basic theory and properties of statistically optimized near field acoustical holography to avoid the requirement set by standard near field acoustical holography nah to measure an area that fully covers the source a set of so called patch nah methods has been introduced one such method is the statistically optimized nah sonah in this method the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy the present paper gives an overview of the basic theory of sonah including a description of phenomena such as spatial aliasing and wave number domain leakage a revised and generalized mathematical formulation is given covering the calculation of all three components of particle velocity and the use of up to six virtual source planes a set of formulas for the inherent estimation error level of the method is derived and used to visualize the regions of validity of the sonah predictions for some typical microphone array geometries the sensitivity of the inherent error level distribution to changes in the parameters of the sonah algorithm is also investigated

an adaptive secret image sharing with a new bitwise steganographic property recently numerous studies have been conducted in the area of secret image sharing and steganography the main objective of these schemes is to produce high quality tampering resistant stego images a number of these methods are based on least significant bit embedding and hence the presence of hidden data can be detected by well designed steganalysis algorithms this paper proposes a new sharing scheme for critical images so that stego images are obtained with better visual quality and at the same time the authentication ability can be adjusted to any desired level adaptive in order to achieve these objectives the construction of cellular automata is modified so that visual quality is improved although authentication bits are hidden in cover images furthermore authentication bits are computed in such a way that any tampering with one block affects more than one block for steganographic purposes least significant bit replacement is substituted with a new blockwise xor operation so that the scheme can withstand steganalysis attacks the other interesting property of the proposed method is that the size of blocks is determined dynamically therefore our approach can be adapted with secret cover images of different sizes

sound field reconstruction using compressed modal equivalent point source method the accuracy resolution and economic cost of near field acoustic holography nah are highly dependent on the number of spatial sampling points generally higher accuracy and resolution require more spatial sampling points which may increase the workload of measurement or the hardware cost compressive sensing cs is able to solve the underdetermined problems by utilizing the sparsity of signals and thus it can be applied to nah to reduce the number of spatial sampling points but at the same time provide a high resolution reconstruction image based on the cs theory this paper proposes a compressed modal equivalent point source method cmesm in the method a sparse basis that is obtained from the eigen decomposition of the power resistance matrix is introduced to compress the equivalent point source strengths and the l1 norm minimization is used to promote sparse solutions both numerical simulation and experimental results demonstrate the validity of the proposed cmesm and show its advantage over the existing methods when the number of spatial sampling points is reduced

extending the bandwidth of an acoustic beamforming array using phase unwrapping and array interpolation a method is presented to suppress grating lobes in beamforming using phase unwrapping and array interpolation when the phase of each cross spectrum is successfully unwrapped the magnitude and phase of the cross spectral matrix may be interpolated for cases where these quantities vary smoothly interpolation is straightforward even above the spatial nyquist frequency two applications are presented localization of a broadband source and characterization of a source with frequency dependent location in both cases grating lobes are suppressed and the source is localized at frequencies up to at least 8 times the spatial nyquist frequency

congruences for the coefficients of weakly holomorphic modular forms recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli we show that this type of phenomenon is completely general by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup gamma 0 n in particular we give congruences for a wide class of partition functions and for traces of cm values of arbitrary modular functions on certain congruence subgroups of prime level

two verifiable multi secret sharing schemes based on nonhomogeneous linear recursion and lfsr public key cryptosystem we shall propose two new efficient verifiable multi secret sharing schemes based on linear feedback shift register lfsr public key and new nonhomogeneous linear recursions compared with previous schemes these schemes have better performance and shorter private public key length moreover they have fewer public values and simpler construction as well as various methods for the reconstruction phase altogether they are easy to use and provide great capabilities for many applications

a t n multi secret sharing scheme in the t n multi secret sharing scheme there are n participants in the system at least t or more participants can easily pool their secrets shadows and reconstruct p secrets at the same time chien et al ieice trans fundamentals e83 a 2000 2762 used n p t 1 public values 2 n p t x n p storages and solved n p t simultaneous equations to share p secrets in this article we shall propose an alternative t n multi secret sharing based on shamir s secret sharing we shall use n p t 1 or n 1 public values 2 t 1 or 2 p 1 storages and employ the lagrange interpolation polynomial to share p secrets our scheme will have exactly the same power as chien et al s scheme

a new efficient t n verifiable multi secret sharing vmss based on ych scheme a verifiable multi secret sharing scheme vmss is a multi secret sharing scheme with the verifiable property this paper presents a new efficient verifiable multi secret sharing based on ych c c yang t y chang m s hwang a t n multi secret sharing scheme appl math comput 151 2004 483 490 scheme and the intractability of the discrete logarithm dl and it just needs few public values and low modular exponentiation operation

