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

a direct branching algorithm for checking the equivalence of two deterministic pushdown transducers one of which is real time strict abstract a new direct branching algorithm is presented for checking the equivalence of deterministic pushdown transducers one of whose associated deterministic pushdown automata dpdas is real time strict it is a straightforward extension of the corresponding algorithm for dpdas tomita 1982 and then proves the general applicability of our approach

an extended direct branching algorithm for checking equivalence of deterministic pushdown automata abstract this paper extends the direct branching algorithm of 25 for checking equivalence of deterministic pushdown automata it does so by providing a technique called halting for dealing with nodes with unbounded degree in the comparison tree this may occur when a skipping step may be applied infinitely many times to a certain node as a result of infinite sequences of e moves this extension allows the algorithm to check equivalence of two deterministic pushdown automata when none of them is real time but in a certain condition that properly contains a case where one of them is real time strict

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

upwind finite difference calculation of traveltimes seismic traveltimes can be computed efficiently on a regular grid by an upwind finite difference method the method solves a conservation law that describes changes in the gradient components of the traveltime field the traveltime field itself is easily obtained from the solution of the conservation law by numerical integration the conservation law derives from the eikonal equation and its solution depicts the first arrival time field the upwind finite difference scheme can be implemented in fully vectorized form in contrast to a similar scheme proposed recently by vidale the resulting traveltime field is useful both in kirchhoff migration and modeling and in seismic tomography many reliable methods exist for the numerical solution of conservation laws which appear in fluid mechanics as statements of the conservation of mass momentum etc a first order upwind finite difference scheme proves accurate enough for seismic applications upwind schemes are stable because they mimic the behavior of flu

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

on some decision questions concerning pushdown machines abstract certain decision questions e g equivalence ambiguity single valuedness monotonicity etc concerning pushdown transducers and acceptors are investigated examples of results shown are the following 1 1 there is an algorithm to decide given two deterministic pushdown transducers one of which has a finite turn counter for a pushdown stack whether they are equivalent i e they define the same input output relation 2 2 there are subclasses of pushdown acceptors which have a decidable ambiguity problem but an undecidable inherent ambiguity problem it seems that these classes are the first known to exhibit this property 3 3 there is an algorithm to decide given a homomorphism h and a language l accepted by a finite turn nondeterministic counter automaton whether h is one to one on l in contrast there is no such algorithm if l is accepted by a 1 turn deterministic pushdown automaton or by an unrestricted deterministic counter automaton

shortest path calculation of seismic rays like the traveling salesman who wants to find the shortest route from one city to another in order to minimize his time wasted on traveling one can find seismic raypaths by calculating the shortest traveltime paths through a network that represents the earth the network consists of points that are connected with neighboring points by connections as long as the traveltime of a seismic wave along it the shortest traveltime path from one point to another is an approximation to the seismic ray between them by fermat s principle the shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously there are no restrictions of classical ray theory diffracted raypaths and paths to shadow zones are found correctly there are also no restrictions to the complexity or the dimensionality of the velocity model furthermore there are no problems with convergence of trial raypaths toward a specified receiver nor with ray

a direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata a new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata dpda s after korenjak and hopcroft s branching algorithm it is not only powerful enough to be applicable to two dpda s accepting by empty stack one of which is real time but also simple even for dpda s in lower subclasses this is the first time the branching algorithm has been used to give such a general decision procedure without ever mixing the two languages in question in other words it deals with only the equivalence equation whose left hand side consists of a pure reachable configuration of one dpda and whose right hand side that of the other

on transductions of formal power series over complete semirings abstract rational and pushdown transductions of formal languages are generalized to formal power series with coefficients in a complete semiring a characterization similar to nivat s theorem is given commutativity requirements for the coefficients are especially studied

