new schemes for sharing points on an elliptic curve a multiple secret sharing scheme can share a group of secrets in each sharing session this scheme is deemed to be very useful in sharing important secrets however previously no scheme on sharing points on an elliptic curve has been devised in responding to the problem this paper proposes a new t n multi point sharing scheme using self pairing on an elliptic curve the security of the proposed scheme was examined towards the end of the study the researchers concluded that the new scheme was computationally secure if at least n t 1 users in the scheme are honest and if o lgq points at most are shared therefore the threshold digital signature scheme on an elliptic curve can be designed and implemented easily

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

secure multiparty computation of solid geometric problems and their applications secure multiparty computation is an area of recent research in the international cryptographic community and secure computational geometry is an essential field of secure multiparty computation most of the existing studies of secure multiparty computational geometric problems have focused on plane geometry while very few have addressed solid geometry because solid geometry is an integral part of geometry and describes the real world better than plane geometry research on secure computational solid geometry is appealing motivated by an interesting application we first examine the problem of the secure multiparty computation of a tetrahedron propose a solution and prove that the solution is private using an accepted simulation paradigm using the solution to the tetrahedron problem as a building block we further solve the secure multiparty computation of three other solid geometric problems including the relationship between a point and a plane the relationship between a line and a plane and the relationship between two planes we also demonstrate that the solutions to these problems are private we analyze the computational and communication complexities of these solutions and show that the computational complexities are near or equal to the problems minimum theoretical computational complexity and that the communication complexities are equal to the minimum theoretical communication complexity thus these solutions are optimal finally we show an interesting application of secure computational solid geometry

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

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

isomorphism classes of short gorenstein local rings via macaulay s inverse system in this paper we study the isomorphism classes of artinian gorenstein local rings with socle degree three by means of macaulay s inverse system we prove that their classification is equivalent to the projective classification of the hypersurfaces of p n of degree three this is an unexpected result because it reduces the study of this class of local rings to the homogeneous case the result has applications in problems concerning the punctual hilbert scheme hilbd p n and

secret sharing schemes from binary linear codes in principle every linear code can be used to construct a secret sharing scheme however in general determining the access structure of the scheme is very hard on the other hand finding error correcting codes that produce secret sharing schemes with efficient access structures is also difficult in this paper we study a set of minimal codewords for certain classes of binary linear codes and then determine the access structure of secret sharing schemes based on these codes furthermore we prove that the secret sharing schemes obtained are democratic in the sense that every participant is involved in the same number of minimal access sets

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

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

witness sets of projections abstract elimination is a basic algebraic operation which geometrically corresponds to projections this article describes using the numerical algebraic geometric concept of witness sets to compute the projection of an algebraic set the ideas described in this article apply to computing the image of an algebraic set under any linear map

a secret sharing scheme based on cellular automata a new secret sharing scheme based on a particular type of discrete delay dynamical systems memory cellular automata is proposed specifically such scheme consists of a k n threshold scheme where the text to be shared is considered as one of the k initial conditions of the memory cellular automata and the n shares to be distributed are n consecutive configurations of the evolution of such cellular automata it is also proved to be perfect and ideal

a generalization of the structured singular value and its application to model validation the structured singular value spl mu gives a means of assessing the stability and performance of a system under a class of norm bounded structured perturbations this paper introduces a generalization of spl mu which guarantees stability with respect to perturbations where some elements of the perturbation structure are bounded from above and some are bounded from below this generalization is used to solve the frequency domain robust control model validation problem model validation determines whether or not there exist a model in the model set and a bounded noise signal that are consistent with the experimental input output measurements a computable convex upper bound to the generalized spl mu problem is presented and the relationship between the generalized spl mu problem and the standard spl mu and model validation problems is discussed

a mixed h2 h approach to simultaneous fault detection and control this paper considers the simultaneous fault detection and control sfdc problem this problem is formulated as a mixed h 2 h optimization problem and its solution is presented in terms of two coupled riccati equations this solution yields controller detector systems of modest complexity an easily implementable design algorithm summarizes the methodology presented in the paper

free extensions and jordan type abstract free extensions of graded artinian algebras were introduced by t harima and j watanabe and were shown to preserve the strong lefschetz property the jordan type of a multiplication map m by a nilpotent element of an artinian algebra is the partition determining the sizes of the blocks in a jordan matrix for m we show that a free extension c of the artinian algebra a with fiber b is a deformation of the usual tensor product this has consequences for the generic jordan types of a b and c we show that the jordan type of c is at least that of the usual tensor product in the dominance order theorem 2 5 in particular this gives a different proof of the t harima and j watanabe result concerning the strong lefschetz property of a free extension examples illustrate that a non strong lefschetz graded gorenstein algebra a with non unimodal hilbert function may nevertheless have a non homogeneous element with strong lefschetz jordan type and may have an a free extension that is strong lefschetz we apply these results to algebras of relative coinvariants of linear group actions on a polynomial ring

on secret sharing systems a secret sharing system permits a secret to be shared among n trustees in such a way that any k of them can recover the secret but any k 1 have complete uncertainty about it a linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by shamir and can also be viewed as a deterministic version of blakley s probabilistic method bounds on the maximum value of n for a given k and secret size are derived for any system linear or nonlinear the proposed scheme achieves the lower bound which for practical purposes differs insignificantly from the upper bound the scheme may be extended to protect several secrets methods to protect against deliberate tampering by any of the trustees are also presented

design and analysis of robust fault detection filter using lmi tools in this paper the robust fault detection filter design problem for linear time invariant lti systems with unknown inputs and modeling uncertainties is studied the basic idea of our study is to formulate the robust fault detection filter design as a h model matching problem a solution of the optimal problem is then presented via a linear matrix inequality lmi formulation the main results include the formulation of robust fault detection filter design problems the derivation of a sufficient condition for the existence of a robust fault detection filter and construction of a robust fault detection filter based on the iterative of lmi algorithm

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

vector bundles give equations of cactus varieties abstract we prove that vector bundles give equations of cactus varieties we derive from it that equations coming from vector bundles are not enough to define secant varieties of veronese varieties in general

efficient verifiable multi secret sharing scheme based on hash function abstract a verifiable k t n multi secret sharing scheme vmss allows a dealer to share k secrets among n players in particular 1 the secret shadow given by the dealer or some player can be verifiable and 2 t or more players can cooperate to reveal the k secrets while less than t players cannot reveal any secret vmss can be used in many applications such as access control however the existing vmss schemes either require costly computation or miss some important properties of vmss these two weaknesses make the vmss scheme not so good as expected in this paper we propose a novel vmss scheme which does not need any costly computation while holds all properties of vmss

on varieties of commuting triples abstract the problem of approximating triples of commuting n n matrices by triples of generic matrices is equivalent to that whether the variety c 3 n of triples of commuting matrices is irreducible it is known that the variety is irreducible for n 7 and reducible for n 30 using simultaneous commutative perturbations of pairs of matrices in the centralizer of the third matrix we prove that c 3 8 is irreducible

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

communication efficient secret sharing a secret sharing scheme is a method to store information securely and reliably particularly in a threshold secret sharing scheme a secret is encoded into n shares such that any set of at least t 1 shares suffice to decode the secret and any set of at most t 2 shares reveal no information about the secret assuming that each party holds a share and a user wishes to decode the secret by receiving information from a set of parties the question we study is how to minimize the amount of communication between the user and the parties we show that the necessary amount of communication termed decoding bandwidth decreases as the number of parties that participate in decoding increases we prove a tight lower bound on the decoding bandwidth and construct secret sharing schemes achieving the bound particularly we design a scheme that achieves the optimal decoding bandwidth when d parties participate in decoding universally for all t 1 le d le n the scheme is based on a generalization of shamir s secret sharing scheme and preserves its simplicity and efficiency in addition we consider the setting of secure distributed storage where the proposed communication efficient secret sharing schemes not only improve decoding bandwidth but further improve disk access complexity during decoding

