multivariate polynomial products over modular rings using residue arithmetic a computational system called the polynomial residue number system prns has previously been proposed and analyzed it solves the problem of multiplying two univariate polynomials modulo x sup n spl plusmn 1 over the modular ring z sub p in the present paper extensions of prns for computing the product of two multivariate polynomials modulo a polynomial are developed such a number system is termed as multivariate polynomial residue number system mprns mprns is essentially an isomorphic representation between the ring z sub p x spl pi sub i 1 sup l x sub i n sub i spl plusmn 1 of l variate polynomials in the indeterminate vector x x sub 1 x sub 2 x sub l and the ring z sub p n sub 1 n sub 2 n sub l issues related to existence of isomorphic mappings their properties and multiplicative complexity of the resulting algorithm have been addressed the applications of the mprns scheme are also presented

color image encryption based on one time keys and robust chaotic maps we designed a stream cipher algorithm based on one time keys and robust chaotic maps in order to get high security and improve the dynamical degradation we utilized the piecewise linear chaotic map as the generator of a pseudo random key stream sequence the initial conditions were generated by the true random number generators the md5 of the mouse positions we applied the algorithm to encrypt the color image and got the satisfactory level security by two measures npcr and uaci when the collision of md5 had been found we combined the algorithm with the traditional cycle encryption to ensure higher security the ciphered image is robust against noise and makes known attack unfeasible it is suitable for application in color image encryption

a family of hyperchaotic multi scroll attractors in rn abstract in this work we present a mechanism how to yield a family of hyperchaotic multi scroll systems in r n based on unstable dissipative systems this class of systems is constructed by a switching control law changing the equilibrium point of an unstable dissipative system for each equilibrium point presented in the system a scroll emerges the switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor thus if two systems display different numbers of scrolls they have different switching control laws this paper also presents a generalized theory that explains different approaches such as hysteresis and step functions from a unified viewpoint extending the concept of chaos in r 3 to hyperchaotic multi scroll systems in r n n 4 an illustrative example of synchronizing a communication system is given based on the developed theory

hyperchaotic encryption based on multi scroll piecewise linear systems a hyperchaotic multi scroll piecewise linear system in r4 is binarized to generate a pseudo random sequence which encrypt a grayscale image via symmetric key algorithm the sequence is analyzed throughout statistical tests according to the national institute of standards and technology nist specifications the scrolls of the system are the result of a switching law that changes between the saddle hyperbolic equilibria of piecewise linear systems with eigenvalues as follows two negative real and one pair of complex conjugate eigenvalues with positive real part thus the encryption quality is evaluated depending on the variation of the number of scrolls

a secret sharing scheme based on cellular automata a new secret sharing scheme based on a particular type of discrete delay dynamical systems memory cellular automata is proposed specifically such scheme consists of a k n threshold scheme where the text to be shared is considered as one of the k initial conditions of the memory cellular automata and the n shares to be distributed are n consecutive configurations of the evolution of such cellular automata it is also proved to be perfect and ideal

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

on the bifurcation of marotto s map and its application in image encryption abstract the aim of this paper is to address the codimension one bifurcation of marotto s map and its utility in image encryption first of all local stability analysis and local bifurcation analysis of fixed points of the considered map are investigated in details according to the classical bifurcation theory and the center manifold theorem the map exhibits various bifurcation types such as transcritical flip and neimark sacker bifurcations second of all the map is proven to be chaotic in the sense of marotto since image encryption based on chaotic maps is very promising for cryptography marotto s map compound chaos and spatiotemporal chaos are combined to encrypt and decrypt images numerical simulations agree with the analytical framework for the complex dynamics of the map furthermore different test images are used to demonstrate the effectiveness of the method implemented for encryption

letter to the editor adaptive control for modified projective synchronization of a four dimensional chaotic system with uncertain parameters this article is concerned with the modified projective synchronization problem for a class of four dimensional chaotic system with uncertain parameters by utilizing lyapunov method an adaptive control scheme for the synchronization has been presented the control performances are verified by a numerical simulation

on the application of a fast polynomial transform and the chinese remainder theorem to compute a two dimensional convolution in this paper a fast algorithm is developed to compute two dimensional convolutions of an array of d 1 d 2 complex number points where d 2 2mand d 1 2m r 1for some 1 leq r leq m this new algorithm requires fewer multiplications and about the same number of additions as the conventional fft method for computing the two dimensional convolution it also has the advantage that the operation of transposing the matrix of data can be avoided

a novel lossless color image encryption scheme using 2d dwt and 6d hyperchaotic system this paper proposes a new lossless encryption algorithm for color images based on a six dimensional 6d hyperchaotic system and the two dimensional 2d discrete wavelet transform dwt different from the current image encryption methods our image encryption scheme is constructed using the 2d dwt and 6d hyperchaotic system in both the frequency domain and the spatial domain where the key streams depend on not only the hyperchaotic system but the plain image in the presented algorithm the plain image is firstly divided into four image sub bands by means of the 2d dwt secondly the sub bands are permutated by a key stream and then the size of them is decreased by a constant factor thirdly the 2d inverse dwt is employed to reconstruct an intermediate image by the four encrypted image sub bands finally to further enhance the security the pixel values of the intermediate image are modified by using another key stream experimental results and security analysis demonstrate that the proposed algorithm has a high security fast speed and can resist various attacks

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

fingerprint images encryption via multi scroll chaotic attractors this paper proposes a chaotic fingerprint images encryption approach an image of a fingerprint is encrypted via a two dimensional 2d chaotic sequence obtained from multi scroll chaotic attractors initial values of the chaotic attractors are served as the private key which can be generated from the pixel distribution of the binary images of the captured fingerprints due to the dynamic uncertainties in the acquisition process of fingerprint images the keys generated from the pixel value distribution are virtually random with the elaborately designed 2d chaotic sequence the encrypted fingerprint images have balanced 0 1 ratio and ideal nonlinearity only with the valid private key can the images of fingerprint be recovered simulation results and 2d dft validate this chaotic encryption approach

generating 3 d multi scroll chaotic attractors a hysteresis series switching method this paper introduces a systematic method a hysteresis series switching approach for generating multi scroll chaotic attractors from a three dimensional linear autonomous system including 1 d n scroll 2 d nxm grid scroll and 3 d nxmxl grid scroll chaotic attractors the chaos generation mechanism is studied by analyzing the system trajectories and the hysteresis switching dynamics of the controlled chaotic systems are explored moreover a two dimensional poincare return map is rigorously derived this map and its maximum lyapunov exponent are applied to verifying the chaotic behaviors of the generated 3 d multi scroll chaotic attractors

h synchronization of time delayed chaotic systems abstract this paper considers h synchronization of a class of time delayed chaotic systems with external disturbance based on lyapunov theory and linear matrix inequality lmi formulation the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems but also reduce the effect of external disturbance to an h norm constraint then a criterion for existence of the controller is given in terms of lmis finally a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme

permutation and sampling with maximum length ca or pseudorandom number generation abstract in this paper we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata ca dynamic permutation and sampling have not been explored in previous ca work and a suitable implementation is shown using a two ca model three different schemes that incorporate these two operations are suggested weighted permutation vector sampling with controlled multiplexing weighted permutation vector sampling with irregular decimation and permutation programmed ca sampling the experiment results show that the resulting sequences have varying degrees of improvement in diehard results and linear complexity compared to the ca

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

image encryption with chaotically coupled chaotic maps abstract we present a novel secure cryptosystem for direct encryption of color images based on chaotically coupled chaotic maps the proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels colors information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible the encryption algorithm guarantees the three main goals of cryptography strong cryptographic security short encryption decryption time and robustness against noise and other external disturbances due to the high speed the proposed cryptosystem is suitable for application in real time communication systems

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

multidimensional cyclic convolution algorithms with minimal multiplicative complexity this paper presents novel multidimensional cyclic convolution algorithms which achieve the theoretically minimum number of multiplications the proposed algorithms are compared to the well known and used polynomial transform and split nesting convolution algorithms

predictive feedback control and synchronization of hyperchaotic systems the paper deals with the problem of control and synchronization of hyperchaotic systems the proposed control method is based on the predictive principle which employ an instantaneous control input to guarantee the convergence of the chaotic trajectory towards an unstable equilibrium point the synchronization is constructed around the drive response principle numerical simulations on some hyperchaotic systems are given to demonstrate the main results

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

on the generation of high quality random numbers by two dimensional cellular automata finding good random number generators rngs is a hard problem that is of crucial import in several fields ranging from large scale statistical physics simulations to hardware self test in this paper we employ the cellular programming evolutionary algorithm to automatically generate two dimensional cellular automata ca rngs applying an extensive suite of randomness tests to the evolved cas we demonstrate that they rapidly produce high quality random number sequences moreover based on observations of the evolved cas we are able to handcraft even better rngs which not only outperform previously demonstrated high quality rngs but can be potentially tailored to satisfy given hardware constraints

non conventional algorithm for representing and recognizing complicated two dimensional objects abstract a non conventional method for representing and recognizing shape descriptions is described for any shape s a modified cobweb form representation which is referred to as a shell descriptor sd is established for the most significant vertex v the shell descriptor is then used as a registered description for the shape s at vertex v this method is computationally efficient as compared to most of the conventional techniques in shape recognition the new algorithm provides an effective and reliable tool for shape representation and classification especially for complicated objects such as logos

security analysis of the public key algorithm based on chebyshev polynomials over the integer ring zn recently kocarev and tasev 20 proposed to use chebyshev polynomials over real numbers to design a public key algorithm by employing the semigroup property bergamo et al 4 pointed out that the public key algorithm based on chebyshev polynomials working on real numbers is not secure and devised an attack which permits to recover the corresponding plaintext from a given ciphertext later kocarev et al 19 generalized the chebyshev polynomials from real number fields to finite fields and finite rings to make the public key algorithm more secure and practical however we analyzed the period distribution of the sequences generated by the chebyshev polynomials over finite fields 21 when the modulus n is prime we found this algorithm was also not secure and proposed an attack on this algorithm over finite fields we then proposed some schemes to improve the security in this paper we further analyze in detail the period distribution of the sequences generated by chebyshev polynomials over the integer ring z n when n is composite it turns out that the period distribution is poor if n is not chosen properly and there are many small periods which are not secure in the sense of cryptology based on these findings we devise an attack on the public key algorithm based on chebyshev polynomials over the integer ring z n we also propose some suggestions to avoid this attack

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area