new bounds on the average information rate of secret sharing schemes for graph based weighted threshold access structures a secret sharing scheme is a protocol by which a dealer distributes shares of a secret key among a set of n participants in such a way that only qualified subsets of participants can reconstruct the secret key from the shares they received while unqualified subsets have no information about the secret key the collection of all qualified subsets is called the access structure of this scheme the information rate resp average information rate of a secret sharing scheme is the ratio between the size of the secret key and the maximum size resp average size of the shares in a weighted threshold scheme each participant has his or her own weight a subset is qualified if and only if the sum of the weights of participants in the subset is not less than the given threshold morillo et al 19 considered the schemes for weighted threshold access structure that can be represented by graphs called k weighted graphs they characterized this kind of access structures and derived a result on the information rate in this paper we deal with the average information rate of the secret sharing schemes for these structures two sophisticated constructions are presented each of which has its own advantages and both of them perform very well when n k is large

visual multiple secret sharing based upon turning and flipping the secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies called shares in the form of rectangles which reveal the secret image to the human visual system when they are superimposed recently visual secret sharing schemes involving multiple secrets have attracted much attention by adopting rotations on one of the two encoded circle shares more than two secrets could be shared yet the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones in this paper we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares specifically we define some operations onto a transparency based upon turning over or flipping around then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations the proposed schemes which solidly elaborate the relationship between the encoded shares and the shared secrets broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically

realizing secret sharing with general access structure secret sharing ss is one of the most important cryptographic primitives used for data outsourcing the t n ss was introduced by shamir and blakley separately in 1979 the secret sharing policy of the t n threshold ss is far too simple for many applications because it assumes that every shareholder has equal privilege to the secret or every shareholder is equally trusted ito et al introduced the concept of a general secret sharing scheme gss in a gss a secret is divided among a set of shareholders in such a way that any qualified subset of shareholders can access the secret but any unqualified subset of shareholders cannot access the secret the secret access structure of gss is far more flexible than threshold ss in this paper we propose an optimized implementation of gss our proposed scheme first uses boolean logic to derive two important subsets one is called min which is the minimal positive access subset and the other is called max which is the maximal negative access subset of a given general secret sharing structure then conditions of parameters of a gss are established based on these two important subsets furthermore integer linear non linear programming is used to optimize the size of shares of a gss the complexity of linear non linear programming is o n where n is the number of shares generated by the dealer this proposed design can be applied to implement gss based on any classical ss however our proposed method is limited to be applicable to some general secret sharing policies we use two gsss one is based on shamir s weighted ss wss using linear polynomial and the other is based on asmuth bloom s ss using chinese remainder theorem crt to demonstrate our design in comparing with existing gsss our proposed scheme is more efficient and can be applied to all classical sss

robust adaptive control in the presence of bounded disturbances the model reference adaptive control of a linear plant subjected to bounded disturbances is considered by analyzing a set of nonlinear differential equations it is shown that the global behavior of the adaptive system depends upon the persistent excitation of the reference input as well as the amplitude of the external disturbances the principal contribution of the paper is the derivation of sufficient conditions on the persistent excitation of the reference input given the maximum amplitude of disturbance for the signals in the adaptive system to be globally bounded

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

computing the kalman decomposition an optimal method in this paper we describe a method for computing the complete kalman decomposition of a linear dynamical system and we show that this method is optimal in a certain sense specifically we describe an algorithm to compute a mapping that when applied to the original system yields a complete kalman decomposition we show that of all transformations that yield a kalman decomposition the one we construct here has the lowest condition number

aliasing and oblique dual pair designs for consistent sampling abstract in this paper we study some aspects of oblique duality between finite sequences of vectors f and g lying in finite dimensional subspaces w and v respectively we compute the possible eigenvalue lists of the frame operators of oblique duals to f lying in v we compute the spectral and geometrical structure of minimizers of convex potentials among oblique duals for f with norm restrictions as an application we show that these optimal duals are the closest to being tight frames and therefore have their spectrum as concentrated as possible among oblique duals with norm restrictions we obtain a complete quantitative analysis of the impact that the relative geometry between the subspaces v and w has in oblique duality we apply this analysis to compute those rigid rotations u for w such that the canonical oblique dual of u f minimize every convex potential we also introduce a notion of aliasing for oblique dual pairs and compute those rigid rotations u for w such that the canonical oblique dual pair associated to u f minimize the aliasing we point out that these two last problems are intrinsic to oblique duality within the context of consistent sampling