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

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

some spherical uniqueness theorems for multiple trigonometric series we prove that if a multiple trigonometric series is spherically abel summable everywhere to an everywhere flnite functionf x which is bounded below by an integrable function then the series is the fourier series of f x i f the coe cients of the multiple trigonometric series satisfy a mild growth condition as a consequence we show that if a multiple trigonometric series is spherically convergent everywhere to an everywhere flnite integrable function f x then the series is the fourier series of f x we also show that a singleton is a set of uniqueness these results are generalizations of a recent theorem of j bourgain and some results of v shapiro

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

a scheme for threshold multi secret sharing a multi secret sharing scheme is a natural generalization of the secret sharing scheme we show the close similarity between the chinese remainder theorem and the uniqueness theorem of interpolating polynomial based on the similarity we propose a threshold multi secret sharing scheme that is a generalization of the shamir threshold scheme we also show that the proposed scheme with the proposed deletion procedure can realize all possible monotone access structures

fast wideband acoustical holography patch near field acoustical holography methods like statistically optimized near field acoustical holography and equivalent source method are limited to relatively low frequencies where the average array element spacing is less than half of the acoustic wavelength while beamforming provides useful resolution only at medium to high frequencies with adequate array design both methods can be used with the same array but for holography to provide good low frequency resolution a small measurement distance is needed whereas beamforming requires a larger distance to limit sidelobe issues the wideband holography method of the present paper was developed to overcome that practical conflict only a single measurement is needed at a relatively short distance and a single result is obtained covering the full frequency range the method uses the principles of compressed sensing a sparse sound field representation is assumed with a chosen set of basis functions a measurement is taken with an irregular array and the inverse problem is solved with a method that enforces sparsity in the coefficient vector instead of using regularization based on the 1 norm of the coefficient vector an iterative solution procedure is used that promotes sparsity the iterative method is shown to provide very similar results in most cases and to be computationally much more efficient

a verifiable threshold secret sharing scheme based on lattices abstract the generalized compact knapsack function is defined as f a x i a i x i where a a 1 a m r for some ring r and x x 1 x m s for a specified subset s r it is known that for appropriate choice of r and s inverting this function is at least as hard as solving certain worst case problems on cyclic lattices in this paper we exploit collision resistance as well as homomorphic properties of this function to propose a threshold verifiable secret sharing scheme with two distinguished features first the security of the scheme is completely based on lattice problems and second upon receiving shares participants can verify consistency of their shares with the secret without any communication

compact sequences of co primes and their applications to the security of crt based threshold schemes crt based threshold secret sharing schemes use sequences of pairwise co prime positive integers in their construction if these sequences are not compact then the crt based threshold secret sharing schemes may have a weak security in the sense of a massive loss of entropy or an arbitrarily large information rate in this paper compact sequences of co primes are introduced and their applications to the security of crt based threshold secret sharing schemes is throughout investigated it is shown that all the results regarding the security of crt based threshold secret sharing schemes that use sequences of consecutive primes also hold for threshold secret sharing schemes that use compact sequences of co primes moreover compact sequences of co primes may be significantly denser than sequences of consecutive primes of the same length and their use in the construction of crt based threshold secret sharing schemes may lead to better security properties

a multiple level visual secret sharing scheme without image size expansion in traditional vss schemes the size of the share image is substantially expanded since each pixel of the secret image is mapped onto a block consisting of several pixels in addition the quality of the reconstructed secret image is normally degraded in contrast especially for halftone images this study proposes a vss scheme that maps a block in a secret image onto one corresponding equal sized block in each share image without image size expansion two types of techniques including histogram width equalization and histogram depth equalization are proposed to generate the corresponding share blocks containing multiple levels rather than two levels based on the density of black pixels on the blocks for a secret block in the former technique the gray scale image histogram is obtained by uniformly splitting the range of the pixel gray levels in the secret image while in the latter the buckets are created so that the area of each bucket is roughly constant by containing approximately the same number of pixels the proposed schemes significantly improve the quality of the reconstructed secret image compared to several previous investigations

