on the invertible cellular automata 150 over f p in this work the reversibility problem for cellular automata with rule number 150 over the finite field f p is tackled it is shown that when null boundary conditions are stated the reversibility is independent of the state set f p and it appears when the number of cells of the cellular space satisfies some conditions furthermore the explicit expressions of the inverse cellular automata are computed

decrypting a class of stream ciphers using ciphertext only pseudonoise sequences generated by linear feedback shift registers 1 with some nonlinear combining function have been proposed 2 5 for cryptographic applications as running key generators in stream ciphers in this correspondence it will be shown that the number of trials to break these ciphers can be significantly reduced by using correlation methods by comparison of computer simulations and theoretical results based on a statistical model the validity of this analysis is demonstrated rubin 6 has shown that it is computationally feasible to solve a cipher proposed by pless 2 in a known plaintext attack using as few as 15 characters here the number of ciphertext symbols is determined to perform a ciphertext only attack on the pless cipher using the correlation attack our conclusion from the analysis is that the pseudonoise generator s output sequence and the sequences generated by the linear feedback shift registers should be uncorrelated this leads to constraints for the nonlinear combining function to be used

rigorous application of the stochastic functional method to plane wave scattering from a random cylindrical surface the stochastic functional method is applied to plane wave scattering from a random cylindrical surface whereupon the dirichlet boundary condition is rigorously imposed analytical results accurate to second and fourth order in surface roughness are obtained for the coefficients of the wiener hermite expansion of the secondary scattered wave field the validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion the former which is introduced herein states that any approximate solution should be in conformity with the boundary condition whereas the latter pertains to the energy conservation law the numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration moreover it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion the latter may lead to underestimating deficiencies of the approximate solution under test

group properties of cellular automata and vlsi applications the study of one dimensional cellular automata exhibiting group properties is presented the results show that only a certain class of cellular automata rules exhibit group characteristics based on rule multiplication however many other of these automata reveal groups based on permutations of their global states it is further shown how these groups may be utilized in the design of modulo arithmetic units the communication properties of cellular automata are observed to map favorably to optimal communication graphs for vlsi layouts they exploit the implementation medium and properly address the physical limits on computational structures comparisons of cellular automata based modulo arithmetic units with other vlsi algorithms are presented using area time complexity measures

correlation immunity of nonlinear combining functions for cryptographic applications corresp pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers these running key generators eau sometimes be broken by ciphertext only correlation attacks on individual subsequences a new class of combining functions is presented which provides better security against such attacks the security is quantified by the smallest number m 1 of subsequences that must be simultaneously considered in a correlation attack a necessary condition for such m th order correlation immunity is proved a recursive construction is given that permits the construction of an m th order immune combining function for n subsequences for any m and n with 1 leq m finally the trade off between the length of the linear equivalent of the nonlinear generator and the order m of its immunity against correlation attacks is considered

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

characterisation of a particular hybrid transformation of two dimensional cellular automata abstract nowadays one dimensional 1d cellular automata ca based models and machines were demonstrated for various applications 1 7 2d ca based machines have not yet been used fruitfully mainly due to the lack of analytical insight into the behaviour of the underlying evolutionary process the set of papers 8 11 dealt with the behaviour of the uniform 2d cas in the present paper for the first time an attempt has been made to characterize a particular hybrid linear 2d ca transformation in gf 2 using matrix algebra also we deal with the synthesis problem of this particular hybrid transformation

vector space theoretic analysis of additive cellular automata and its application for pseudoexhaustive test pattern generation a novel scheme for utilizing the regular structure of three neighborhood additive cellular automata cas for pseudoexhaustive test pattern generation is introduced the vector space generated by a ca can be decomposed into several cyclic subspaces a cycle corresponding to an m dimensional cyclic subspace has been shown to pseudoexhaustively test an n input circuit n or m such a cycle is shown to supply a m 1 bit exhaustive pattern including the all zeros m 1 tuple schemes have been reported specifying how one or more subsets of m 1 cell positions of an n cell ca can be identified to generate exhaustive patterns in an m dimensional cyclic subspace

a formula on the wiener hermite expansion two mathematical formulas are given in an explicit form one develops a product of two different multiple wiener integrals in a series of wiener hermite expansions the other one develops a product of two random variables each of which is described by a wiener hermite expansions in a series of another wiener hermite expansion

scattering of a scalar wave from a slightly random surface scalar wave scattering from a slightly random surface is analyzed by a probabilistic method we make use of the homogeneity of an infinite random surface that is the shift invariance property of the strictly homogeneous random field by the group theoretic consideration of such a shift invariance property the wave solution proves to be a homogeneous random field multiplied by an exponential function then such a homogeneous random field is approximately solved for a slightly random surface to yield a wave solution involving multiple scattering several statistical properties of the scattering are calculated and shown in the figures the accuracy of the approximate solution is examined in terms of the error of the boundary value equation

comments on theory and applications of cellular automata in cryptography with reply this paper argues that the cipher systems based on cellular automata ca proposed by s nandi et al 1994 are affine and are insecure a reply by s nandi and p pal chaudhuri is given the reply emphasizes the point that the regular modular cascadable structure of local neighborhood ca can be employed for building low cost cipher system hardware this cost effective engineering solution can achieve desired level of security with larger size ca

scattering of waves from a random spherical surface mie scattering the stochastic theory developed by the authors for the scattering from a random planar surface is extended to the case of a random spherical surface which is assumed to be a homogeneous random field on the sphere homogeneous with respect to spherical rotations based on the group theoretical analogies between the two the formulation of the theory is closely connected to the representation theory of the rotation group the concept of the stochastic spherical harmonics associated with the rotation group and their several formulas are introduced and discussed at the beginning for the plane wave incident on a random spherical surface the scattered random wave field can be expanded systematically in terms of the stochastic spherical harmonics in much the same way as the nonrandom case and several formulas are derived for the coherent scattering amplitude the coherent and incoherent power flows and the coherent and incoherent scattering cross sections the power flow conservation law is cast into the stochastic version of the optical theorem stating that the total scattering cross section consisting of the coherent and incoherent power flow is equal to the imaginary part of the coherent forward scattering amplitude approximate solutions are obtained for the mie scattering with a slightly random spherical surface where the single scattering approximation is valid due to the absence of a real resonance as shown in the previous work on the two dimensional case some numerical calculations are made for the coherent and incoherent scattering cross sections

economic return to the previous state for any nearest neighborhood reversible autonomous finite state machines abstract finite state machines are widely used to model systems in diverse areas viz sequential circuits pattern matching communication protocols d lee m yannakakis proceedings of ieee 84 8 1996 1090 1123 autonomous machines cellular automata or ca belong to a special class of finite state machines where previous output acts as the present input also for variety of applications a k das p p chaudhuri ieee trans comput 42 3 1993 340 352 d r chowdhury s basu i s gupta p p chaudhuri ieee trans comput 43 6 1994 756 764 d r chowdhury i s gupta p p chaudhuri ieee trans comput 43 3 1994 371 382 s nandi b k kar p p chaudhuri ieee trans comput 43 12 1994 1346 1357 n h packard s wolfram j statist phys 38 5 6 1985 901 946 d r chowdhury i s gupta p p chaudhuri j electron testing theory appl 5 1994 65 80 d r chowdhury phd thesis i i t kharagpur india 1992 we consider two valued n cell 1 dimensional nearest neighbourhood ca transformations where cycle length could be of the order of 2 n for such machines it is often useful to get back to the just previous state or configuration from the current one so if n is of the order of 100 which is quite likely in a ca machine doing the worst possible forward journey will take quite appreciable time of the order of 2 100 in our work we have settled that in much lesser time we can get back to the previous state

on the semantic security of cellular automata based pseudo random permutation using results from the luby rackoff construction this paper proposes a semantically secure construction of pseudo random permutations using second order reversible cellular automata we show that the proposed construction is equivalent to the luby rackoff model if it is built using non uniform transition rules and we prove that the construction is strongly secure if an adequate number of iterations is performed moreover a corresponding symmetric block cipher is constructed and analysed experimentally in comparison with popular ciphers obtained results approve robustness and efficacy of the construction while achieved performances overcome those of some existing block ciphers

a multisecret sharing scheme for color images based on cellular automata in this work a new multisecret sharing scheme for secret color images among a set of users is proposed the protocol allows that each participant in the scheme to share a secret color image with the rest of participants in such a way that all of them can recover all the secret color images only if the whole set of participants pools their shadows the proposed scheme is based on the use of bidimensional reversible cellular automata with memory the security of the scheme is studied and it is proved that the protocol is ideal and perfect and that it resists the most important statistical attacks

fast inverse qr factorization for toeplitz matrices fast orthogonalization schemes for m times n toeplitz matrices t introduced by bojanczyk brent and de hoog bbh and chun kailath and lev ari ckl are extended to compute directly an inverse qr factorization of t using only o mn operations an inverse factorization allows for an efficient parallel implementation and the algorithm is computationally less expensive for computing a solution to the toeplitz least squares problem than previously studied inverse qr methods in addition it is shown that regularization can be incorporated into the algorithm with virtually no extra work thus it is possible to compute regularized solutions to ill conditioned toeplitz least squares problems using only o mn operations an application to ill conditioned problems occurring in signal restoration is provided illustrating the effectiveness of this method

schur type methods for solving least squares problems with toeplitz structure we give an overview of fast algorithms for solving least squares problems with toeplitz structure based on generalization of the classical schur algorithm and discuss their stability properties in order to obtain more accurate triangular factors of a toeplitz matrix as well as accurate solutions for the least squares problems methods based on corrected seminormal equations csne can be used we show that the applicability of the generalized schur algorithm is considerably enhanced when the algorithm is used in conjunction with csne several numerical tests are reported where different variants of the generalized schur algorithm and csne are compared for their accuracy and speed

wiener analysis of a binary hysteresis system nonlinear transformation of an independent gaussian sequence by a binary hysteresis is studied by wiener s method nonlinear problems in random theory mit cambrige ma 1958 the output sequence of the hysteresis is represented by a series of wiener hermite functionals which are random and orthogonal uncorrelated to each other from the hysteresis equation a set of linear equations for the wiener hermite functionals is derived without approximation the equations directly show that the hysteresis is decomposed into equivalent subsystems consisting of static nonlinear elements multipliers adders and linear filters they are solved by use of random numbers generated in a computer in order to get a sample output sequence approximated by a finite sum of the wiener hermite functionals another set of equations is derived for the mean square values of the wiener hermite functionals in terms of its numerical solutions the convergence property of the wiener hermite functional series is discussed

analysis of periodic and intermediate boundary 90 150 cellular automata considerable interest has been recently generated in the study of cellular automata ca behavior polynomial and matrix algebraic tools are employed to characterize some of the properties of null periodic boundary ca some other results of group ca behavior have been reported based on simulation studies this paper reports a formal proof for the conjecture there exists no primitive characteristic polynomial of 90 150 ca with periodic boundary condition for generation of high quality pseudorandom patterns it is necessary to employ ca having primitive characteristic polynomial there exist two null boundary ca for every primitive polynomial however for such cs the quality of pseudorandomness suffers in general particularly in the regions around the terminal cells because of null boundary condition in this background a new concept of intermediate boundary ca has been proposed to generate pseudorandom patterns that are better in quality than those generated with null boundary ca some interesting properties of intermediate boundary ca are also reported

analysis of complemented ca derived from a linear tpmaca abstract by using basic paths in the 0 tree of a linear tpmaca c we obtain the state transition diagram of complemented ca c derived from c such that the complement vector is a nonzero attractor of c also we analyze the behavior of c

cryptanalysis of a partially known cellular automata cryptosystem cellular automata provide simple discrete deterministic mathematical models for physical biological and computational systems despite their simple construction cellular automata are shown to be capable of complicated behavior and to generate complex and random patterns there have been constant efforts to exploit cellular automata for cryptography since the very beginning of the research on cellular automata unfortunately most of the previous cryptosystems based on cellular automata are either insecure or inefficient in icics 0 2 sen et al made a new effort in cellular automata cryptosystems cacs design where the affine cellular automata are combined with nonaffine transformations it is claimed that the weakness in some of the previous cacs due to the affine property is removed in this paper we show that the new cac is still insecure it can be broken by a chosen plaintext attack the attack is very efficient requiring only hundreds of chosen plaintexts and a small computation amount we also consider the possibility of modifying the new cac our results show however that it is not easy to secure the scheme by minor modifications

text compression using two dimensional cellular automata abstract this paper presents an elegant mathematical model using simple matrix algebra for characterising the behaviour of two dimensional nearest neighbourhood linear cellular automata with periodic boundary conditions based on this mathematical model the vlsi architecture of a cellular automata machine cam has been proposed for text compression experimental results of comparisons with adaptive huffman coding scheme also presented

vlsi architecture of a cellular automata machine abstract in the past cellular automata based models and machines 1 have been proposed for simulation of physical systems without any analytical insight into the behaviour of the underlying simulation machine this paper makes a significant departure from this traditional approach an elegant mathematical model using simple matrix algebra is reported in this paper for characterizing the behaviour of two dimensional nearest neighbourhood linear cellular automata with null and periodic boundary conditions based on this mathematical model a vlsi architecture of a cellular automata machine cam has been proposed interesting applications of cam in the fields of image analysis and fractal image generation are also reported

on the combination of self organized systems to generate pseudo random numbers cellular automata ca is a self organizing structure with complex behavior which can be used to generating pseudo random numbers pure ca has a simple structure and has no ability to produce long sequences of random numbers but in order to resolve this problem a programmable controllable ca pcca using actuating factor or combination of different self organizing criticality phenomena can be used the purpose of the aforementioned methods is the use of the ca speed while preventing the automata self organizing factor for specific use in generating random numbers in this paper a pcca by using sandpile model is proposed the sandpile model is a complex system that operates at a critical state between chaos and order this state is known as self organized criticality soc and is characterized by displaying invariant scale behavior in the precise case of the sandpile model by randomly and continuously dropping sand grains on top of a two dimensional grid lattice a power law relationship between the frequency and size of sand avalanches is observed the avalanche behavior and the pure ca behavior are combined in a novel method which can be used as the pseudo random number generator prng experimental results show that this generator is able to reach a random behavior from a pseudo chaotic one by combining two self organized systems in addition to independency of the initial state it has been also indicated that the generated numbers are independent and its probability distribution is likely to be uniform accordingly some tests of prngs such as entropy chi square diehard and several basic statistical tests have been performed and all of them have been successfully passed

theory and applications of cellular automata in cryptography this paper deals with the theory and application of cellular automata ca for a class of block ciphers and stream ciphers based on ca state transitions certain fundamental transformations are defined which are block ciphering functions of the proposed enciphering scheme these fundamental transformations are found to generate the simple alternating group of even permutations which in turn is a subgroup of the permutation group these functions are implemented with a class of programmable cellular automata pca built around rules 51 153 and 195 further high quality pseudorandom pattern generators built around rule 90 and 150 programmable cellular automata with a rule selector i e combining function has been proposed as running key generators in stream ciphers both the schemes provide better security against different types of attacks with a simple regular modular and cascadable structure of ca hardware implementation of such schemes idealy suit vlsi implementation

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

stability analysis and fast algorithms for triangularization of toeplitz matrices a new o mn algorithm for triangularizing an m times n toeplitz matrix is presented the algorithm is based on the previously developed recursive algorithms that exploit the toeplitz structure and compute each row of the triangular factor via updating and downdating steps a forward error analysis for this existing recursive algorithm is presented which allows us to monitor the conditioning of the problem and use the method of corrected semi normal equations to obtain higher accuracy for certain ill conditioned matrices numerical experiments show that the new algorithm improves the accuracy significantly while the computational complexity stays in o mn

hybrid algorithm for fast toeplitz orthogonalization new techniques for fast toeplitz qr decomposition are presented the methods are based on the shift invariance property of a toeplitz matrix the numerical properties of the algorithms are discussed and some comparisons are made with two other fast toeplitz orthogonalization methods

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

analysis of complemented ca derived from linear hybrid group ca in this paper we analyze complemented group cellular automata ca derived from linear hybrid group ca with rules 60 102 and 204 we analyze some properties of the ca and we give rule vectors which determine the state transition of the ca dividing the entire state space into smaller spaces of equal lengths and find conditions for the complement vectors corresponding to the rule vectors and we extend and generalize mukhopadhyay s results d mukhopadhyay d r chowdhury characterization of a class of complemented group cellular automata in proc acri 2004 in lncs vol 3305 2004 pp 775 784