicts certain critical exponents without prior
knowledge of the order parameters, and reveals previously unknown ordering
phenomena. This technique should provide a quantitative measure of organization
in condensed matter and other systems exhibiting collective phase transitions
in and out of equilibrium
Finite Fields: Theory and Applications
Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation
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