a polynomial time algorithm for deciding the equivalence problem for 2 tape deterministic finite state acceptors the equivalence problem for the class of one way deterministic 2 tape finite state acceptors is the problem of deciding l m 1 l m 2 where m 1 and m 2 are machines in this class a new algorithm for deciding equivalence is provided having time complexity proportional to p n where p is a polynomial and n is the size of the machines this improves upon the best previously known upper bound having order 2 cn 6 where c is a constant c beeri theoret comput sci 3 1976 pp 305 320

selecting an optimal aperture in kirchhoff migration using dip angle images we present a method for selecting a migration aperture in kirchhoff migration we first split migrated data into constant dip angle partial images then in every partial image we estimate the consistency between each event and the constant dip of the analyzed section we filter out events whose slope is far from the corresponding dip stacking of the filtered partial images corresponds to migration having an optimal aperture synthetic and real data examples demonstrate that the proposed approach to migration aperture optimization is able to reduce migration noise while preserving diffraction energy which characterizes small geologic objects and brings additional resolution to the image

l a l b decidability results from complete formal systems abstract the equivalence problem for deterministic pushdown automata is shown to be decidable we exhibit a complete formal system for deducing equivalent pairs of deterministic rational boolean series on the alphabet associated with a dpda m we then extend the result to deterministic pushdown transducers from a free monoid into an abelian group a general algebraic and logical framework inspired by harrison et al theoret comput sci 9 1979 173 205 conrcelle theoret comput sci 6 1978 255 279 and meitus kybernetika 5 1989 14 25 in russian is developed

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 direct branching algorithm for checking equivalence of strict deterministic vs ll k grammars abstract we present here an equivalence checking algorithm which operates directly on a pair of strict deterministic vs ll k grammars it is also straightforwardly applicable to a pair of ll k grammars though an ll k grammar is not necessarily strict deterministic the basic idea is from korenjak and hopcroft s branching algorithm for simple deterministic grammars but ours is so distinguished that it is throughout free from mixing the nonterminals of the respective grammars in question and then very simple

finite difference solution of the eikonal equation along expanding wavefronts we show that a scheme to solve the 2 d eikonal equation by a finite difference method can violate causality for moderate to large velocity contrasts v2 v1 2 as an alternative we present a finite difference scheme in which the solution region progresses outward from an expanding wavefront rather than an expanding square and therefore honors causality our method appears to be stable and reasonably accurate for a variety of velocity models with moderate to large velocity contrasts the penalty is a large increase in computational cost and programming effort

riemannian wavefield extrapolation riemannian spaces are described by nonorthogonal curvilinear coordinates we generalize one way wavefield extrapolation to semiorthogonal riemannian coordinate systems that include but are not limited to ray coordinate systems we obtain a one way wavefield extrapolation method that can be used for waves propagating in arbitrary directions in contrast to downward continuation which is used for waves propagating mainly in the vertical direction ray coordinate systems can be initiated in many different ways for example from point sources or from plane waves incident at various angles since wavefield propagation happens mostly along the extrapolation direction we can use inexpensive finite difference or mixed domain extrapolators to achieve high angle accuracy the main applications of our method include imaging of steeply dipping or overturning reflections

fast phase space computation of multiple arrivals we present a fast general computational technique for computing the phase space solution of static hamilton jacobi equations starting with the liouville formulation of the characteristic equations we derive escape equations which are static time independent eulerian pdes they represent all arrivals to the given boundary from all possible starting configurations the solution is numerically constructed through a one pass formulation building on ideas from semi lagrangian methods dijkstra like methods for the eikonal equation and ordered upwind methods to compute all possible trajectories corresponding to all possible boundary conditions the technique is of computational order o n log n where n is the total number of points in the computational phase space domain any particular set of boundary conditions then is extracted through rapid post processing suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance as an application we apply the technique to the problem of computing first multiple and most energetic arrivals to the eikonal equation

sharing dss by the chinese remainder theorem in this paper we propose a new threshold scheme for the digital signature standard dss using asmuth bloom secret sharing based on the chinese remainder theorem crt to achieve the desired result we first show how to realize certain other threshold primitives using asmuth bloom secret sharing such as joint random secret sharing joint exponential random secret sharing and joint exponential inverse random secret sharing we prove the security of our scheme against a static adversary to the best of our knowledge this is the first provably secure threshold dss scheme based on crt

domain limited solution of the wave equation in riemannian coordinates we propose to solve the two way time domain acoustic wave equation in a generalized riemannian coordinate system via finite differences the coordinate system is defined in such a way that one of its independent variables conforms to the primary wavefront for example using a ray coordinate system with the traveltime being one of the coordinates at each finite difference time step the solution domain is limited to a narrow corridor around the primary wavefront leading to an increase in the computational performance a new finite difference scheme is introduced to stabilize the solution and facilitate its implementation this new scheme is a blend of the simple explicit and the stable implicit schemes as a proof of concept the proposed method is compared to the classical explicit finite difference scheme performed in cartesian coordinates on two synthetic velocity models with varying complexities at a reduced cost the proposed method produces similar results to the classical one however some amplitude differences arise due to various implementation issues the most direct application for the proposed method is the source side of reverse time migration

traveltime and amplitude estimation using wavefront construction we have developed and implemented a new method for estimating traveltimes and amplitudes in a general smooth two dimensional 2 d model the basic idea of this wavefront wf construction approach is to use ray tracing to estimate a new wf from the old one the wf is defined as a curve in 2 d of constant traveltime from the source the ray direction and amplitude will then be a function of s the distance along the front to maintain a sufficiently small sampling distance along the wf it is scanned at every time step and new rays are interpolated whenever the distance between two rays becomes larger than a predefined limit as the wavefronts are constructed the data i e traveltimes amplitude coefficients etc are transferred to the receivers by interpolation within the ray cells advantages of the wf construction method are its flexibility robustness and accuracy first second and later arrivals may be found at any point in the model any shape of the initial wavefront is possible the drawb

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

3 d traveltime computation using huygens wavefront tracing traveltime computation is widely used in seismic modeling imaging and velocity analysis the two most commonly used methods are ray tracing and numerical solutions to the eikonal equation eikonal solvers are fast and robust but are limited to computing only the first arrival traveltimes ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers we propose a robust and complete method of traveltime computation it is based on a system of partial differential equations which is equivalent to the eikonal equation but formulated in the ray coordinates system we use a first order discretization scheme that is interpreted very simply in terms of the huygens s principle our explicit finite difference solution to the eikonal equation solved in the ray coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step the finite difference method has proven to be a robust alternative to conventional ray tracing while being faster and having a better ability to handle rough velocity media and penetrate shadow zones

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 weaker sufficient condition for the equivalence of a pair of dpda s to be decidable abstract this short paper further extends the result of tomita 1984 to have a weaker sufficient condition for the equivalence of a pair of non real time deterministic pushdown automata to be decidable

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 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

the equivalence problem for real time dpdas the equivalence problem for deterministic real time pushdown automata is shown to be decidable this result is obtained by showing that valiant s parallel stacking technique using a replacement function introduced in this paper succeeds for deterministic real time pushdown automata equivalence is also decidable for two deterministic pushdown automata one of which is real time

nivat s theorem for pushdown transducers abstract the notions of an extended pushdown automaton pda and a pushdown transducer pdt are formalized in matrix notation by generalizing the concept of a pushdown transition matrix the resulting matrices form a semiring the equivalence to nonextended pdas and pdts is shown the semiring structure gives a new proof that the types reset pushdown and one counter are real time types moreover it allows the construction of the functional composition of a pushdown transduction and a finite transducer mapping as an important application nivat s theorem is generalized to rational and polynomial pdts over arbitrary semirings examples include the mirror image of the input and the dyck reduction

a fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization abstracttraveltime computation is essential for many seismic data processing applications and velocity analysis tools high resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics moreover computation of auxiliary quantities such as amplitude and take off angle relies on highly accurate traveltime solutions however the finite difference based eikonal solution for a point source initial condition has upwind source singularity at the source position because the wavefront curvature is large near the source point therefore all finite difference solvers even the high order ones show inaccuracies because the errors due to source singularity spread from the source point to the whole computational domain we address the source singularity problem for tilted transversely isotropic tti eikonal solvers using factorization we solve a sequence of factored tilted elliptically anisotropic tea eikonal equations iteratively