an iterative error free algorithm to solve vandermonde systems the paper describes an algorithm to solve vandermonde system of linear equations the algorithm is error free i e it does not introduce either rounding off errors or errors caused by finite length of computer word into the solution cost analysis and its comparison to alternative error free method are included

an improvement on the lin wu t n threshold verifiable multi secret sharing scheme lin and wu iee proc comput digit tech 146 1999 264 have proposed an efficient t n threshold verifiable multi secret sharing vmss scheme based on the factorization problem and the discrete logarithm modulo a large composite problem in their scheme the dealer can arbitrarily give any set of multiple secrets to be shared and only one reusable secret shadow is to be kept by every participant on the other hand they have claimed that their scheme can provide an efficient solution to the cheating problems between the dealer and any participant however he and wu iee proc comput digit tech 148 2001 139 have shown that lin and wu s scheme is in fact insecure against a cheating participant in this paper we shall try to improve the security of lin and wu s scheme while providing more efficient performance than other vmss schemes in terms of computational complexity

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

visual secret sharing for multiple secrets conventional visual secret sharing schemes are designed for a single secret image so it is inefficient to generate numerous share images for multiple secret images simultaneously therefore a novel visual secret sharing scheme for multiple secret images is proposed in this paper in the proposed encryption process a stacking relationship graph of secret pixels and share blocks is generated to indicate the encryption functions and a set of visual patterns is defined to produce two share images according to this graph based on the stacking properties of these patterns the secret images can be obtained from the two share images at aliquot stacking angles the proposed scheme makes the number of secret images not restricted and further extends it to be general as a result the proposed scheme enhances visual secret sharing schemes ability for multiple secrets

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

k3 surfaces of genus 8 and varieties of sums of powers of cubic fourfolds the main result of this paper is that the variety of presentations of a general cubic form f in 6 variables as a sum of 10 cubes is isomorphic to the fano variety of lines of a cubic 4 fold f in general different from f z f a general k3 surface s of genus 8 determines uniquely a pair of cubic 4folds the apolar cubic f s and the dual pfaffian cubic f s or for simplicity f and f as beauville and donagi have shown the fano variety tf of lines on the cubic f is isomorphic to the hilbert scheme hilb2 s of length two subschemes of s the first main result of this paper is that hilb2 s parametrizes the variety vsp f 10 of presentations of the cubic form f with f z f as a sum of 10 cubes which yields an isomorphism between nff and vsp f 10 furthermore we show that vsp f 10 sets up a 6 10 correspondence between f and ff the main result follows by a deformation argument 1 pfaffian and apolar cubic 4 folds associated to k3 surfaces of genus 8 1 1 let v be a 6 dimensional vector space over c fix a basis e e5 for v then ei a ej for 0 i j aijei aej e a2v a skewsymmetric matrix m g aij with aji aj with pliicker coordinates xij the embedding of the grassmannian g g 2 v in p14 p a2v is then precisely the locus of rank 2 skewsymmetric 6 x 6 matrices 0 x01 x02 x03 x04 x05 x0i 0 x12 x13 x14 x15 m x02 x12 0 x23 x24 x25 x03 x13 x23 0 x34 x35 x04 x14 x24 x34 0 x45 x05 x15 x25 x35 x45 0 since the sum of two rank 2 matrices has rank at most 4 and any rank 4 skewsymmetric matrix is the sum of two rank 2 skewsymmetric matrices the secant variety of g is the cubic hypersurface k defined by the 6 x 6 pfaffian m of the matrix m the dual variety of g in p14 p a2v is a cubic hypersurface k k cf 10 k is the secant variety of g g v 2 the grassmannian of rank 2 quotient spaces of v and of course g c g received by the editors july 5 1999 2000 mathematics subject classification primary 14j70 secondary 14m15 14n99 2000 american mathematical society

reversible cellular automata with memory two dimensional patterns from a single site seed standard cellular automata ca are ahistoric memoryless i e the new state of a cell depends on its neighborhood configuration only at the preceding time step historic memory of all past iterations can be incorporated into ca by featuring each cell by a weighted mean of all its past states in this paper a new kind of reversible ca which incorporates memory is introduced in a two dimensional scenario

