Linear multi-secret sharing schemes based on multi-party computation

In multi-secret sharing schemes, publishing shares during the process of reconstructing partial secrets may leak some information of the secrets unrecovered yet. By using a multi-party computation (MPC) protocol, we solve this problem for any linear multi-secret sharing scheme (MSSS). We also show that LMSSS usually involve more complicated reconstruction algorithms than “direct sum” schemes, but from the point of reducing share expansion, the former is preferred.     

Rearrangements of access structures and their realizations in secret sharing schemes

Firstly, the definitions of the secret sharing schemes (SSS), i.e. perfect SSS, statistical SSS and computational SSS are given in an uniform way, then some new schemes for several familiar rearrangements of access structures with respect to the above three types of SSS are constructed from the old schemes. It proves that the new schemes and the old schemes are of the same security. A method of constructing the SSS which realizes the general access structure by rearranging some basic access structures is developed. The results of this paper can be used to key managements and access controls.     

基于线性码的新的秘密分享方案

A secret sharing system can be damaged when the dealer cheating occurs. In this paper,two kinds of secret sharing schemes based on linear code are proposed. One is a verifiable scheme which each participant can verify his own share from dealer‘s distribution and ensure each participant to receive valid share. Another does not have a trusted center, here, each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.     

FCSR序列的线性复杂度

§ 1　 IntroductionFeedback with carry shift register(FCSR) was first introduced by Klapper andGoresky in1 994[1 ] .The main idea of FCSR is to add a memory to linearfeedback shiftreg-ister(LFSR) .The structure is depicted in Fig.1 ,Fig.1where mn- 1 ∈Z,ai,qi∈ { 0 ,1 } and qr=1 .We refer to mn- 1 as memory,(mn- 1 ,an- 1 ,...,an- r)as state,r=log(q+ 1 ) as length,and q=-1 + q1 · 2 + ...+ qr· 2 ras connection integerof FCSR.The operation of the shiftregister is defined as follows:(1 …     

Linear Secret Sharing Schemes and Rearrangements of Access Structures

In this paper we study linear secret sharing schemes by monotone span programs, according to the relation between realizing access structures by linear secret sharing schemes and computing monotone Boolean functions by monotone span programs. We construct some linear secret sharing schemes. Furthermore, we study the rearrangements of access structures that is very important in practice.     

Constructions of projective linear codes by the intersection and difference of sets

Projective linear codes are a special class of linear codes whose dual codes have minimum distance at least 3. Projective linear codes with only a few weights are useful in authentication codes, secret sharing schemes, data storage systems and so on. In this paper, two constructions of q-ary linear codes are presented with defining sets given by the intersection and difference of two sets. These constructions produce several families of new projective two-weight or three-weight linear codes. As applications, our projective codes can be used to construct secret sharing schemes with interesting access structures, strongly regular graphs and association schemes with three classes.     

The expectation and variance of the joint linear complexity of random periodic multisequences

The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. By using the generalized discrete Fourier transform for multisequences, Meidl and Niederreiter determined the expectation of the joint linear complexity of random N-periodic multisequences explicitly. In this paper, we study the expectation and variance of the joint linear complexity of random periodic multisequences. Several new lower bounds on the expectation of the joint linear complexity of random periodic multisequences are given. These new lower bounds improve on the previously known lower bounds on the expectation of the joint linear complexity of random periodic multisequences. By further developing the method of Meidl and Niederreiter, we derive a general formula and a general upper bound for the variance of the joint linear complexity of random N-periodic multisequences. These results generalize the formula and upper bound of Dai and Yang for the variance of the linear complexity of random periodic sequences. Moreover, we determine the variance of the joint linear complexity of random periodic multisequences with certain periods.     

Two classes of two-weight linear codes

Two-weight linear codes have many wide applications in authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we present two classes of two-weight binary or ternary linear codes. In some cases, they are optimal or almost optimal. They can also be used to construct secret sharing schemes.     

Successive minima profile,lattice profile,and joint linear complexity profile of pseudorandom multisequences

In this paper we use the successive minima profile to measure structural properties of pseudorandom multisequences. We show that both the lattice profile and the joint linear complexity profile of a multisequence can be expressed in terms of the successive minima profile.     

Optimal error estimate of two linear and momentum-preserving Fourier pseudo-spectral schemes for the RLW equation

In this paper, two novel linear-implicit and momentum-preserving Fourier pseudo-spectral schemes are proposed and analyzed for the regularized long-wave equation. The numerical methods are based on the blend of the Fourier pseudo-spectral method in space and the linear-implicit Crank–Nicolson method or the leap-frog scheme in time. The two fully discrete linear schemes are shown to possess the discrete momentum conservation law, and the linear systems resulting from the schemes are proved uniquely solvable. Due to the momentum conservative property of the proposed schemes, the Fourier pseudo-spectral solution is proved to be bounded in the discrete L^∞ norm. Then by using the standard energy method, both the linear-implicit Crank–Nicolson momentum-preserving scheme and the linear-implicit leap-frog momentum-preserving scheme are shown to have the accuracy of in the discrete L^∞ norm without any restrictions on the grid ratio, where N is the number of nodes and τ is the time step size. Numerical examples are carried out to verify the correction of the theory analysis and the efficiency of the proposed schemes.     

Webs, Lenard schemes, and the local geometry of bi-Hamiltonian Toda and Lax structures

We introduce a criterion that a given bi-Hamiltonian structure admits a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bi-Hamiltonian open Toda lattice in a generic point, which is shown to be locally isomorphic to a Kronecker odd-dimensional pair of brackets with constant coefficients. This shows that the open Toda lattice cannot be locally represented as a product of two bi-Hamiltonian structures. Near, a generic point, the bi-Hamiltonian periodic Toda lattice is shown to be isomorphic to a product of two open Toda lattices (one of which is a (trivial) structure of dimension 1). While the above results might be obtained by more traditional methods, we use an approach based on general results on geometry of webs. This demonstrates the possibility of applying a geometric language to problems on bi-Hamiltonian integrable systems; such a possibility may be no less important than the particular results proved in this paper. Based on these geometric approaches, we conjecture that decompositions similar to the decomposition of the periodic Toda lattice exist in local geometry of the Volterra system, the complete Toda lattice, the multidimensional Euler top, and a regular bi-Hamiltonian Lie coalgebra. We also state general conjectures about the geometry of more general "homogeneous" finite-dimensional bi-Hamiltonian structures. The class of homogeneous structures is shown to coincide with the class of systems integrable by Lenard scheme. The bi-Hamiltonian structures which admit a non-degenerate Lax structure are shown to be locally isomorphic to the open Toda lattice.     

A potential of fuzzy relations with a linear structure: The contractive case

In this paper we develop a potential theory of fuzzy relations on the positive orthant in a Euclidean space. By introducing a linear structure for fuzzy relations, the existence of a potential and its characterization by fuzzy relational equation are derived under the assumption of contraction and compactness. In the one-dimensional unimodal case, a potential is given explicity. Also, a numerical example is shown to illustrate our approaches.     

The uniqueness theorems of meromorphic functions sharing three values and a set with two elements

In this paper, we deal with a uniqueness theorem of two meromorphic functions that have three weighted sharing values and a sharing set with two elements. The results in this paper improve those given by G. Brosch, K. Tohge, T.C. Alzahary and H.X. Yi and other authors.     

The blue and minque in Gauss-Markoff model with linear transformation of the observable variables

For a singular linear model A = (y, Xβ, σ2 V) and its transformed model AF = (Fy, FXβ, σ2FVF'), where V is nonnegative definite and X can be rank-deficient,the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala (1981) are strengthened and consequences in Puntanen and Nurhonen (1992), and Puntanen (1996) are extended.     

The impact of sharing customer returns information in a supply chain with and without a buyback policy

In this paper, we examine a single period problem in a supply chain in which a Stackelberg manufacturer supplies a product to a retailer who faces customer returns and demand uncertainty. We show that the manufacturer incurs a significant profit loss with and without a buyback policy if it fails to account for customer returns in the wholesale price decision. Under the assumption that the retailer is better informed than the manufacturer on customer returns information, we show that without a buyback policy, the retailer prefers not to share if the manufacturer overestimates while it prefers to share customer returns information if the manufacturer underestimates this information. If the manufacturer offers a buyback policy, we have the opposite results. We also discuss incentives to share the customer returns information and some of the issues that are raised in sharing this information.     

The stability and convergence of two linearized finite difference schemes for the nonlinear epitaxial growth model

The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE model. The linearized backward Euler difference scheme and the linearized Crank‐Nicolson difference scheme are derived. The unique solvability, unconditional stability and convergence are proved. The linearized Euler scheme is convergent with the convergence order of O(τ + h²) and linearized Crank‐Nicolson scheme is convergent with the convergence order of O(τ² + h²) in discrete L²‐norm, respectively. Numerical stability with respect to the initial conditions is also obtained for both schemes. Numerical experiments are carried out to demonstrate the theoretical analysis. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Detection and identification of cheaters in (<Emphasis Type="Italic">t</Emphasis>, <Emphasis Type="Italic">n</Emphasis>) secret sharing scheme

In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir’s secret sharing scheme.      

Tables of linear congruential generators of different sizes and good lattice structure

We provide sets of parameters for multiplicative linear congruential generators (MLCGs) of different sizes and good performance with respect to the spectral test. For , we take as a modulus the largest prime smaller than , and provide a list of multipliers such that the MLCG with modulus and multiplier has a good lattice structure in dimensions 2 to 32. We provide similar lists for power-of-two moduli , for multiplicative and non-multiplicative LCGs.