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

3 d traveltime computation using the fast marching method we present a fast algorithm for solving the eikonal equation in three dimensions based on the fast marching method the algorithm is of the order o n log n where n is the total number of grid points in the computational domain the algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain the method is unconditionally stable and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity in addition the method resolves any overturning propagation wavefronts we begin with the mathematical foundation for solving the eikonal equation using the fast marching method and follow with the numerical details we then show examples of traveltime propagation through the seg eage salt model using point source and planewave initial conditions and analyze the error in constant velocity media the algorithm allows for any shape of the initial wavefront while a point source is the most commonly used initial condition initial plane waves can be used for controlled illumination or for downward continuation of the traveltime field from one depth to another or from a topographic depth surface to another the algorithm presented here is designed for computing first arrival traveltimes nonetheless since it exploits the fast marching method for solving the eikonal equation we believe it is the fastest of all possible consistent schemes to compute first arrivals

efficient traveltime solutions of the acoustic ti eikonal equation numerical solutions of the eikonal hamilton jacobi equation for transversely isotropic ti media are essential for imaging and traveltime tomography applications such solutions however suffer from the inherent higher order nonlinearity of the ti eikonal equation which requires solving a quartic polynomial for every grid point analytical solutions of the quartic polynomial yield numerically unstable formulations thus it requires a numerical root finding algorithm adding significantly to the computational load using perturbation theory we approximate in a first order discretized form the ti eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter such perturbation applied to the discretized form of the eikonal equation does not impose any restrictions on the complexity of the perturbed parameter field therefore it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter such as that for the complicated marmousi model the formulation allows for large cost reduction compared to using the direct ti eikonal solver furthermore comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm without any addition to the computational cost

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

lattice based threshold changeability for standard shamir secret sharing schemes we consider the problem of increasing the threshold parameter of a secret sharing scheme after the setup share distribution phase without further communication between the dealer and the shareholders previous solutions to this problem require one to start off with a nonstandard scheme designed specifically for this purpose or to have communication between shareholders in contrast we show how to increase the threshold parameter of the standard shamir secret sharing scheme without communication between the shareholders our technique can thus be applied to existing shamir schemes even if they were set up without consideration to future threshold increases our method is a new positive cryptographic application for lattice reduction algorithms inspired by recent work on lattice based list decoding of reed solomon codes with noise bounded in the lee norm we use fundamental results from the theory of lattices geometry of numbers to prove quantitative statements about the information theoretic security of our construction these lattice based security proof techniques may be of independent interest

riemannian wavefield extrapolation nonorthogonal coordinate systems riemannian wavefield extrapolation rwe is used to model one way wave propagation on generalized coordinate meshes previous rwe implementations assume that coordinate systems are defined by either orthogonal or semiorthogonal geometry this restriction leads to situations where coordinate meshes suffer from problematic bunching and singularities nonorthogonal rwe is a procedure that avoids many of these problems by posing wavefield extrapolation on smooth but generally nonorthogonal and singularity free coordinate meshes the resulting extrapolation operators include additional terms that describe nonorthogonal propagation these extra degrees of complexity however are offset by smoother coefficients that are more accurately implemented in one way extrapolation operators remaining coordinate mesh singularities are then eliminated using a differential mesh smoothing procedure analytic extrapolation examples and the numerical calculation of 2d and 3d green s functions for cylindrical and near spher