constructing symmetric boolean functions with maximum algebraic immunity symmetric boolean functions with even variables 2k and maximum algebraic immunity ai f k have been constructed in braeken s thesis 2006 in this paper we show more constructions of such boolean functions including the generalization of a result and prove a conjecture raised in braeken s thesis 2006

support vector machines for 3d object recognition support vector machines svms have been recently proposed as a new technique for pattern recognition intuitively given a set of points which belong to either of two classes a linear svm finds the hyperplane leaving the largest possible fraction of points of the same class on the same side while maximizing the distance of either class from the hyperplane the hyperplane is determined by a subset of the points of the two classes named support vectors and has a number of interesting theoretical properties in this paper we use linear svms for 3d object recognition we illustrate the potential of svms on a database of 7200 images of 100 different objects the proposed system does not require feature extraction and performs recognition on images regarded as points of a space of high dimension without estimating pose the excellent recognition rates achieved in all the performed experiments indicate that svms are well suited for aspect based recognition

local autocorrelation of similarities with subspaces for shift invariant scene classification this paper presents a shift invariant scene classification method based on local autocorrelation of similarities with subspaces although conventional scene classification methods used bag of visual words for scene classification superior accuracy of kernel principal component analysis kpca of visual words to bag of visual words was reported here we also use kpca of visual words to extract rich information for classification in the original kpca of visual words all local parts mapped into subspace were integrated by summation to be robust to the order the number and the shift of local parts this approach discarded the effective properties for scene classification such as the relation with neighboring regions to use them we use normalized local autocorrelation lac feature of the similarities with subspaces outputs of kpca of visual words the feature has both the relation with neighboring regions and the robustness to shift of objects in scenes the proposed method is compared with conventional scene classification methods using the same database and protocol and we demonstrate the effectiveness of the proposed method

weighted kpca degree of homogeneity amended nonclassical receptive field inhibition model for salient contour extraction in low light level image the stimulus response of the classical receptive field crf of neuron in primary visual cortex is affected by its periphery i e non crf ncrf this modulation exerts inhibition which depends primarily on the correlation of both visual stimulations the theory of periphery and center interaction with visual characteristics can be applied in night vision information processing in this paper a weighted kernel principal component analysis wkpca degree of homogeneity dh amended inhibition model inspired by visual perceptual mechanisms is proposed to extract salient contour from complex natural scene in low light level image the core idea is that multifeature analysis can recognize the homogeneity in modulation coverage effectively computationally a novel wkpca algorithm is presented to eliminate outliers and anomalous distribution in crf and accomplish principal component analysis precisely on this basis a new concept and computational procedure for dh is defined to evaluate the dissimilarity between periphery and center comprehensively through amending the inhibition from ncrf to crf by dh our model can reduce the interference of noises suppress details and textures in homogeneous regions accurately it helps to further avoid mutual suppression among inhomogeneous regions and contour elements this paper provides an improved computational visual model with high performance for contour detection from cluttered natural scene in night vision image

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

multilinear supervised neighborhood embedding of a local descriptor tensor for scene object recognition in this paper we propose to represent an image as a local descriptor tensor and use a multilinear supervised neighborhood embedding msne for discriminant feature extraction which is able to be used for subject or scene recognition the contributions of this paper include 1 a novel feature extraction approach denoted as the histogram of orientation weighted with a normalized gradient nhog for local region representation which is robust to large illumination variation in an image 2 an image representation framework denoted as the local descriptor tensor which can effectively combine a moderate amount of local features together for image representation and be more efficient than the popular existing bag of feature model and 3 an msne analysis algorithm which can directly deal with the local descriptor tensor for extracting discriminant and compact features and at the same time preserve neighborhood structure in tensor feature space for subject scene recognition we demonstrate the performance advantages of our proposed approach over existing techniques on different types of benchmark database such as a scene data set i e ot8 face data sets i e yale and pie and view based object data sets coil 100 and eth 80

local co occurrence features in subspace obtained by kpca of local blob visual words for scene classification this paper presents a scene classification method based on local co occurrence in a kpca space of local blob words scene classification based on local correlation of binarized projection lengths in subspaces obtained by kernel principal component analysis kpca of visual words has been recently proposed and its effectiveness has been demonstrated however the local correlation of two binary features 0 or 1 becomes 1 only when both features take a value of 1 the local correlation becomes 0 in all other cases 0 1 1 0 and 0 0 which might lead to the loss of useful information for effective classification in this study all combinations of co occurrence of binary features are used instead of local correlation we conducted the experiments using a database containing 13 scene categories and found that the proposed method using local co occurrence features achieves an accuracy of more than 84 which is higher than the accuracy of conventional methods based on local correlation features

