11,842 research outputs found
Bicategorical Semantics for Nondeterministic Computation
We outline a bicategorical syntax for the interaction between public and
private information in classical information theory. We use this to give
high-level graphical definitions of encrypted communication and secret sharing
protocols, including a characterization of their security properties.
Remarkably, this makes it clear that the protocols have an identical abstract
form to the quantum teleportation and dense coding procedures, yielding
evidence of a deep connection between classical and quantum information
processing. We also formulate public-key cryptography using our scheme.
Specific implementations of these protocols as nondeterministic classical
procedures are recovered by applying our formalism in a symmetric monoidal
bicategory of matrices of relations.Comment: 21 page
A Modified Multi-secret Visual Cryptography with Ring Shares
Abstract. A visual cryptography scheme encoding multiple secret images into two ring shares is proposed in this paper. In the secret sharing process, two shares are produced by the marked areas and the basis matrices of (2, 2)-VCS. Using ring shift right function, the secret images are recovered by stacking two shares. The security and contrast properties of the scheme have been proved. Compared with the previous ones, the scheme makes the number of secret images unlimited. Furthermore, the pixel expansion and the relative difference are improved greatly
Secure distributed matrix computation with discrete fourier transform
We consider the problem of secure distributed matrix computation (SDMC), where a user queries a function of data matrices generated at distributed source nodes. We assume the availability of N honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called the upload cost, while guaranteeing that no T colluding servers can learn any information about the source matrices, and the user cannot learn any information beyond the computation result. We first focus on secure distributed matrix multiplication (SDMM), considering two matrices, and propose a novel polynomial coding scheme using the properties of finite field discrete Fourier transform, which achieves an upload cost significantly lower than the existing results in the literature. We then generalize the proposed scheme to include straggler mitigation, and to the multiplication of multiple matrices while keeping the input matrices, the intermediate computation results, as well as the final result secure against any T colluding servers. We also consider a special case, called computation with own data, where the data matrices used for computation belong to the user. In this case, we drop the security requirement against the user, and show that the proposed scheme achieves the minimal upload cost. We then propose methods for performing other common matrix computations securely on distributed servers, including changing the parameters of secret sharing, matrix transpose, matrix exponentiation, solving a linear system, and matrix inversion, which are then used to show how arbitrary matrix polynomials can be computed securely on distributed servers using the proposed procedur
The Visual Secret Sharing Scheme Based on the Rgb Color System
The visual secret sharing (VSS) scheme is a method to maintain the confidentiality of a se-cret image by sharing it to some number participants. A (k, n) VSS divides the secret images into n parts, that are called shadows ; to recover the secret back, k shadows should be stacked. Some methods have been developed to implement VSS for color images. However, the methods are only suitable for images with limited number of colors. When more colors are used, the resulted stacked shadow image becomes unclear. Besides that, the size of the shadows becomes bigger as more colors are used. We develop a new method implementing the VSS using the RGB color system. Using our method, the problem related to the unclear stacked shadow image can be overcome
Secret Sharing Based on a Hard-on-Average Problem
The main goal of this work is to propose the design of secret sharing schemes
based on hard-on-average problems. It includes the description of a new
multiparty protocol whose main application is key management in networks. Its
unconditionally perfect security relies on a discrete mathematics problem
classiffied as DistNP-Complete under the average-case analysis, the so-called
Distributional Matrix Representability Problem. Thanks to the use of the search
version of the mentioned decision problem, the security of the proposed scheme
is guaranteed. Although several secret sharing schemes connected with
combinatorial structures may be found in the bibliography, the main
contribution of this work is the proposal of a new secret sharing scheme based
on a hard-on-average problem, which allows to enlarge the set of tools for
designing more secure cryptographic applications
Bounds for Visual Cryptography Schemes
In this paper, we investigate the best pixel expansion of the various models
of visual cryptography schemes. In this regard, we consider visual cryptography
schemes introduced by Tzeng and Hu [13]. In such a model, only minimal
qualified sets can recover the secret image and that the recovered secret image
can be darker or lighter than the background. Blundo et al. [4] introduced a
lower bound for the best pixel expansion of this scheme in terms of minimal
qualified sets. We present another lower bound for the best pixel expansion of
the scheme. As a corollary, we introduce a lower bound, based on an induced
matching of hypergraph of qualified sets, for the best pixel expansion of the
aforementioned model and the traditional model of visual cryptography realized
by basis matrices. Finally, we study access structures based on graphs and we
present an upper bound for the smallest pixel expansion in terms of strong
chromatic index
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