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1.
Improved Schemes for Visual Cryptography 总被引:8,自引:0,他引:8
Carlo Blundo Annalisa De Bonis Alfredo De Santis 《Designs, Codes and Cryptography》2001,24(3):255-278
A (k,n)-threshold visual cryptography scheme ((k,n)-threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the visual recovery of the secret image, but by inspecting less than k shares one cannot gain any information on the secret image. The visual recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation.In this paper we analyze visual cryptography schemes in which the reconstruction of black pixels is perfect, that is, all the subpixels associated to a black pixel are black. For any value of k and n, where 2 k n, we give a construction for (k,n)-threshold VCS which improves on the best previously known constructions with respect to the pixel expansion (i.e., the number of subpixels each pixel of the original image is encoded into). We also provide a construction for coloured (2,n)-threshold VCS and for coloured (n,n)-threshold VCS. Both constructions improve on the best previously known constructions with respect to the pixel expansion. 相似文献
2.
Let P = {1, 2, . . . , n} be a set of elements called participants. In this paper we construct a visual cryptography scheme (VCS) for the strong access structure specified by the set Γ0 of all minimal qualified sets, where ${\Gamma_0=\{S: S\subseteq P, 1\in S}$ and |S| = k}. Any VCS for this strong access structure is called a (k, n)*-VCS. We also obtain bounds for the optimal pixel expansion and optimal relative contrast for a (k, n)*-VCS. 相似文献
3.
Avishek Adhikari 《Designs, Codes and Cryptography》2014,73(3):865-895
Though the monochrome (black and white) visual cryptography has a very rich literature, a very few papers have been published for the construction of general access structure. In this paper we put forward a method of construction of a strong monochrome visual cryptographic scheme (VCS) for general access structure using linear algebra. As a particular case of general access structure, \((k,n)\) -VCS for \(2 \le k \le n\) is obtained. The \((n,n)\) -VCS obtained from the scheme attains the optimal pixel expansion as well as optimal relative contrast. We provide an efficient construction of \((n-1,n)\) -VCS. We further extend our monochrome VCS to color VCS for restricted access structures. Finally, we provide some interesting examples that will lead to some future research directions in the area of VCS. 相似文献
4.
Axel Hultman 《Journal of Algebraic Combinatorics》2002,16(1):83-96
Let
n,k,k
and
n,k,h
, h < k, denote the intersection lattices of the k-equal subspace arrangement of type
n
and the k,h-equal subspace arrangement of type
n
respectively. Denote by
the group of signed permutations. We show that (
n,k,k
)/
is collapsible. For (
n,k,h
)/
, h < k, we show the following. If n 0 (mod k), then it is homotopy equivalent to a sphere of dimension
. If n h (mod k), then it is homotopy equivalent to a sphere of dimension
. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of
on the homology groups of (
n,k,k
) and (
n,k,h
) are stated.The collapsibility of (
n,k,k
)/
is established using a discrete Morse function. The same method is used to show that (
n,k,h
)/
, h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Björner and M. Wachs (Trans. Amer. Math. Soc.
4 (1996), 1299–1327) when the cell complex is an order complex of a poset. 相似文献
5.
We find exact values of upper bounds for the best approximations of q-ellipsoids by polynomials of degree n in the spaces
in the case where the approximating polynomials are constructed on the basis of n-dimensional subsystems chosen successively from a given orthonormal system . 相似文献
6.
In this paper we give an explicit construction of basis matrices for a (k, n)-visual cryptography scheme \((k,n){\hbox {-}}\mathrm{VCS}\) for integers k and n with \(2\le k \le n\). In balanced VCS every set of participants with equal cardinality has same relative contrast. The VCS constructed in this paper is a balanced \((k,n){\hbox {-}}\mathrm{VCS}\) for general k. Also we obtain a formula for pixel expansion and relative contrast. We also prove that our construction gives optimal contrast and minimum pixel expansion when \(k=n\) and \(n-1\). 相似文献
7.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
8.
Summary We study the Hellinger type distances
on a filtered space. Herep2 is an arbitrary number andP
T
and
are two probability measures stopped at a random timeT. We give lower and upper bounds for
in predictable terms. 相似文献
9.
Najim Christopher A. Russo Ralph P. 《Methodology and Computing in Applied Probability》2003,5(1):23-33
Let U
1, U
2,... be a sequence of i.i.d. random elements in Rd. For x>0, a graph G
n
(x) may be formed by connecting with an edge each pair of points in
that are separated by a distance no greater than x. The points of G
n
(x) could represent the stations in a telecommunications network and the edge set the lines of communication that exist among them. Let
be a collection of graphs on mn points having a specified form or structure, and let
denote the number of subgraphs embedded in G
n
(x) and contained in
. It is shown that a SLLN, CLT and LIL for
follow easily from the theory of U-statistics. In addition, a uniform (in x) SLLN is proved for collections
that satisfy a certain monotonicity condition. Some applications are mentioned and the results of some simulations presented. The scaling constants appearing in the CLT are usually hard to obtain. These are worked out for some special cases. 相似文献
10.