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

constructions of balanced odd variable rotation symmetric boolean functions with optimal algebraic immunity and high nonlinearity abstract rotation symmetric boolean functions have been used as components of different cryptosystems in this paper two classes of balanced rotation symmetric boolean functions having optimal algebraic immunity on odd number of variables are constructed we give a lower bound on the algebraic degree of the first class of functions and prove that the n variable functions in the second class has optimal algebraic degree if n 2 m 1 for m 2 moreover it is shown that both classes of functions have much better nonlinearity than all the previously obtained rotation symmetric boolean functions with optimal algebraic immunity and have good behavior against fast algebraic attacks at least for small numbers of input variables

geometrical properties of nonlinear maps and their application part i the topological degree of quasiruled fredholm maps on quasicylindrical domains abstract in this paper we introduce the notion of quasicylindrical domains in banach spaces and develop a concept of a degree for quasiruled fredholm mappings on quasicylindrical domains note that this quasicylindrical structure appears in a rather natural way whenever analytically given nonlinear pseudodifferential operators are investigated in spaces of sufficiently smooth functions moreover the class of quasiruled fredholm mappings on quasicylindrical domains is sufficiently large so that within this framework one can study a quite large class of nonlinear boundary value problems which are related to pseudodifferential operators

the lower bounds on the second order nonlinearity of three classes of boolean functions with high nonlinearity the rth order nonlinearity of boolean functions is an important cryptographic criterion associated with some attacks on stream and block ciphers it is also very useful in coding theory since it is related to the covering radii of reed muller codes this paper tightens the lower bounds of the second order nonlinearity of three classes of boolean functions in the form f x tr x d in n variables where 1 d 2 m 1 3 and n 2m or 2 d 2 m 2 m 1 2 1 n 2m and m is odd or 3 d 2 2 r 2 r 1 1 and n 4r

nonlinear riemann hilbert problems with lipschitz continuous boundary data doubly connected domains here we investigate nonlinear riemann hilbert problems for hyperbolic functions w z u z i v z in a given doubly connected domain g 2 where the nonlinear boundary data i e the family of curves are implicitly given by f u v 0 for g 2 in the w plane with a lipshitz continuous function f and these curves for every are non closed but going to infinity in order to prove the solvability of the nonlinear problem we first reduce the problem to a system of nonlinear cauchysingular integral equations on the boundary g 2 employing the topological degree of quasilinear fredholm mappings together with approximation arguments montel theorem we prove the existence of at least one solution

construction of highly nonlinear 1 resilient boolean functions with optimal algebraic immunity and provably high fast algebraic immunity in 2013 tang carlet and tang ieee tit 59 1 653 664 2013 presented two classes of boolean functions the functions in the first class are unbalanced and the functions in the second one are balanced both of those two classes of functions have high nonlinearity high algebraic degree optimal algebraic immunity and high fast algebraic immunity however they are not 1 resilient which represents a drawback for their use as filter functions in stream ciphers in this paper we first propose a large family of 1 resilient boolean functions having high lower bound on nonlinearity optimal algebraic immunity and optimal algebraic degree that is meeting the siegenthaler bound most notably we can mathematically prove that every function in n variables belonging to this family has fast algebraic immunity no less than n 6 which is the first time that an infinite family of 1 resilient functions with provably high fast algebraic immunity has been invented furthermore we exhibit a subclass of the family which has higher lower bound on nonlinearity than all the known 1 resilient functions with potentially optimal algebraic immunity and potentially high fast algebraic immunity

support vector method for robust arma system identification this paper presents a new approach to auto regressive and moving average arma modeling based on the support vector method svm for identification applications a statistical analysis of the characteristics of the proposed method is carried out an analytical relationship between residuals and svm arma coefficients allows the linking of the fundamentals of svm with several classical system identification methods additionally the effect of outliers can be cancelled application examples show the performance of svm arma algorithm when it is compared with other system identification methods

on boundary layer type solutions of nonlinear riemann hilbert problems and related geometric structures we consider a class of holomorphic solutions to nonlinear riemannhilbert problems rhpp for arbitrary pconnected domains the boundary condition bundle here violates the socalled zero conditions

universal analytical forms for modeling image probabilities seeking probability models for images we employ a spectral approach where the images are decomposed using bandpass filters and probability models are imposed on the filter outputs also called spectral components we employ a two parameter family of probability densities called bessel k forms for modeling the marginal densities of the spectral components and demonstrate their fit to the observed histograms for video infrared and range images motivated by object based models for image analysis a relationship between the bessel parameters and the imaged objects is established using l sup 2 metric on the set of bessel k forms we propose a pseudometric on the image space for quantifying image similarities differences some applications including clutter classification and pruning of hypotheses for target recognition are presented

two classes of symmetric boolean functions with optimum algebraic immunity construction and analysis this paper discusses two classes of symmetric boolean functions for each class a necessary and sufficient condition for having optimum algebraic immunity is proposed the algebraic degree and nonlinearity of the boolean functions are also completely determined and then we prove several of braeken s conjectures about the algebraic degree and nonlinearity of the boolean functions with optimum algebraic immunity in the two classes

recursive lower bounds on the nonlinearity profile of boolean functions and their applications the nonlinearity profile of a boolean function i e the sequence of its minimum hamming distances nlr f to all functions of degrees at most r for r ges 1 is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers it plays also a role in coding theory since it is related to the covering radii of reed muller codes we introduce a method for lower bounding its values and we deduce bounds on the second order nonlinearity for several classes of cryptographic boolean functions including the welch and the multiplicative inverse functions used in the s boxes of the advanced encryption standard aes in the case of this last infinite class of functions we are able to bound the whole profile and we do it in an efficient way when the number of variables is not too small this allows showing the good behavior of this function with respect to this criterion as well

hybrid classes of balanced boolean functions with good cryptographic properties abstract cryptographically strong boolean functions play an imperative role in the design of almost every modern symmetric cipher in this context the cryptographic properties of boolean functions such as non linearity algebraic degree correlation immunity and propagation criteria are critically considered in the process of designing these ciphers more recently with the emergence of algebraic and fast algebraic attacks algebraic immunity has also been included as an integral property to be considered as a result several constructions of boolean functions with high non linearity maximal algebraic degree and optimal algebraic immunity have been devised since then this paper focuses on some of these constructions and presents two hybrid classes of boolean functions the functions constructed within these classes possess maximal algebraic degree for balanced functions optimal algebraic immunity high non linearity and good resistance to algebraic and fast algebraic attacks a hybrid class of 1 resilient functions has also been proposed that also possesses high algebraic degree optimal algebraic immunity high non linearity and good resistance to algebraic and fast algebraic attacks

on the construction of cryptographically significant boolean functions using objects in projective geometry spaces recently several construction methods of highly nonlinear boolean functions with relatively good algebraic properties were proposed these approaches manage in optimizing most of the relevant cryptographic criteria but not all of them at the same time usually either the nonlinearity bounds are rather loose though the actual nonlinearity is relatively high or the functions do not provide a good resistance to fast algebraic cryptanalysis in this paper we develop a theoretical framework for using objects in suitable projective geometry spaces for construction of highly nonlinear boolean functions this allows us to establish tight bounds on the nonlinearity using simple counting arguments thus avoiding rather complicated estimates of certain trace sums our method generates a class of almost fully optimized functions that is the functions apart from very high nonlinearity also have the maximum algebraic degree and optimal algebraic immunity compared to the classes of functions proposed by carlet and feng wang and zeng our functions achieve a slightly better nonlinearity which is traded off against a little worse resistance against fast algebraic attacks on the other hand compared to the functions by tang and tu and deng our nonlinearity is somewhat lower but the algebraic properties are slightly better

best affine and quadratic approximations of particular classes of boolean functions in this paper we consider the problem of computing best low order approximations of boolean functions we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation our methodology is developed upon properties of the best affine approximations of quadratic functions for which formulas for their direct computation not by means of the walsh hadamard transform are given we determine the cubic functions in the above subclass that achieve the maximum second order nonlinearity thus yielding a lower bound for the covering radius of the second order reed muller code ssr rm 2 n in ssr rm 3 n simple extensions of these results to some special cases of higher degree functions are seen to hold furthermore a preliminary analysis of well known constructions for bent functions in terms of their second order nonlinearity is performed that indicates potential weaknesses if construction parameters are not properly chosen

spatial multi scale gradient orientation consistency for place instance and scene category recognition gradient orientation consistency goc was proposed to encode local structure of images the goc feature is more robust to illumination variances the spatial multi scale goc histogram could achieve competitive performance for both place instance and scene category recognition this paper presents a novel image feature called gradient orientation consistency goc and an image representation based on the spatial multi scale goc histogram for place instance and scene category recognition gradient orientations have proven to be a more robust descriptor of the image information than intensities in the presence of illumination variances the goc feature is obtained by imposing a local binary pattern lbp type of non parametric operator to the gradient orientation codes hence captures the local structures in an image the histogram of goc further encodes the global structure of the entire image the multi scale analysis and spatial pyramid techniques are also used to enrich the longer range structure information resulting in a comprehensive image representation we apply this representation method for place instance and scene category recognition on five different datasets and show that it outperforms the state of the art

an efficient discriminant based solution for small sample size problem classification of high dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size problem to address the problem of high dimensional data classification in the face of a limited number of samples a novel principal component analysis pca based feature extraction classification scheme is proposed the proposed method yields a piecewise linear feature subspace and is particularly well suited to difficult recognition problems where achievable classification rates are intrinsically low such problems are often encountered in cases where classes are highly overlapped or in cases where a prominent curvature in data renders a projection onto a single linear subspace inadequate the proposed feature extraction classification method uses class dependent pca in conjunction with linear discriminant feature extraction and performs well on a variety of real world datasets ranging from digit recognition to classification of high dimensional bioinformatics and brain imaging data

on the construction of boolean functions with optimal algebraic immunity in this correspondence we introduce a method to construct boolean functions in any number of variables with optimal algebraic immunity remarkably all functions of this type with an odd number of variables can be obtained in this way we study some cryptographic properties such as balancedness algebraic degree of the constructed functions moreover a lower bound of the number of boolean functions with optimal algebraic immunity is given

constructions of cryptographically significant boolean functions using primitive polynomials it is known that boolean functions used in stream and block ciphers should have good cryptographic properties to resist algebraic attacks up until now there have been several constructions of boolean functions achieving optimum algebraic immunity however most of their nonlinearities are very low carlet and feng studied a class of boolean functions with optimum algebraic immunity and deduced the lower bound of its nonlinearity which is good but not very high moreover the main practical problem with this construction is that it cannot be implemented efficiently in this paper we put forward a new method to construct cryptographically significant boolean functions by using primitive polynomials and construct three infinite classes of boolean functions with good cryptographic properties balancedness optimum algebraic degree optimum algebraic immunity and a high nonlinearity

wavelet domain multifractal analysis for static and dynamic texture classification in this paper we propose a new texture descriptor for both static and dynamic textures the new descriptor is built on the wavelet based spatial frequency analysis of two complementary wavelet pyramids standard multiscale and wavelet leader these wavelet pyramids essentially capture the local texture responses in multiple high pass channels in a multiscale and multiorientation fashion in which there exists a strong power law relationship for natural images such a power law relationship is characterized by the so called multifractal analysis in addition two more techniques scale normalization and multiorientation image averaging are introduced to further improve the robustness of the proposed descriptor combining these techniques the proposed descriptor enjoys both high discriminative power and robustness against many environmental changes we apply the descriptor for classifying both static and dynamic textures our method has demonstrated excellent performance in comparison with the state of the art approaches in several public benchmark datasets

efficient face detection by a cascaded support vector machine expansion we describe a fast system for the detection and localization of human faces in images using a nonlinear supportvector machine we approximate the decision surface in terms of a reduced set of expan

local fractal and multifractal features for volumic texture characterization for texture analysis several features such as co occurrence matrices gabor filters and the wavelet transform are used recently fractal geometry appeared to be an effective feature to analyze texture but it is often restricted to 2d images while 3d information can be very important especially in medical image processing moreover applications are limited to the use of fractal dimension this study focuses on the benefits of fractal geometry in a classification method based on volumic texture analysis the proposed methods make use of fractal and multifractal features for a 3d texture analysis of a voxel neighborhood they are validated with synthetic data before being applied on real images their efficiencies are proved by comparison to some other texture features in supervised classification processes adaboost and support vector machine classifiers the results showed that features based on fractal geometry by combining fractal and multifractal features contributed to new texture characterization information on new features was useful and complementary for a classification method this study suggests that fractal geometry can provide a new useful information in 3d texture analysis especially in medical imaging

on symmetric boolean functions with high algebraic immunity on even number of variables in this paper we put forward an efficient method to study the symmetric boolean functions with high algebraic immunity on even number of variables we obtain some powerful necessary conditions for symmetric boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of boolean functions of low degrees with these results we prove that the algebraic immunity of a large class of symmetric correlation immune boolean functions namely the symmetric palindromic functions is not high besides we construct all symmetric boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity we also determine the hamming weight degrees and nonlinearity of the symmetric boolean functions with maximum algebraic immunity