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

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

multiple ramp schemes a t k n s ramp scheme is a protocol to distribute a secret s chosen in s among a set p of n participants in such a way that 1 sets of participants of cardinality greater than or equal to k can reconstruct the secret s 2 sets of participants of cardinality less than or equal to t have no information on s whereas 3 sets of participants of cardinality greater than t and less than k might have some information on s in this correspondence we analyze multiple ramp schemes which are protocols to share many secrets among a set p of participants using different ramp schemes in particular we prove a tight lower bound on the size of the shares held by each participant and on the dealer s randomness in multiple ramp schemes

vsps of cubic fourfolds and the gorenstein locus of the hilbert scheme of 14 points on a6 abstract to a cubic fourfold one may associate a geometric object a hyperkahler manifold via the theory of vsp and an algebraic object a finite gorenstein algebra via apolarity we prove that the associated algebra is smoothable if and only if the fourfold lies on the iliev ranestad divisor which parameterizes certain cubics whose vsp is isomorphic to the hilbert scheme of two points on a k3 surface this bridge allows us to give a detailed description of the algebraic side i e the gorenstein locus of 14 points on a 6 and also to identify the equation of the iliev ranestad divisor as the unique degree 10 invariant of sl 6 as our main technical tool we develop a relative version of apolarity building on ideas of elias rossi

secret image sharing based on cellular automata and steganography recently lin and tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 and yang et al improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 proposed secret image sharing schemes combining steganography and authentication based on shamir s polynomials the schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants to achieve better authentication ability chang et al sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1 16 in this paper we employ linear cellular automata digital signatures and hash functions to propose a novel t n threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255 256 employing cellular automata instead of shamir s polynomials not only improves computational complexity from o nlog 2n to o n but obviates the need to modify pixels of cover images unnecessarily compared to previous methods c lin w tsai secret image sharing with steganography and authentication the journal of systems and software 73 2004 405 414 c yang t chen k yu c wang improvements of image sharing with steganography and authentication the journal of systems and software 80 2007 1070 1076 c chang y hsieh c lin sharing secrets in stego images with authentication pattern recognition 41 2008 3130 3137 we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed we further present some experimental results

brief robust fault detection in uncertain dynamic systems the work reported in this paper focuses on the design of optimal filters for fault detection in uncertain dynamic systems a design procedure dealing with interval type parameter uncertainties is proposed for residual generation via a frequency domain approach robustness enhancement is based on the design of optimal detection filters maximizing the effect of faults while minimizing the influence of disturbances in this framework in order to cope with parameter uncertainties kharitonov polynomials and dasgupta geometry are introduced and an extension of previous results to worst case situation is proposed an example is also included to illustrate the method efficiency

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

h h fault detection filter design for discrete time takagi sugeno fuzzy system abstract in this note a robust fault detection observer is designed for a t s takagi sugeno fuzzy model with sensor faults and unknown bounded disturbances the method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable the idea is to formulate the robust fault detection observer design as an h h problem based on nonquadratic lyapunov functions a solution of the considered problem is then given via a linear matrix inequality lmi formulation an example is proposed to illustrate the design conditions

the structure of the inverse system of gorenstein k algebras abstract macaulay s inverse system gives an effective method to construct artinian gorenstein k algebras to date a general structure for gorenstein k algebras of any dimension and codimension is not understood in this paper we extend macaulay s correspondence characterizing the submodules of the divided power ring in one to one correspondence with gorenstein d dimensional k algebras we discuss effective methods for constructing gorenstein graded rings several examples illustrating our results are given

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

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

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

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

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

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature