98,106 research outputs found
Construction of sequences with high Nonlinear Complexity from the Hermitian Function Field
We provide a sequence with high nonlinear complexity from the Hermitian
function field over . This sequence was
obtained using a rational function with pole divisor in certain
collinear rational places on , where . In
particular we improve the lower bounds on the th-order nonlinear complexity
obtained by H. Niederreiter and C. Xing; and O. Geil, F. \"Ozbudak and D.
Ruano
Generating a Strong Key for a Stream Cipher Systems Based on Permutation Networks
The choice of binary Pseudonoise (PN) sequences with specific properties, having long period high complexity, randomness, minimum cross and auto- correlation which are essential for some communication systems.
In this research a nonlinear PN generator is introduced . It consists of a combination of basic components like Linear Feedback Shift Register (LFSR), ?-element which is a type of RxR crossbar switches.
The period and complexity of a sequence which are generated by the proposed generator are computed and the randomness properties of these sequences are measured by well-known randomness tests
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Layered cellular automata for pseudorandom number generation
The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used
Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series
We investigate for evidence of complex-deterministic dynamics in financial returns time series. By combining the Surrogate Data Analysis inferential framework with the MG-GARCH (Kyrtsou and Terraza, 2003) modelling approach, we examine whether the sequences are characterized by aperiodic and nonlinear deterministic cycles or pure randomness. Our results support the hypothesis of complex nonlinear and non-stochastic dynamics in the data generating processes. According to our approach, markets can be assumed to be highly complex, high-dimensional, open and dissipative dynamical systems that need feedback as well as other kinds of inputs in order to operate. These inputs may come in the guise of noise or news. The inputs may also control the evolution of the system dynamics and the knowledge of their nature may allow us to forecast the future states of the market with greater accuracy. To this extent the MG-GARCH model provides a valuable insight on how a feedback mechanism can operate within the structure of stock returns processes and explain stylized facts.MG-GARCH, Surrogate Data Analysis, Chaos, Complexity
Multisequences with high joint nonlinear complexity
We introduce the new concept of joint nonlinear complexity for multisequences
over finite fields and we analyze the joint nonlinear complexity of two
families of explicit inversive multisequences. We also establish a
probabilistic result on the behavior of the joint nonlinear complexity of
random multisequences over a fixed finite field
Intrinsic chaos and external noise in population dynamics
We address the problem of the relative importance of the intrinsic chaos and
the external noise in determining the complexity of population dynamics. We use
a recently proposed method for studying the complexity of nonlinear random
dynamical systems. The new measure of complexity is defined in terms of the
average number of bits per time-unit necessary to specify the sequence
generated by the system. This measure coincides with the rate of divergence of
nearby trajectories under two different realizations of the noise. In
particular, we show that the complexity of a nonlinear time-series model
constructed from sheep populations comes completely from the environmental
variations. However, in other situations, intrinsic chaos can be the crucial
factor. This method can be applied to many other systems in biology and
physics.Comment: 13 pages, Elsevier styl
Global Linear Complexity Analysis of Filter Keystream Generators
An efficient algorithm for computing lower bounds on the global linear
complexity of nonlinearly filtered PN-sequences is presented. The technique
here developed is based exclusively on the realization of bit wise logic
operations, which makes it appropriate for both software simulation and
hardware implementation. The present algorithm can be applied to any arbitrary
nonlinear function with a unique term of maximum order. Thus, the extent of its
application for different types of filter generators is quite broad.
Furthermore, emphasis is on the large lower bounds obtained that confirm the
exponential growth of the global linear complexity for the class of nonlinearly
filtered sequences
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