reed muller codes achieve capacity on erasure channels we introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding rather than relying on the precise structure of the codes our method exploits code symmetry in particular the technique applies to any sequence of linear codes where the blocklengths are strictly increasing the code rates converge and the permutation group of each code is doubly transitive in other words we show that symmetry alone implies near optimal performance an important consequence of this result is that a sequence of reed muller codes with increasing blocklength and converging rate achieves capacity this possibility has been suggested previously in the literature but it has only been proven for cases where the limiting code rate is 0 or 1 moreover these results extend naturally to all affine invariant codes and thus to extended primitive narrow sense bch codes this also resolves in the affirmative the existence question for capacity achieving sequences of binary cyclic codes the primary tools used in the proof are the sharp threshold property for symmetric monotone boolean functions and the area theorem for extrinsic information transfer functions

support vector machine for breast mr image classification mr images have been used extensively in clinical trials in recent years because they are harmless to the human body and can obtain detailed information by scanning the same slice with various frequencies and parameters in this paper we want to detect the breast tissues within multi spectral mr images in the image classification we apply a support vector machine svm to breast multi spectral magnetic resonance images to classify the tissues of the breast in order to verify the feasibility and efficiency of this method evaluations using classification rate and likelihood ratios are adopted based on manifold assessment and a series of experiments are conducted and compared with the commonly used c means cm for performance evaluation the results show that the svm method is a promising and effective spectral technique for mr image classification

a note on symmetric boolean functions with maximum algebraic immunity in odd number of variables in this note it is proved that for each odd positive integer n there are exactly two n variable symmetric boolean functions with maximum algebraic immunity

cost constraint based multiple kernel least squares support vector machine and its application considering the neglect of kernel function cost and lack of sparsity of multiple kernel least squares support vector machine mk lssvm a cost constraint based multiple kernel least squares vector machine with sparsity is pro posed the primal optimal problem of mk lssvm is converted into second order cone programming and then the weight of complex kernel function is restricted by introducing cost factors so as to save storage space and computing time of variable quantity furthermore the kernel matrices are reduced by schmidt orthogonalization theory to lower computational com plexity the total cost of multiple kernel learning can be evaluated according to the number of support vectors and active kernel functions the simulation results on testing datasets show that the proposed method can achieve the same accuracy as mk lssvm by using less support vectors and simpler mixture kernel functions with cheaper consumption and better real time performance the cost vaule of froth flotation mineral recovery prediction used the proposed method reduces 27 56

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

more balanced boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks in this paper three constructions of balanced boolean functions with optimal algebraic immunity are proposed it is checked that at least for small numbers of input variables these functions have good behavior against fast algebraic attacks as well other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed lower bounds on the nonlinearity are proved which are similar to the best bounds obtained for known boolean functions resisting algebraic attacks and fast algebraic attacks moreover it is checked that for the number n of variables with 5 n 19 the proposed n variable boolean functions have in fact very good nonlinearity

local normalized linear summation kernel for fast and robust recognition kernel based methods are effective for object detection and recognition however the computational cost when using kernel functions is high except when using linear kernels to realize fast and robust recognition we apply normalized linear kernels to local regions of a recognition target and the kernel outputs are integrated by summation this kernel is referred to as a local normalized linear summation kernel here we show that kernel based methods that employ local normalized linear summation kernels can be computed by a linear kernel of local normalized features thus the computational cost of the kernel is nearly the same as that of a linear kernel and much lower than that of radial basis function rbf and polynomial kernels the effectiveness of the proposed method is evaluated in face detection and recognition problems and we confirm that our kernel provides higher accuracy with lower computational cost than rbf and polynomial kernels in addition our kernel is also robust to partial occlusion and shadows on faces since it is based on the summation of local kernels

on the resistance of boolean functions against algebraic attacks using univariate polynomial representation in the past few years algebraic attacks against stream ciphers with linear feedback function have been significantly improved as a response to the new attacks the notion of algebraic immunity of a boolean function f was introduced defined as the minimum degree of the annihilators of f and f 1 an annihilator of f is a nonzero boolean function g such that f g 0 while several constructions of boolean functions with optimal algebraic immunity have been proposed there is no significant progress concerning the resistance against the so called fast algebraic attacks in this paper we provide a framework to assess the resistance of boolean functions against the new algebraic attacks including fast algebraic attacks the analysis is based on the univariate polynomial representation of boolean functions and necessary and sufficient conditions are presented for a boolean function to have optimal behavior against all the new algebraic attacks finally we introduce a new infinite family of balanced boolean functions described by their univariate polynomial representation by applying the new framework we prove that all the members of the family have optimal algebraic immunity and we efficiently evaluate their behavior against fast algebraic attacks

improving the lower bound on the higher order nonlinearity of boolean functions with prescribed algebraic immunity the recent algebraic attacks have received a lot of attention in cryptographic literature the algebraic immunity of a boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function very few results have been found concerning its relation with the other cryptographic parameters or with the rth order nonlinearity as recalled by carlet at crypto 06 many papers have illustrated the importance of the r th order nonlinearity profile which includes the first order nonlinearity the role of this parameter relatively to the currently known attacks has been also shown for block ciphers recently two lower bounds involving the algebraic immunity on the rth order nonlinearity have been shown by carlet none of them improves upon the other one in all situations in this paper we prove a new lower bound on the rth order nonlinearity profile of boolean functions given their algebraic immunity that improves significantly upon one of these lower bounds for all orders and upon the other one for low orders

geometrical properties of nonlinear maps and their application part ii nonlinear riemann hilbert problems with closed boundary data for multiply connected domains abstract we use the degree of quasiruled fredholm maps on quasicylindrical domains developed in part i to prove the existence of at least two homotopically different solutions of classical nonlinear riemann hilbert problems for multiply connected domains

a new upper bound on the block error probability after decoding over the erasure channel motivated by cryptographic applications we derive a new upper bound on the block error probability after decoding over the erasure channel the bound works for all linear codes and is in terms of the generalized hamming weights it turns out to be quite useful for reed muller codes for which all the generalized hamming weights are known whereas the full weight distribution is only partially known for these codes the error probability is related to the cryptographic notion of algebraic immunity we use our bound to show that the algebraic immunity of a random balanced m variable boolean function is of order m 2 1 o 1 with probability tending to 1 as m goes to infinity

highly nonlinear boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks inspired by the previous work of tu and deng we propose two infinite classes of boolean functions of 2k variables where k 2 the first class contains unbalanced functions having high algebraic degree and nonlinearity the functions in the second one are balanced and have maximal algebraic degree and high nonlinearity as shown by a lower bound that we prove as a byproduct we also prove a better lower bound on the nonlinearity of the carlet feng function thanks to a combinatorial fact first conjectured by the authors and later proved by cohen and flori we are able to show that they both possess optimal algebraic immunity it is also checked that at least for numbers of variables n 16 functions in both classes have a good behavior against fast algebraic attacks compared with the known boolean functions resisting algebraic attacks and fast algebraic attacks both of them possess the highest lower bounds on nonlinearity these bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack nevertheless as for previously found functions with the same features there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables n 38 moreover these values are very good the infinite class of functions we propose in construction 2 presents among all currently known constructions the best provable tradeoff between all the important cryptographic criteria

improving the upper bounds on the covering radii of binary reed muller codes by deriving bounds on character sums of boolean functions and by using the characterizations due to kasami of those elements of the reed muller codes whose hamming weights are smaller than twice and a half the minimum distance we derive an improved upper bound on the covering radius of the reed muller code of order 2 and we deduce improved upper bounds on the covering radii of the reed muller codes of higher orders

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input

fuzzy kernel perceptron a new learning method the fuzzy kernel perceptron fkp in which the fuzzy perceptron fp and the mercer kernels are incorporated is proposed in this paper the proposed method first maps the input data into a high dimensional feature space using some implicit mapping functions then the fp is adopted to find a linear separating hyperplane in the high dimensional feature space compared with the fp the fkp is more suitable for solving the linearly nonseparable problems in addition it is also more efficient than the kernel perceptron kp experimental results show that the fkp has better classification performance than fp kp and the support vector machine

counting boolean functions with specified values in their walsh spectrum the problem of counting boolean functions with specified number s of walsh coefficients w in their walsh spectrum is discussed in this paper strategies to solve this problem shall help solving many more problems related to desired cryptographic features of boolean functions such as nonlinearity resiliency algebraic immunity etc in an attempt to study this problem we present a new framework of solutions we give results for w 2 n 1 and for all s in line with a previous work of wu 1998 12 we also provide various results such as existence and construction for some s when w 0 multiplicities for all w and naive bounds on s for w 2 n 2