a modular approach to key safeguarding a method is proposed for a key safeguarding scheme threshold scheme in which the shadows are congruence classes of a number associated with the original key a variation of this scheme provides efficient error detection and even exposes deliberate tampering certain underlying similarities of this scheme with shamir s interpolation method make it possible to incorporate these protective features in that method as well

a novel efficient t n threshold proxy signature scheme all previously proposed threshold proxy signature schemes have been based on discrete logarithms required for a protocol to generate and verify a shared secret among the proxy group therefore it is necessary for the proxy signers to perform many expensive modular exponential computations and communications to obtain and verify a shared secret moreover most of the existing threshold proxy signature schemes reveal that the receiver cannot find out who signed the proxy signatures we propose an efficient t n threshold proxy signature scheme based on schnorr s scheme compared with existing t n threshold proxy signature schemes our scheme can reduce the amount of computations and communications in our method not only the original signer can know who generated the proxy signature but also the receiver can certify the actuality of the group signers who made the proxy signature we offer convenience and fair distribution of auditing a document s signers

divisibility and distribution of partitions into distinct parts abstract we study the generating function for q n the number of partitions of a natural number n into distinct parts using the arithmetic properties of fourier coefficients of integer weight modular forms we prove several theorems on the divisibility and distribution of q n modulo primes p 5

a study on regularization parameter choice in near field acoustical holography regularization plays an important role in near field acoustical holography nah and choosing the right amount of regularization is crucial in order to get a meaningful solution an automated method such as the l curve or generalized cross validation gcv is often used in nah to choose a regularization parameter these parameter choice methods pcms are attractive since they require no a priori knowledge about the noise however there seems to be no clear understanding of when one pcm is better than the other this paper presents comparisons of three pcms gcv l curve and normalized cumulative periodogram ncp the latter method is new within nah and it is based on the fourier transform of the residual vector the methods are used in connection with three nah methods statistically optimized near field acoustical holography sonah the inverse boundary element method ibem and the equivalent source method esm all combinations of the pcms and the nah methods are investigated using simulated measurements with different types of noise added to the input finally the comparisons are carried out for a practical experiment this aim of this work is to create a better understanding of which mechanisms that affect the performance of the different pcms

public key cryptosystems based on cubic finite field extensions the cryptographic properties of third order linear feedback shift register lfsr sequences over gf p are investigated a fast computational algorithm for evaluating the kth term of a characteristic sequence of order 3 is presented based on these properties a new public key distribution scheme and an rsa type encryption algorithm are proposed their security implementation information rate and computational cost for the new schemes are discussed

chinese remaindering with errors the chinese remainder theorem states that a positive integer m is uniquely specified by its remainder module k relatively prime integers p sub 1 spl middot spl middot spl middot p sub k provided m spl pi sub i 1 sup k p sub i thus the residues of m module relatively prime integers p sub 1 p sub 2 spl middot spl middot spl middot p sub n form a redundant representation of m if m spl pi sub i 1 sup k p sub i and k n this gives a number theoretic construction of an error correcting code that has been considered often in the past in this code a message integer m spl pi sub i 1 sup k p sub i is encoded by the list of its residues module p sub 1 spl middot spl middot spl middot p sub n by the chinese remainder theorem if a codeword is corrupted in e n k 2 coordinates then there exists a unique integer m whose corresponding codesword differs from the corrupted word in at most e places furthermore mandelbaum 1976 1978 shows how m can be recovered efficiently given the corrupted word provided that the p sub i s are very close to one another to deal with arbitrary p sub i s we present a variant of his algorithm that runs in almost linear time and recovers from e log p sub 1 log p sub 1 log p sub n spl middot n k errors our main contribution is an efficient decoding algorithm for the case in which the error e may be larger than n k 2 specifically given n residues r sub 1 spl middot spl middot spl middot r sub n and an agreement parameter t we find a list of all integers m spl pi sub i 1 sup k p sub i such that m mod p sub i r sub i for at least t values of i spl isin 1 spl middot spl middot spl middot n provided t spl omega spl radic kn log p sub n log p sub 1 for n spl gt k and p sub n spl les p sub 1 sup o 1 the fraction of error corrected by the algorithm is almost twice that corrected by the previous work more significantly the algorithm recovers the message even when the amount of agreement between the received word and the codeword is much smaller than the number of errors

