certificateless threshold ring signature we propose a t out of n certificateless threshold ring signature cl trs scheme and prove its security under a new and stronger set of security models the models capture a new adversarial capability called user partial key replacement attack which has been considered practical and realistic but has never been formalized before the new scheme requires only a constant number of bilinear pairing operations for signature verification it also has a compact signature size which is linear to the number of non signers i e n t rather than that of actual signers we also propose a 1 out of n cl trs i e a certificateless ring signature scheme which has the most efficient verification among all the certificateless ring signature schemes currently known

cca secure encryption supporting authorized equality test on ciphertexts in standard model and its applications abstract we present an encryption scheme for authorized equality test on ciphertexts seet which allows the data owner to authorize a tester to compare her ciphertexts without decrypting their values the security of seet is formally proved against three types of adversary two of them for ciphertext confidentiality in the phases before and after authorization respectively and the third for token privacy to the best of our knowledge our seet construction is the first encryption scheme supporting equality test on ciphertexts that is proven secure against the three types of adversary in the standard model our seet construction outperforms existing schemes in terms of ciphertext size and encryption decryption testing costs to show its application in set operations we extend it into schemes for controlled set distance computation such that a curious server is able to deduce the similarity dissimilarity score between two encrypted user sets without knowing their elements

upper and lower bounds of the misadjustment in the lms algorithm the misadjustment is a dimensionless measure of the difference between the optimal weiner performance and the actual performance of the lms least mean squares algorithm this difference is attributed to the gradient noise in the adaptive process present estimates relate the misadjustment to the convergence gain and the trace of the autocorrelation matrix the authors establish tighter lower bounds on the estimate of this misadjustment an upper bound on the misadjustment as a function of the convergence gain is found

performance advantage of complex lms for controlling narrow band adaptive arrays in narrow band adaptive array applications the mean square convergence of the discrete time real least mean square lms algorithm is slowed by image frequency noises generated in the lms loops the complex lms algorithm proposed by widrow et al is shown to eliminate these noises yielding convergence of the mean squared error mse at slightly over twice the rate this paper includes a comprehensive analysis of the mse of adaptation for lms the analysis is based upon the method developed in the 1968 dissertation by k d senne and it represents the most complete treatment of the subject published to date

on the optimum gain parameter in lms adaptation in this correspondence the optimum selection of the adaptation parameter in lms adaptive estimation is discussed for a white data covarianee matrix it is shown via analysis and numerical evaluation that the optimum selection of is a complicated function of the number of filter taps the initial weight setting the wiener weights and the number of learning samples is not chosen in general to yield the most rapid transient response for most cases of interest a smaller value of will be selected for slower adaptation and smaller misadjustment error at the end of the learning phase

stochastic modeling of the transform domain varepsilon rm lms algorithm this paper presents a statistical analysis of the transform domain least mean square tdlms algorithm resulting in a more accurate model than those discussed in the current open literature the motivation to analyze such an algorithm comes from the fact that the tdlms presents a higher convergence speed for correlated input signals as compared with other adaptive algorithms possessing a similar computational complexity such a fact makes it a highly competitive alternative to some applications approximate analytical models for the first and second moments of the filter weight vector are obtained the tdlms algorithm has an orthonormal transformation stage accomplishing a decomposition of the input signal into distinct frequency bands in which the interband samples are practically uncorrelated on the other hand the intraband samples are correlated the larger the number of bands the higher their correlation the model is then derived taking into account such a correlation requiring that a high order hyperelliptic integral be computed in addition to the proposed model an approximate procedure for computing high order hyperelliptic integrals is presented a regularization parameter is also considered in the model expressions permitting to assess its impact on the adaptive algorithm behavior an upper bound for the step size control parameter is also obtained through simulation results the accuracy of the proposed model is assessed

nonlinear schrodinger equation with singular potential and initial data abstract we consider a nonlinear schrodinger equation with singular potential and initial data when the nonlinear term is an l loc function which does not satisfy the lipschitz condition to avoid non lipshitz nonlinearity we use the cut off method of regularization and as a framework for existence uniqueness theorems we employ colombeau vector space g c 1 w 2 2 0 t r n n 3 as an example we prove the existence uniqueness result for nonlinear mapping f u u p 1 u p 1 in the space g c 1 w 2 2 0 t r n n 3

a knapsack based probabilistic encryption scheme knapsack based cryptosystems had been viewed as the most attractive and the most promising asymmetric cryptographic algorithms for a long time due to their np completeness nature and high speed in encryption decryption unfortunately most of them are broken for the low density feature of the underlying knapsack problems in this paper we investigate a new easy compact knapsack problem and propose a novel knapsack based probabilistic public key cryptosystem in which the cipher text is non linear with the plaintext for properly chosen parameters the underlying knapsack problem enjoys a high density larger than 1 06 in the worst case hence it is secure against the low density subset sum attacks our scheme can also defeat other potential attacks such as the brute force attacks and the simultaneous diophantine approximation attack compared with previous knapsack based cryptosystems our scheme is efficient and practical

a measure of the tracking capability of recursive stochastic algorithms with constant gains a criterion is given for measuring the tracking capability of recursive algorithms when applied to slowly time varying systems the optimal gain for a given disturbance is also calculated this criterion is seen to have some connection with the fisher information matrix and allows us to select a priori the best algorithm for identifying a given unknown parameter which may be subject to smooth unknown disturbances examples of applications are given in the areas of identification theory and data communication theory

a family of shrinkage adaptive filtering algorithms a family of adaptive filtering algorithms that uses a variable step size is proposed a variable step size is obtained by minimizing the energy of the noise free a posteriori error signal which is obtained by using a known l 1 hbox l 2 minimization formulation based on this methodology a shrinkage affine projection shap algorithm a shrinkage least mean squares shlms algorithm and a shrinkage normalized least mean squares shnlms algorithm are proposed the shap algorithm yields a significantly reduced steady state misalignment as compared to the conventional affine projection ap variable step size ap and set membership ap algorithms for the same convergence speed although the improvement is achieved at the cost of an increase in the average computational effort per iteration in the amount of 11 to 14 the shlms algorithm yields a significantly reduced steady state misalignment and faster convergence as compared to the conventional lms and variable step size lms algorithms similarly the shnlms algorithm yields a significantly reduced steady state misalignment and faster convergence as compared to the conventional normalized least mean squares nlms and set membership nlms algorithms

adaptive lms l filters for noise suppression in images several adaptive least mean squares lms l filters both constrained and unconstrained ones are developed for noise suppression in images and compared in this paper first the location invariant lms l filter for a nonconstant signal corrupted by zero mean additive white noise is derived it is demonstrated that the location invariant lms l filter can be described in terms of the generalized linearly constrained adaptive processing structure proposed by griffiths and jim 1982 subsequently the normalized and the signed error lms l filters are studied a modified lms l filter with nonhomogeneous step sizes is also proposed in order to accelerate the rate of convergence of the adaptive l filter finally a signal dependent adaptive filter structure is developed to allow a separate treatment of the pixels that are close to the edges from the pixels that belong to homogeneous image regions

steady state performance of spline adaptive filters recently a novel class of nonlinear adaptive filters called spline adaptive filters safs has been introduced and demonstrated to be very effective in many practical applications the learning rules of these architectures are based on the least mean square lms algorithm in order to provide theoretical foundation to the saf in this paper we provide a steady state performance evaluation in particular after the stochastic analysis of the mean behavior of the saf approach under the gaussian assumption the analytical derivation of the theoretical excess mean square error emse and the normalized misadjustment are derived and discussed the proposed analysis of emse and misadjustment is based on the energy conservation approach that has been extended to saf architecture the derived theoretical analysis allows to accurately predict the steady state performance therefore some properties for the correct choice of filter parameters are also provided experimental results demonstrate the effectiveness of the analysis results

the complex lms adaptive algorithm transient weight mean and covariance with applications to the ale the transient and steady state mean and covariance of the complex valued lms adaptive element weights are investigated when the inputs are samples from circularly normal processes it is shown that the data covariance diagonalizing matrix also diagonalizes the weight covariance matrix this result permits describing the complete transient behavior of the adaptive line enhancer ale weight covariance matrix in closed form for the case of multiple equal power narrow band statistically independent orthogonal rayleigh fading sinusoids in broad band noise based on these transient covariance results it is shown that for any stage of adaptation there exists an optimum ale gain constant that minimizes the excess mean squared prediction error this result is of particular significance when processing time limited data

a chaos based symmetric image encryption scheme using a bit level permutation in recent years a variety of chaos based digital image encryption algorithms have been suggested most of these algorithms implement permutations and diffusions at the pixel level by considering the pixel as the smallest atomic element of an image in fact a permutation at the bit level not only changes the position of the pixel but also alters its value here we propose an image cryptosystem employing the arnold cat map for bit level permutation and the logistic map for diffusion simulations have been carried out and analyzed in detail demonstrating the superior security and high efficiency of our cryptosystem

asymptotic and finite sample properties of estimators based on stochastic gradients stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets however their statistical properties are not well understood in theory and in practice avoiding numerical instability requires careful tuning of key parameters here we introduce implicit stochastic gradient descent procedures which involve parameter updates that are implicitly defined intuitively implicit updates shrink standard stochastic gradient descent updates the amount of shrinkage depends on the observed fisher information matrix which does not need to be explicitly computed thus implicit procedures increase stability without increasing the computational burden our theoretical analysis provides the first full characterization of the asymptotic behavior of both standard and implicit stochastic gradient descent based estimators including finite sample error bounds importantly analytical expressions for the variances of these stochastic gradient based estimators reveal their exact loss of efficiency we also develop new algorithms to compute implicit stochastic gradient descent based estimators for generalized linear models cox proportional hazards m estimators in practice and perform extensive experiments our results suggest that implicit stochastic gradient descent procedures are poised to become a workhorse for approximate inference from large data sets

the error variance of lms with time varying weights a calculation of weight error variance of the lms least mean square algorithm is made in the presence of time varying true weights with time varying weights the lms error system has in general several time scales operating at once this causes difficulties in the variance calculation which seem hitherto to have passed unnoticed to handle this problem a sort of perturbation expansion is developed based on weak convergence methods or stochastic averaging the main concern in carrying out the error variance calculation is to study the effect on lms performance of adaptation speed as it relates to true speed of parameter change three cases are covered with reference to considering adaptation speed with respect to true speed first where the adaptation speed is too slow second where it is matched and third where it is faster

the limiting behavior of lms a realization oriented analysis is given of the gradient noise misadjustment and lag misadjustment performance of the lms least mean square algorithm new formulas are given for both of these components of excess mean square error it is shown that the traditional formula for lag misadjustment needs to be modified by adding further terms due to gradient noise and noise variance to perform the analysis it is necessary to study the convergence with probability one of the noise free fixed parameter lms algorithm convergence is found under simple conditions that improve on those previously obtained

efficient subspace based algorithm for adaptive bearing estimation and tracking in some practical applications of array processing the directions of the incident signals should be estimated adaptively and or the time varying directions should be tracked promptly in this paper an adaptive bearing estimation and tracking abest algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow band signals impinging on a uniform linear array ula based on the subspace based method without eigendecomposition sumwe where a linear operator is obtained from the array data to form a basis for the null space by exploiting the array geometry and its shift invariance property specifically the null space is estimated using the least mean square lms or normalized lms nlms algorithm and the directions are updated using the approximate newton method the transient analyses of the lms and nlms algorithms are studied where the weight i e the linear operator is in the form of a matrix and there is a correlation between the additive noise and input data that involve the instantaneous correlations of the received array data in the updating equation and the step size stability conditions are derived explicitly in addition the analytical expressions for the mean square error mse and mean square deviation msd learning curves of the lms algorithm are clarified the effectiveness of the abest algorithm is verified and the theoretical analyses are corroborated through numerical examples simulation results show that the abest algorithm is computationally simple and has good adaptation and tracking abilities

on the convergence rate performance of the normalized least mean square adaptation this paper compares the convergence rate performance of the normalized least mean square nlms algorithm to that of the standard least mean square lms algorithm which is based on a well known interpretation of the nlms algorithm as a form of the lms via input normalization with this interpretation the analysis is considerably simplified and the difference in rate of parameter convergence can be compared directly by evaluating both the condition number of the normalized and unnormalized input correlation matrix this paper derives the condition number expressions for the normalized input correlation matrix of which the arbitrary length filter model is linear with respect to its adaptable parameters and contain only two distinct unnormalized eigenvalues these expressions which require that the input samples be statistically stationary and zero mean gaussian distributed provide an important insight into the relative convergence performance of the nlms algorithm to that of the lms as a function of filter length this paper also provides a conjecture which set bounds on the nlms condition number for any arbitrary number of distinct unnormalized eigenvalues

convergence and performance analysis of the normalized lms algorithm with uncorrelated gaussian data it is demonstrated that the normalized least mean square nlms algorithm can be viewed as a modification of the widely used lms algorithm the nlms is shown to have an important advantage over the lms which is that its convergence is independent of environmental changes in addition the authors present a comprehensive study of the first and second order behavior in the nlms algorithm they show that the nlms algorithm exhibits significant improvement over the lms algorithm in convergence rate while its steady state performance is considerably worse

speech enhancement in discontinuous transmission systems using the constrained stability least mean squares algorithm in this paper a novel constrained stability least mean squares lms algorithm for filtering speech sounds is proposed in the adaptive noise cancellation anc problem it is based on the minimization of the squared euclidean norm of the weight vector change under a stability constraint over the a posteriori estimation errors to this purpose the lagrangian methodology has been used in order to propose a nonlinear adaptation in terms of the product of differential input and error convergence analysis is also studied in terms of the evolution of the natural modes to the optimal wiener hopf solution so that the stability performance depends exclusively on the adaptation parameter and the eigenvalues of the difference matrix r1 the algorithm shows superior performance over the referenced algorithms in the anc problem of speech discontinuous transmission systems which are characterized by rapid transitions of the desired signal the experimental analysis carried out on the aurora 3 speech databases provides an extensive performance evaluation together with an exhaustive comparison to the standard lms algorithms i e the normalized lms nlms and other recently reported lms algorithms such as the modified nlms the error nonlinearity lms or the normalized data nonlinearity lms adaptation

how much does transmit correlation affect the sum rate scaling of mimo gaussian broadcast channels this paper considers the effect of spatial correlation between transmit antennas on the sum rate capacity of the mimo gaussian broadcast channel i e downlink of a cellular system specifically for a system with a large number of users n we analyze the scaling laws of the sum rate for the dirty paper coding and for different types of beamforming transmission schemes when the channel is i i d it has been shown that for large n the sum rate is equal to m log log n m log p m o 1 where m is the number of transmit antennas p is the average signal to noise ratio and o 1 refers to terms that go to zero as n rarr infin when the channel exhibits some spatial correlation with a covariance matrix r non singular with tr r m we prove that the sum rate of dirty paper coding is m log log n m log p m log det r o 1 we further show that the sum rate of various beamforming schemes achieves m log log n m log p m m log c o 1 where c les 1 depends on the type of beamforming we can in fact compute c for random beamforming proposed in and more generally for random beamforming with preceding in which beams are pre multiplied by a fixed matrix simulation results are presented at the end of the paper

transient and steady state analysis of the affine combination of two adaptive filters in this paper we propose an approach to the transient and steady state analysis of the affine combination of one fast and one slow adaptive filters the theoretical models are based on expressions for the excess mean square error emse and cross emse of the component filters which allows their application to different combinations of algorithms such as least mean squares lms normalized lms nlms and constant modulus algorithm cma considering white or colored inputs and stationary or nonstationary environments since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant its adaptation is also taken into account in the transient analysis furthermore we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance good agreement between analysis and simulation results is always observed

region based wavelet packet adaptive algorithm for identification of sparse impulse responses identification of systems with sparse impulse response encounters large applicability numerous techniques have been proposed to identify such systems efficiently one strategy that leads to specially good results is to detect the active nonzero response samples and update only the corresponding adaptive coefficients wavelet based approaches have been shown to be specially effective to this end this paper proposes a new region based wavelet packet rbwp algorithm for efficient identification of systems with sparse impulse responses with arbitrary frequency spectra and with any delay of the effective response the discrete wavelet packet transform dwpt is adaptively tailored to the energy distribution of the unknown system s response spectrum the new algorithm leads to a reduced number of active weights and to a reduced computational complexity when compared with competing wavelet based algorithms monte carlo simulation results show good performances regarding convergence speed and robustness to design parameter choice

convergence behavior of affine projection algorithms a class of equivalent algorithms that accelerate the convergence of the normalized lms nlms algorithm especially for colored inputs has previously been discovered independently the affine projection algorithm apa is the earliest and most popular algorithm in this class that inherits its name the usual apa algorithms update weight estimates on the basis of multiple unit delayed input signal vectors we analyze the convergence behavior of the generalized apa class of algorithms allowing for arbitrary delay between input vectors using a simple model for the input signal vectors conditions for convergence of the apa class are derived it is shown that the convergence rate is exponential and that it improves as the number of input signal vectors used for adaptation is increased however the rate of improvement in performance time to steady state diminishes as the number of input signal vectors increases for a given convergence rate apa algorithms are shown to exhibit less misadjustment steady state error than nlms simulation results are provided to corroborate the analytical results

one time encryption key technique for the traditional dl based encryption scheme with anonymity in modern cryptosystem anonymity means that in some sense any adversary cannot tell which one of public keys has been used for encrypting a plaintext and was first formally defined as the indistinguishability of keys by bellare et al in 2001 recently several well known techniques have been proposed in order to achieve the anonymity of public key encryption schemes in this paper anonymity is considered first from a new perspective and then basing on this new perspective a one time encryption key technique is proposed to achieve the anonymity of traditional discrete logarithm based dl based encryption scheme in this new technique for each encryption a random one time encryption key will be generated to encrypt the plaintext instead of the original public key consequently in roughly speaking by the randomness of the generated one time encryption key this new technique should achieve the anonymity furthermore in the formal proof of anonymity only based on several weaker conditions the one time encryption key technique efficiently achieves the provable indistinguishability of keys under chosen ciphertext attack ik cca anonymity as a result compared with the work of hayashi and tanaka in 2006 the one time encryption key technique presented here has fewer requirements for achieving the provable anonymity

generalized solutions of a nonlinear parabolic equation with generalized functions as initial data abstract in h brezis a friedman nonlinear parabolic equations involving measures as initial conditions j math pure appl 9 1983 73 97 brezis and friedman prove that certain nonlinear parabolic equations with the measure as initial data have no solution however in j f colombeau m langlais generalized solutions of nonlinear parabolic equations with distributions as initial conditions j math anal appl 1990 186 196 colombeau and langlais prove that these equations have a unique solution even if the measure is substituted by any colombeau generalized function of compact support here we generalize colombeau and langlais result proving that we may take any generalized function as the initial data our approach relies on recent algebraic and topological developments of the theory of colombeau generalized functions and results from j aragona colombeau generalized functions on quasi regular sets publ math debrecen 2006 371 399

variable length stochastic gradient algorithm the transversal variable length stochastic gradient algorithm is described it is a modification of the stochastic gradient algorithm that allows dynamic allocation of coefficients of an adaptive filter the order of the filter and the adaptation step size are changed automatically when an appropriate level of performance is reached during the course of the adaptation process in this way the algorithm results in fast convergence typical of low order filters and good steady state performance typical of high order filters

an efficient incomparable public key encryption scheme public keys are closely related to the identity of recipients in public key encryption setting in privacy sensitive applications of public key encryption it is desirable to hide the relation between the public key and the identity of the recipient the main functional approach in the privacy enhanced public key encryption scheme is to give anonymity of the public keys of recipients in this case all the users in the system are potential recipients of every ciphertext waters felten and sahai proposed an incomparable public key encryption scheme which guarantees the anonymity of recipients against both eavesdroppers and senders in their scheme all the recipients must complete the same amount of computations to identify the ciphertexts which direct to them in this paper we focus on reducing the number of computations for the recipients while preserving the security level of waters et al s scheme our method is to separate the decryption process into two steps first the recipient determines whether a ciphertext is directed to him or her and only if the direction is correct the recipient recovers the corresponding plaintext this improves the efficiency of the system

tracking properties and steady state performance of rls adaptive filter algorithms adaptive signal processing algorithms derived from ls least squares cost functions are known to converge extremely fast and have excellent capabilities to track an unknown parameter vector this paper treats analytically and experimentally the steady state operation of rls recursive least squares adaptive filters with exponential windows for stationary and nonstationary inputs a new formula for the estimation noise has been derived involving second and fourth order statistics of the filter input as well as the exponential windowing factor and filter length furthermore it is shown that the adaptation process associated with lag effects depends solely on the exponential weighting parameter in addition the calculation of the excess mean square error due to the lag for an assumed markov channel provides the necessary information about tradeoffs between speed of adaptation and steady state error it is also the basis for comparison to the simple lms algorithm in a simple case of channel identification it is shown that the lms and rls adaptive filters have the same tracking behavior finally in the last part we present new rls restart procedures applied to transversal structures for mitigating the disastrous results of the third source of noise namely finite precision arithmetic

behavior of the e normalized lms algorithm with gaussian inputs the first and second moment behavior of one variation of the normalized lms e nlms algorithm is investigated for a white covariance matrix and gaussian statistics for the data for this model it is shown that the e nlms algorithm has neither behavior independent of the input data power nor a performance significantly better than the lms algorithm for which the input power level also must be known a priori hence based upon the results of the analysis it is recommended that the algorithm not be used in place of the lms for known input power levels or in place of the nlms for unknown input power levels

stochastic gradient adaptation under general error criteria examines a family of adaptive filter algorithms of the form w sub k 1 w sub k spl mu f d sub k w sub k sup t x sub k x sub k in which f spl middot is a memoryless odd symmetric nonlinearity acting upon the error such algorithms are a generalization of the least mean square lms adaptive filtering algorithm for even symmetric error criteria for this algorithm family the authors derive general expressions for the mean and mean square convergence of the filter coefficients for both arbitrary stochastic input data and gaussian input data they then provide methods for optimizing the nonlinearity to minimize the algorithm misadjustment for a given convergence rate using the calculus of variations it is shown that the optimum nonlinearity to minimize misadjustment near convergence under slow adaptation conditions is independent of the statistics of the input data and can be expressed as p x p x where p x is the probability density function of the uncorrelated plant noise for faster adaptation under the white gaussian input and noise assumptions the nonlinearity is shown to be x 1 spl mu spl lambda x sup 2 spl sigma sub k sup 2 where spl lambda is the input signal power and spl sigma sub k sup 2 is the conditional error power thus the optimum stochastic gradient error criterion for gaussian noise is not mean square it is shown that the equations governing the convergence of the nonlinear algorithm are exactly those which describe the behavior of the optimum scalar data nonlinear adaptive algorithm for white gaussian input simulations verify the results for a host of noise interferences and indicate the improvement using non mean square error criteria

a note on the convergence analysis of lms adaptive filters with gaussian data necessary and sufficient conditions for the convergence of lms least mean squares adaptive filters with gaussian data have been established by l l horowitz and k d senne 1981 with the recent support of a feuer and e weinstein 1985 a feature of both of these studies is the necessity to investigate bounds on the roots of rather unwieldy characteristic equations the authors show how such an investigation can be avoided through the use of a theorem of f r gantmacher 1959 in formally applying this theorem similar results to those of the above studies are obtained in a precise and straightforward manner

secure public key encryption scheme without random oracles since the first practical and secure public key encryption scheme without random oracles proposed by cramer and shoup in 1998 cramer shoup s scheme and its variants remained the only practical and secure public key encryption scheme without random oracles until 2004 in 2004 canetti et al proposed a generic transformation from a selective identity based encryption scheme to a public key encryption by adding a one time strongly signature scheme since then some transformation techniques from a selective identity based encryption scheme to a public key encryption have been proposed to enhance the computational efficiency for example boneh katz s construction and boyen mei waters scheme these transformations have either traded off the publicly verifiable properties or tightness of security reduction in 2007 zhang proposed another generic transformation by adding chameleon hash functions in this paper we introduce another technique from the boneh boyen s selective identity based encryption scheme to a public key encryption which is publicly verifiable and is slightly more efficient than zhang s transformation the proposed public key encryption scheme is based on the decisional bilinear diffie hellman assumption and the target collision resistant hash functions

fast transversal filters with data sequence weighting a fast o n algorithm is presented for the adaptive recursive least squares design of transversal filters data sequence weighting is introduced to allow for arbitrarily time varying weighting strategies facilitating the tracking of arbitrary nonstationary phenomena a novel weighting adaptation mechanism is presented that has various desirable features and optimal performance under certain conditions the algorithm is derived for the prewindowed given data case and the underlying principles of the derivation are clearly exposed exact and soft constraint initialization are discussed and an improved restart procedure is proposed

certificateless threshold cryptosystem secure against chosen ciphertext attack this paper proposes the first certificateless threshold decryption scheme which avoids both the single point of failure in the distributed networks and the inherent key escrow problem in identity based cryptosystem the scheme is secure against threshold chosen ciphertext attack it tolerates the type i adversary that can replace public key and the type ii adversary that has access to the system s master key the formal proof of security is presented in the random oracle model assuming some underlying problems closely related to the bilinear diffie hellman problem are computationally hard

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

on the learning mechanism of adaptive filters this paper highlights both analytically and by simulations some interesting phenomena regarding the behavior of ensemble average learning curves of adaptive filters that may have gone unnoticed among other results the paper shows that even ensemble average learning curves of single tap lms filters actually exhibit two distinct rates of convergence one for the initial time instants and another faster one for later time instants in addition such curves tend to converge faster than predicted by mean square theory and can converge even when a mean square stability analysis predicts divergence these effects tend to be magnified by increasing the step size two of the conclusions that follow from this work are 1 the mean square stability alone may not be the most appropriate performance measure especially for larger step sizes a combination of mean square stability and almost sure a s stability seems to be more appropriate 2 care is needed while interpreting ensemble average curves for larger step sizes the curves can lead to erroneous conclusions unless a large number of experiments are averaged at times of the order of tens of thousands or higher

chosen ciphertext security from identity based encryption we propose simple and efficient cca secure public key encryption schemes i e schemes secure against adaptive chosen ciphertext attacks based on any identity based encryption ibe scheme our constructions have ramifications of both theoretical and practical interest first our schemes give a new paradigm for achieving cca security this paradigm avoids proofs of well formedness that have been shown to underlie previous constructions second instantiating our construction using known ibe constructions we obtain cca secure encryption schemes whose performance is competitive with the most efficient cca secure schemes to date our techniques extend naturally to give an efficient method for securing ibe schemes even hierarchical ones against adaptive chosen ciphertext attacks coupled with previous work this gives the first efficient constructions of cca secure ibe schemes

quantifying the effects of dimension on the convergence rate of the lms adaptive fir estimator the convergence rate of an lms adaptive fir filter to an unknown stationary channel may be influenced by the filter parameter dimension as well as by the input signal s characteristics this dimension influence may be of importance in applications such as adaptive acoustic echo cancellation in which the unknown channel is typically modeled as a long fir filter the paper includes the development and proposal of a novel measure of the expected convergence rate of the lms fir filter followed by analysis of this convergence rate measure the analysis indicates that unless the input signal is white the expected convergence rate decreases with increasing dimension down to a limiting value which is determined by the input signal s autocorrelation level

fixed point error analysis of the normalized ladder algorithm an attempt is made to analyze the fixed point error performance of the normalized ladder algorithm for autoregressive system identification assuming rounding arithmetic a preliminary simulation study of this algorithm has shown that the bias in the estimated reflection coefficients is much more predominant than the variance of the error in the estimate the study therefore is directed to find a model for predicting the bias in the estimated reflection coefficients the analysis shows that the roundoff errors associated with the square root operations in one of the algorithm equations are mainly responsible for the bias in the estimated reflection coefficients these errors arise because of the normalization procedure that makes the quantities under the square root operations very close to one two main results are presented in the paper 1 a simplified theoretical expression for predicting the average bias in the estimated reflection coefficients at any stage is derived 2 a recursive relation for the average error arising from the finite precision arithmetic in the squared residuals is derived this relation illustrates how the errors made in one stage affect the errors in the succeeding stages simulations are performed to check the theoretical models the experimental results agree very closely with the theoretical predictions

analysis of the normalized lms algorithm with gaussian inputs the lms adaptive filter algorithm requires a priori knowledge of the input power level to select the algorithm gain parameter for stability and convergence since the input power level is usually one of the statistical unknowns it is normally estimated from the data prior to beginning the adaptation process it is then assumed that the estimate is perfect in any subsequent analysis of the lms algorithm behavior in this paper the effects of the power level estimate are incorporated in a data dependent that appears explicitly within the algorithm the transient mean and second moment behavior of the modified lms nlms algorithm are evaluated taking into account the explicit statistical dependence of upon the input data the mean behavior of the algorithm is shown to converge to the wiener weight a constant coefficient matrix difference equation is derived for the weight fluctuations about the wiener weight the equation is solved for a white data covariance matrix and for the adaptive line enhancer with a single frequency input in steady state for small expressions for the misadjustment error are also presented it is shown for the white data covariance matrix case that the averaging of about ten data samples causes negligible degradation as compared to the lms algorithm in the ale application the steady state weight fluctuations are shown to be mode dependent being largest at the frequency of the input

heat equation with singular potential and singular data nets of schrodinger c 0 semigroups s e e with the polynomial growth with respect to e are used for solving the cauchy problem t u vu f t u u 0 x u 0 x in a suitable generalized function algebra or space where v and u 0 are singular generalized functions while f satisfies a lipschitz type condition the existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

fast recursive least squares transversal filters for adaptive filtering fast transversal filter ftf implementations of recursive least squares rls adaptive filtering algorithms are presented in this paper substantial improvements in transient behavior in comparison to stochastic gradient or lms adaptive algorithms are efficiently achieved by the presented algorithms the true not approximate solution of the rls problem is always obtained by the ftf algorithms even during the critical initialization period first n iterations of the adaptive filter this true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic gradient algorithms factor of 1 6 to 3 5 depending upon application additionally the fast transversal filter algorithms are shown to offer substantial reductions in computational requirements relative to existing fast rls algorithms such as the fast kalman algorithms of morf ljung and falconer 1976 and the fast ladder lattice algorithms of morf and lee 1977 1981 they are further shown to attain steady state unnormalized or improve upon first n initialization steps the very low computational requirements of the efficient rls solutions of carayannis manolakis and kalouptsidis 1983 finally several efficient procedures are presented by which to ensure the numerical stability of the transversal filter algorithms including the incorporation of soft constraints into the performance criteria internal bounding and rescuing procedures and dynamic range increasing square root normalized variations of the transversal filters

a stochastic newton algorithm with data adaptive step size a stochastic newton algorithm for adaptive filtering which is a generalization of the so called normalized least mean square algorithm is proposed expressions for the expected value of the algorithm weight error vector and second moment of the weight error vector norm are derived and have been verified by computer simulation experimental results which demonstrate the improved convergence of the algorithm over the algorithm after a large number of iterations are given

transient analysis of data normalized adaptive filters this paper develops an approach to the transient analysis of adaptive filters with data normalization among other results the derivation characterizes the transient behavior of such filters in terms of a linear time invariant state space model the stability of the model then translates into the mean square stability of the adaptive filters likewise the steady state operation of the model provides information about the mean square deviation and mean square error performance of the filters in addition to deriving earlier results in a unified manner the approach leads to stability and performance results without restricting the regression data to being gaussian or white the framework is based on energy conservation arguments and does not require an explicit recursion for the covariance matrix of the weight error vector

almost sure convergence of adaptive algorithms by projections a convergence proof is discussed for the normalized least mean square lms algorithm for ergodic inputs the approach is based on interpreting the algorithm as a sequence of relaxed projection operators by which the key contraction property is derived the proof technique is strongly motivated by physical intuition and provides additional insight into lms type algorithms under ergodic inputs embedded in the development is a slight generalization to a random time varying gain parameter this allows the incorporation of variations such as the lms and signed lms algorithms

system of nonlinear volterra s integral equations with polar kernel and singularities abstract we study an existence uniqueness theorem for a system of nonlinear volterra type integral equations with polar kernel and singularities to do so we use a method of regularization of fractional derivatives with a delta sequence to avoid singularities over diagonal y x y 0 the other singularities we regularize with delta sequences with different growth as a framework we use colombeau special algebra

design and analysis of practical public key encryption schemes secure against adaptive chosen ciphertext attack a new public key encryption scheme along with several variants is proposed and analyzed the scheme and its variants are quite practical and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions these appear to be the first public key encryption schemes in the literature that are simultaneously practical and provably secure

a unified approach to the steady state and tracking analyses of adaptive filters most adaptive filters are inherently nonlinear and time variant systems the nonlinearities in the update equations tend to lead to difficulties in the study of their steady state performance as a limiting case of their transient performance this paper develops a unified approach to the steady state and tracking analyses of adaptive algorithms that bypasses many of these difficulties the approach is based on the study of the energy flow through each iteration of an adaptive filter and it relies on a fundamental error variance relation

error energy bounds for adaptive gradient algorithms the paper establishes robustness optimality and convergence properties of the widely used class of instantaneous gradient adaptive algorithms the analysis is carried out in a purely deterministic framework and assumes no a priori statistical information it employs the cauchy schwarz inequality for vectors in an euclidean space and derives local and global error energy bounds that are shown to highlight as well as explain relevant aspects of the robust performance of adaptive gradient filters along the lines of h sup spl infin theory

adaptive recovery of a chirped sinusoid in noise ii performance of the lms algorithm the authors study the ability of the exponentially weighted recursive least square rls algorithm to track a complex chirped exponential signal buried in additive white gaussian noise power p sub n the signal is a sinusoid whose frequency is drifting at a constant rate psi lt is recovered using an m tap adaptive predictor five principal aspects of the study are presented the methodology of the analysis proof of the quasi deterministic nature of the data covariance estimate r k a new analysis of rls for an inverse system modeling problem a new analysis of rls for a deterministic time varying model for the optimum filter and an evaluation of the residual output mean square error mse resulting from the nonoptimality of the adaptive predictor the misadjustment in terms of the forgetting rate beta of the rls algorithm it is shown that the misadjustment is dominated by a lag term of order beta sup 2 and a noise term of order beta thus a value beta sub opt exists which yields a minimum misadjustment it is proved that beta sub opt m 1 rho psi sup 2 sup 1 3 and the minimum misadjustment is equal to 3 4 p sub n m 1 beta sub opt where rho is the input signal to noise ratio snr

in the optimum design of the block adaptive fir digital filter a general optimum block adaptive goba algorithm for adaptive fir finite impulse response filtering is presented in this algorithm the correction terms for the filter coefficients in each block instead of the convergence factors are optimized in a least squares sense there are no constraints on the block length l and the filter tap number n it is shown that the goba algorithm is reduced to the normalized lms algorithm when l or n the convergence of the goba algorithm can be assured if the correlation matrix of the input signal is positive definite computer simulations based on an efficient computing procedure confirm that the goba algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on l and n

a global gradient noise covariance expression for stationary real gaussian inputs supervised parameter adaptation in many artificial neural networks is largely based on an instantaneous version of gradient descent called the least mean square lms algorithm this paper considers only neural models which are linear with respect to their adaptable parameters and has two major contributions first it derives an expression for the gradient noise covariance under the assumption that the input samples are real stationary gaussian distributed but can be partially correlated this expression relates the gradient correlation and input correlation matrices to the gradient noise covariance and explains why the gradient noise generally correlates maximally with the steepest principal axis and minimally with the one of the smallest curvature regardless of the magnitude of the weight error second a recursive expression for the weight error correlation matrix is derived in a straightforward manner using the gradient noise covariance and comparisons are drawn with the complex lms algorithm

on the convergence behavior of the lms and the normalized lms algorithms it is shown that the normalized least mean square nlms algorithm is a potentially faster converging algorithm compared to the lms algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics a very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the lms and nlms algorithms is proposed using this model answers can be obtained to questions for which no answers are currently available using other perhaps more realistic models examples are given to illustrate that even quantitatively the answers obtained can be good approximations it is emphasized that the convergence of the nlms algorithm can be speeded up significantly by employing a time varying step size the optimal step size sequence can be specified a priori for the case of a white input signal with arbitrary distribution

quasiasymptotic analysis in colombeau algebra we consider the main notions of g quasiasymptotic g q a analysis g q a behavior at zero g q a expansion at infinity sc asymptotic and boundedness sc expansion at infinity and their applications to the asymptotic behavior of the solution to some types of nonlinear pdes in colombeau algebra of generalized functions g

normalized data nonlinearities for lms adaptation properly designed nonlinearly modified lms algorithms in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities have been shown to perform better than the lms algorithm in system identification type problems the authors investigate one such algorithm given by w sub k l w sub k spl mu d sub k w sub k sup t x sub k x sub k f x sub k in which the function f x sub k is a scalar function of the sum of the squares of the n elements of the input data vector x sub k this form of algorithm generalizes the so called normalized lms nlms algorithm they evaluate the expected behavior of this nonlinear algorithm for both independent input vectors and correlated gaussian input vectors assuming the system identification model by comparing the nonlinear algorithm s behavior with that of the lms algorithm they then provide a method of optimizing the form of the nonlinearity for the given input statistics in the independent input case they show that the optimum nonlinearity is a single parameter version of the nlms algorithm with an additional constant in the denominator and show that this algorithm achieves a lower excess mean square error mse than the lms algorithm with an equivalent convergence rate additionally they examine the optimum step size sequence for the optimum nonlinear algorithm and show that the resulting algorithm performs better and is less complex to implement than the optimum step size algorithm derived for another form of the nlms algorithm simulations verify the theory and the predicted performance improvements of the optimum normalized data nonlinearity algorithm

asymptotic behavior of an adaptive estimation algorithm with application to m dependent data theoretical results are presented concerning the asymptotic behavior of the parameter estimates generated by an adaptive algorithm in stationary dependent random situations proofs are exhibited in the general case and derived for the case of statistical dependence in the input for a finite number of lags it is found that the estimate mean error norm converges to an asymptotic bound giving a finite bias generally nonzero and that the asymptotic mean norm square error is bounded and can be arbitrarily reduced by decreasing the adaptation factor

exact performance analysis of the epsilon nlms algorithm for colored circular gaussian inputs this paper presents exact mean square analysis of the nlms algorithm for circular complex correlated gaussian input the analysis is based on the derivation of a closed form expression for the cumulative distribution function cdf of random variables of the form ui d12 ui d12 and using that to derive the first and second moments of such variables these moments in turn completely characterize the mean square ms behavior of the nlms in explicit closed form expressions both transient and steady state behavior are analyzed consequently new explicit closed form expressions for the mean square error mse behavior are derived our simulations of the transient and steady state behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of