On the isomorphisms and automorphism groups of circulants 总被引:2,自引:0,他引:2
Denote byC
n(S) the circulant graph (or digraph). LetM be a minimal generating element subset ofZ
n, the cyclic group of integers modulon, and
In this paper, we discuss the problems about the automorphism group and isomorphisms ofC
n(S). When M
S
, we determine the automorphism group ofC
n(S) and prove that for any T
if and only ifT = S, where is an integer relatively prime ton. The automorphism groups and isomorphisms of some other types of circulant graphs (or digraphs) are also considered. In the last section of this paper, we give a relation between the isomorphisms and the automorphism groups of circulants. 相似文献
11.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
相似文献
12.
A (k,n)-arc in PG(2,q) is usually defined to be a set
of k points in the plane such that some line meets
in n points but such that no line meets
in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow
to be a multiset, that is, permit
to contain multiple points. The case k=q
2+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q
2+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q
2+q+2 and minimum distance q
2. Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q
2+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem. 相似文献
13.
Helena Ferreira 《Extremes》2000,3(4):385-392
Let
be a sequence of identically distributed variables. We study the asymptotic distribution of
, where Y
[r:n] denotes the concomitant of the rth order statistic X
r:n
, corresponding to
, and
is held fixed while
. Conditions are given for the
and
to have the same asymptotic behavior as that we would apply if
were i.i.d. The result is illustrated with a simple linear regression model
, where
is a stationary sequence with extremal index
. 相似文献
14.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
15.
A. N. Khisamiev 《Algebra and Logic》2000,39(6):423-428
We study into the question of which linearly ordered sets are intrinsically enumerable. In particular, it is proved that every countable ordinal lacks this property. To do this, we state a criterion for hereditarily finite admissible sets being existentially equivalent, which is interesting in its own right. Previously, Yu. L. Ershov presented the criterion for elements h
0
, h
1
in HF
) to realize a same type as applied to sufficiently saturated models
. Incidentally, that criterion fits with every model
on the condition that we limit ourselves to 1-types. 相似文献
16.
E. S. Dubtsov 《Journal of Mathematical Sciences》2001,107(4):4002-4021
Let K be a compact space, let X be a closed subspace of C(K), and let
be a positive measure on K. The triple
is said to be regular if, for any positive function
and for any
, there exists a function
such that
on K and
. The case where K is the unit sphere in
and the subspace X is invariant with respect to the unitary group is investigated. Sufficient spectral conditions and a necessary condition for the regularity of a triple are obtained. Connections with compactness of certain Hankel operators and applications to interpolation problems are presented. Bibliography: 16 titles. 相似文献
17.
Josef Stoer 《Mathematical Programming》1975,9(1):313-335
This paper presents a local convergence analysis of Broyden's class of rank-2 algorithms for solving unconstrained minimization problems,
,h C1(R
n
), assuming that the step-size ai in each iterationx
i+1 =x
i
-
i
H
i
h(x
i
) is determined by approximate line searches only. Many of these methods including the ones most often used in practice, converge locally at least with R-order,
. 相似文献
18.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind
and
where
is a singular Volterra operator,
is continuous and positive on ]a, b],
is a norm in R
n, and [u]+ and [u]– are respectively the positive and the negative part of the vector u R
n. 相似文献
19.
An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is split into the sum of a single-valued operator
, possessing a kind of pseudo Dunn property, and a maximal monotone operator
. The current auxiliary problem is k constructed by fixing
at the previous iterate, whereas
(or its single-valued approximation
k) k is considered at a variable point. Using auxiliary operators of the form
k+
, with k>0, the standard for the auxiliary problem principle assumption of the strong convexity of the function h can be weakened exploiting mutual properties of
and h. Convergence of the general scheme is analyzed and some applications are sketched briefly. 相似文献
20.
Prof. Dr. H. Carnal 《Probability Theory and Related Fields》1970,15(2):168-176
Summary The number of edges A
n
, the length l
n
and the surface F
n
of the convex hull of n independent, identically distributed random points in the plane are considered under the assumption of rotational symmetry. The asymptotic behaviour of the expectations E(A
n
), E(l
n
) and E(F
n
) is studied according to the behaviour of the function Pr(
as x 1 (distributions on the unit disc) or x (distributions on the whole plane).
Herrn Prof. H. Hadwiger zu seinem 60. Geburtstag gewidmet. 相似文献 |