verifiable multi secret sharing based on lfsr sequences in verifiable multi secret sharing schemes vmsss many secrets can be shared but only one share is kept by each user and this share is verifiable by others in this paper we propose two secure efficient and verifiable t n multi secret sharing schemes namely scheme i and scheme ii scheme i is based on the lagrange interpolating polynomial and the lfsr based public key cryptosystem the lagrange interpolating polynomial is used to split and reconstruct the secrets and the lfsr based public key cryptosystem is employed to verify the validity of the data scheme ii is designed according to the lfsr sequence and the lfsr based public key cryptosystem we compare our schemes with the state of the art in terms of attack resistance computation complexity and so on and conclude that our schemes have better performance and incur less computation overhead our schemes can effectively detect a variety of forgery or cheating actions to ensure that the recovery of the secrets is secure and creditable and the length of the private key is only one third of that of others for the same security level

partition identities involving gaps and weights we obtain interesting new identities connecting the famous partition functions of euler gauss lebesgue rogers ramanujan and others by attaching weights to the gaps between parts the weights are in general multiplicative some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2

a new t n multi secret sharing scheme based on shamir s secret sharing in 2000 chien et al proposed a t n multi secret sharing scheme at least t of the n participants can easily reconstruct p secrets at the same time but the secret reconstruction needs to solve simultaneous equations which is a complex process in order to reduce the complexity of the secret reconstruction yang et al proposed an alternative scheme based on shamir s secret sharing in 2004 but there are more public values required in yang s scheme than in chien s scheme when p

distributive weighted threshold secret sharing schemes the concept of distributive weighted threshold access structure is introduced which is an weighted threshold access structure where the participants are distributed on levels the participants on the same level are assigned the same weight and the threshold of the access structure is 1 the weight of the participants on the ith level is of the form 1 ki and therefore the ith level induces a standard threshold access structure with threshold ki we propose a crt based realization of distributive weighted threshold access structures which is asymptotically perfect and perfect zero knowledge we also show that distributive weighted threshold access structures do not generally have ideal realizations in case of just one level our scheme can be viewed as an asymptotically perfect and perfect zero knowledge variation of the asmuth bloom secret sharing scheme

a verifiable multi secret sharing scheme based on cellular automata in this paper we propose a verifiable t n threshold multi secret sharing scheme based on one dimensional cellular automata where the number of secrets is not restricted by n or t we show that our scheme can be used to solve an open problem proposed recently in alvarez et al 2008 g alvarez l hernandez encinas a martin del rey a multisecret sharing scheme for color images based on cellular automata information sciences 178 2008 4382 4395

compressive sensing based spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity a low frequency sound field within a cylindrical cavity can be well approximated by a sparse set of fourier bessel series in a spherical coordinate system the approximation accuracy can be guaranteed as long as the series coefficients are well estimated by use of spherical microphone arrays sma conventional methods like spherical fourier transform and helmholtz equation least square require a large number of sensors and it is difficult to estimate the high order coefficients in the presence of sensor noise to cope with these issues compressive sensing cs is utilized and compared with the conventional methods in this study the estimate of the high order coefficients from contaminated measurements is examined and the effect of modal behavior is analyzed numerical simulations show that sensors can be significantly saved especially for high order cavity modes due to the low sparsity of coefficients which is also stable as the modal frequency increases and the overall accuracy is also improved the optimal sma configuration for the use of cs is studied a large sma with omni microphone deployed by the fliege sampling scheme is suggested the cs results are finally validated through the good simulated reconstructions of cylindrical cavity modes

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

scaling of plane wave functions in statistically optimized near field acoustic holography statistically optimized near field acoustic holography sonah is a patch holography method meaning that it can be applied in cases where the measurement area covers only part of the source surface the method performs projections directly in the spatial domain avoiding the use of spatial discrete fourier transforms and the associated errors first an inverse problem is solved using regularization for each calculation point a multiplication must then be performed with two transfer vectors one to get the sound pressure and the other to get the particle velocity considering sonah based on sound pressure measurements existing derivations consider only pressure reconstruction when setting up the inverse problem so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem the present paper introduces a scaling of the applied plane wave functions that takes the amplification into account and it is