matrix young inequalities for the hilbert schmidt norm abstract let a b and x be n n complex matrices such that a and b are positive semidefinite if p q 1 with 1 p 1 q 1 it is shown that 1 p a p x 1 q xb q 2 2 1 r 2 a p x xb q 2 2 axb 2 2 where r max p q and 2 is the hilbert schmidt norm generalizations and applications of this inequality are also considered

a parameter adaptive controller which provides exponential stability the first order case abstract classical discrete time adaptive controllers provide asymptotic stabilization while the original adaptive controllers did not handle noise or unmodelled dynamics well redesigned versions were proven to have some tolerance however neither exponential stabilization nor a bounded noise gain is typically proven here we consider the first order case and prove that if the original ideal projection algorithm is used in the estimation process subject to the common assumption that the plant parameters lie in a convex compact set and that the parameter estimates are restricted to that set then it guarantees linear like convolution bounds on the closed loop behaviour which implies exponential stability and a bounded noise gain as well an easily proven tolerance to unmodelled dynamics and plant parameter variation

transient performance and robustness of direct adaptive control it is shown that a discrete adaptive controller with a fixed gain gradient estimator can be applied to linear systems that are undermodeled provided that the mismatch is small and the estimated parameters are projected into a compact convex set which contains stabilizing control parameters and excludes the possibility of dividing with small numbers the latter implies that the sign and a lower bound for the high frequency gain of the modeled part of the system are known the performance of the adaptive system is related to the size of the external perturbations and the ideal result as these tend to zero is obtained the main conclusion is that while convergence stability and robustness may be achieved the transient performance may not be acceptable and the gradient estimator should probably not be used unless modifications are added design guidelines are established the results extend readily to indirect adaptive laws like pole assignment linear quadratic optimal and predictive controllers

adaptive control of linear time varying plants a new model reference controller structure the problem of developing a control law which can force the output of a linear time varying plant to track the output of a stable linear time invariant reference model is discussed it is shown that the standard model reference controller used for linear time invariant plants cannot guarantee zero tracking error in general when the plant is time varying a new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time varying plants with known parameters when the time varying plant parameters are unknown but vary slowly with time it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean the assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters

frame representations and parseval duals with applications to gabor frames let x n be a frame for a hilbert space h we investigate the conditions under which there exists a dual frame for x n which is also a parseval or tight frame we show that the existence of a parseval dual is equivalent to the problem whether x n can be dilated to an orthonormal basis under an oblique projection a necessary and sufficient condition for the existence of parseval duals is obtained in terms of the frame excess for a frame g g g induced by a projective unitary representation of a group g it is possible that g g g can have a parseval dual but does not have a parseval dual of the same type the primary aim of this paper is to present a complete characterization for all the projective unitary representations such that every frame g g g with a necessary lower frame bound condition has a parseval dual of the same type as an application of this characterization together with a result about lattice tiling we prove that every gabor frame g g l k again with the same necessary lower frame bound condition has a parseval dual of the same type if and only if the volume of the fundamental domain of l k is less than or equal to 1 2

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

robust continuous time adaptive control by parameter projection the problem of adaptive control of a continuous time plant of arbitrary relative degree in the presence of bounded disturbances as well as unmodeled dynamics is addressed the adaptation considered is the usual gradient update law with parameter projection the latter being the only robustness enhancement modification employed it is shown that if the unmodeled dynamics which consists of multiplicative as well as additive system uncertainty is small enough then all the signals in the closed loop system are bounded this shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics in the nominal case where unmodeled dynamics and disturbances are absent the asymptotic error in tracking a given reference signal is zero moreover the performance of the adaptive controller is also robust

new efficient and practical verifiable multi secret sharing schemes in 2006 zhao et al proposed a practical verifiable multi secret sharing based on yang et al s and feldman s schemes in this paper we propose two efficient computationally secure t n and verifiable multi secret sharing schemes based on homogeneous linear recursion the first scheme has the advantage of better performance a new simple construction and various techniques for the reconstruction phase the second scheme requires fewer public values with respect to zhao et al s and shao and cao schemes these schemes are easy to implement and provide great capabilities for many applications

new bounds on the information rate of secret sharing schemes spl acute a secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret but any nonqualified subset has absolutely no information on the secret we derive new limitations on the information rate of secret sharing schemes that measures how much information is being distributed as shares as compared to the size of the secret key and the average information rate that is the ratio between the secret size and the arithmetic mean of the size of the shares by applying the substitution technique we are able to construct many new examples of access structures where the information rate is bounded away from 1 the substitution technique is a method used to obtain a new access structure by replacing a participant in a previous structure with a new access structure

an ideal multi secret sharing scheme based on msp a multi secret sharing scheme is a protocol to share m arbitrarily related secrets s 1 s m among a set of n participants in this paper we propose an ideal linear multi secret sharing scheme based on monotone span programs where each subset of the set of participants may have the associated secret our scheme can be used to meet the security requirement in practical applications such as secure group communication and privacy preserving data mining etc we also prove that our proposed scheme satisfies the definition of a perfect multi secret sharing scheme

decomposition constructions for secret sharing schemes the paper describes a very powerful decomposition construction for perfect secret sharing schemes the author gives several applications of the construction and improves previous results by showing that for any graph g of maximum degree d there is a perfect secret sharing scheme for g with information rate 2 d 1 as a corollary the maximum information rate of secret sharing schemes for paths on more than three vertices and for cycles on more than four vertices is shown to be 2 3

singular value estimates of oblique projections abstract let w and m be two finite dimensional subspaces of a hilbert space h such that h w m and let p w m denote the oblique projection with range w and nullspace m in this article we get the following formula for the singular values of p w m 2 s k p w m 1 min f h x w m 2 where the minimum is taken over the set of all operator pairs f h on h such that r f w r h m and fh p w m and k 1 dim w we also characterize all the pairs where the minimum is attained

strong n t n verifiable secret sharing scheme a t n secret sharing divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret but fewer than t shares cannot reconstruct the secret in this paper we extend the idea of a t n secret sharing scheme and give a formal definition on the n t n secret sharing scheme based on pedersen s t n secret sharing scheme we will show that the t n verifiable secret sharing vss scheme proposed by benaloh can only ensure that all shares are t consistent i e any subset of t shares defines the same secret but shares may not satisfy the security requirements of a t n secret sharing scheme then we introduce new notions of strong t consistency and strong vss a strong vss can ensure that a all shares are t consistent and b all shares satisfy the security requirements of a secret sharing scheme we propose a strong n t n vss based on benaloh s vss we also prove that our proposed n t n vss satisfies the definition of a strong vss

canonical angles of unitary spaces and perturbations of direct complements abstract let n plane1d 4b2 be a given direct sum decomposition we determine the largest number r i such that all subspaces for which the gap between and plane1d 4b2 satisfies have the property dim plane1d 4b2 the problem involves angles between subspaces i e singular values of products of projections

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

stability of discrete model reference adaptive control revisited abstract we demonstrate that the model reference adaptive controller is robust with respect to small model plant mismatch the sign and a lower bound on the high frequency gain are known and the control parameters are constrained to belong to a compact set which contains the parameters of a stabilizing controller data normalization and deadzones do not play a role in the analysis a constructive proof is used to develop bounds for the allowable gain of the model mismatch when the algorithm state is far from equilibrium the signals are measured by a decaying exponential the rate of convergence is estimated an expression which can be used to calculate the size of an overbounding set is developed its size scales uniformly with respect to the external disturbances the inverse of the adaptive gain and the reference the ideal case is obtained as these tend to zero this result holds true even when there is a model mismatch

paper discrete time adaptive control for deterministic time varying systems there is currently considerable interest in the application of recently developed self tuning control algorithms to real control problems however there exist few algorithms which will work for other than slow time varying systems a new algorithm which is able to successfully control unknown systems with quite rapidly varying parameters is presented several simulation results are also presented a convergence proof in the linearly time varying parameter case is given

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

probabilistic visual secret sharing schemes for grey scale images and color images visual secret sharing vss scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation pixel expansion has been a major issue of vss schemes a number of probabilistic vss schemes with minimum pixel expansion have been proposed for binary secret images this paper presents a general probabilistic k n vss scheme for grey scale images and another scheme for color images with our schemes the pixel expansion can be set to a user defined value when this value is 1 there is no pixel expansion at all the quality of reconstructed secret images measured by average contrast or average relative difference is equivalent to the contrast of existing deterministic vss schemes previous probabilistic vss schemes for black and white images can be viewed as special cases in the schemes proposed here

a robust adaptive controller with minimal modifications for discrete time varying systems the goal of this paper is to show that an indirect adaptive controller with parameter projection as the only modification on the basis of conventional adaptive control algorithms can globally stabilize systems having fast parasitics bounded external disturbances and time varying parameters without any restriction on signals in the closed loop system such as persistence of excitation further the controller can still retain the properties of earlier unmodified conventional adaptive controllers when the controlled plant satisfies so called ideal assumptions or the rates at which the plant parameters change belong to the l sub 1 or l sub 2 space

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

the lanczos arnoldi algorithm and controllability we present methods for computing the controllable space of a linear dynamic system the methods are based on orthogonalizing krylov sequences and can use much less storage than other methods with little or no loss of numerical stability

secret sharing schemes with bipartite access structure we study the information rate of secret sharing schemes whose access structure is bipartite in a bipartite access structure there are two classes of participants and all participants in the same class play an equivalent role in the structure we characterize completely the bipartite access structures that can be realized by an ideal secret sharing scheme both upper and lower bounds on the optimal information rate of bipartite access structures are given these results are applied to the particular case of weighted threshold access structure with two weights

perturbation of frame sequences and its applications to shift invariant spaces abstract we generalize the main result in o christensen h o kim r y kim j k lim perturbation of frame sequences in shift invariant spaces j geom anal 15 2005 181 191 in order to make it comparable with existing results then we compare the special cases of the three results in the literature in the setting of the perturbation of the generating sets of finitely generated shift invariant spaces of l 2 r d

robust adaptive pole placement for linear time varying systems this paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances the algorithm consists of a projected gradient estimator and a pole assignment controller a unified method of proof is presented for robust stability of both discrete and continuous time adaptively controlled time varying systems the robust performance of an adaptive pole assignment controller is also discussed

global boundedness of discrete time adaptive control just using estimator projection in this paper we study a discrete time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module this adaptive control algorithm does not involve modifications like data normalization use of deadzones or injection of persistently excited signals also it requires no a priori knowledge of system modelling errors it is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics the problem of indirect decentralized adaptive control of interconnected systems is also considered we use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems we show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions reference inputs disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem

space efficient secret sharing for implicit data security this paper presents a k threshold computational secret sharing technique that distributes a secret s into shares of size s k 1 where s denotes the secret size this bound is close to the space optimal bound of s k if the secret is to be recovered from k shares in other words our technique can be looked upon as a new information dispersal scheme that provides near optimal space efficiency the proposed scheme makes use of repeated polynomial interpolation and has potential applications in secure information dispersal on the web and in sensor networks

meaningful secret sharing technique with authentication and remedy abilities lin and tasi yang et al and chang et al s meaningful secret sharing schemes provided authentication mechanisms but none included a remedy ability that would cause the secret image never to be completely obtained while some information of the stego images are losing or tampering with this paper proposes a meaningful secret sharing scheme which includes both authentication and remedy abilities that allow for detection of the corrupted area and use of the hidden information to repair the secret image with reasonable visual quality in comparison with previous schemes this approach results in superior visual qualities of the stego images by an average of more than 3db

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution