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Research on a novel construction of probabilistic visual cryptography scheme (k, n, 0, 1, 1) - PVCS for threshold access structures

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THEORETICAL COMPUTER SCIENCE 2021年 863卷 19-39页

作者： Ju, GwangSu Ko, UnGwang Kim Chaek Univ Technol Inst Informat Technol Pyongyang North Korea Kim Chaek Univ Technol Grad Sch Pyongyang North Korea

In this paper, we propose new algorithms to construct a probabilistic visual cryptography scheme (k, n, 0,1,1) - PVCS for threshold access structures based on the deterministic visual cryptography schemes (DVCS) and classify the probabilistic schemes into online and offline ones according to the reference mode of distribution column vectors. First in consideration of the relationship between DVCS and PVCS we propose a new method for expanded DVCS based on a matrix with binary vectors of V-n(k) as column vectors so as to construct PVCS without pixel expansion. Then, using the extended DVCS we suggest PVCS construction method which does not require storing of the distribution column vectors and delineate the relationship between our online PVCS and visual cryptograms of random grids (VCRG). We also propose a new infinite tree in order to generate binary vectors of V-n(k). (C) 2021 Elsevier B.V. All rights reserved.

关键词： visual cryptography Random grids Deterministic visual cryptography probabilistic visual cryptography Pixel expansion

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A discussion on the relationship between probabilistic visual cryptography and random grid

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INFORMATION SCIENCES 2014年 278卷 141-173页

作者： Yang, Ching-Nung Wu, Chih-Cheng Wang, Dao-Shun Natl Dong Hwa Univ Dept Comp Sci & Informat Engn Shoufeng Taiwan Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China

In a (k,n) visual cryptography scheme (VCS), the dealer encodes the secret into n shadow images. Each pixel of the secret image is "expanded" into in sub-pixels in each share. In a (k,n)-VCS, the secret can be visually reconstructed when k or more shares are available. The reconstruction process employs the human visual system and no computations are required. To solve the pixel expansion problem of VCSs, probabilistic VCSs are directly converted from VCSs with no pixel expansion. Another well-known secret image sharing scheme, random grid (RG), is also provided with this novel stacking-to-see property. Compared with VCS, the most appealing benefit of RG is that there is no pixel expansion. In this paper, we use the probabilistic VCS without pixel expansion, to study the construction and performance of RG. This paper has two main results: (i) We show that each step of the share generation process in all existing (2,2)-RG, (2,n)-RG, (n, n)-RG, (k,n)-RG, incremental RG can be mapped to a corresponding step in PVCSs, and their shadow images between PVCS and RG are perfectly indistinguishable and the reconstructed images are the same, also include our (2,n) RG. (ii) From the quality of reconstructed image, pixel expansion, recognized region size, and image types to be considered for evaluating PVCSs and RGs, we point out that RG and PVCS have no difference other than the terminology. Furthermore, RGs is a subset of PVCSs. (C) 2014 Elsevier Inc. All rights reserved.

关键词： visual cryptography visual secret sharing Random grid probabilistic visual cryptography

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Construction of General (k, n) probabilistic visual cryptography Scheme

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Journal of Electronic Science and Technology 2011年第4期9卷 317-324页

作者： Ching-Nung Yang Chih-Cheng Wu Feng Liu with the Department of Computer Science and Information Engineering National Dong Hwa University with State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences.

visual cryptography scheme （VCS） is a secure method that encrypts a secret image by subdividing it into shadow images. Due to the nature of encryption VCS is categorized into two types： the deterministic VCS （DVCS） and the probabilistie VCS （PVCS）. For the DVCS, we use m （known as the pixel expansion） subpixels to represent a secret pixel. The PVCS uses only one subpixel to represent a secret pixel, while the quality of reconstructed image is degraded. A well-known construction of （k, n）-PVCS is obtained from the （k, n）-DVCS. In this paper, we show another construction of （k, n）-PVCS by extending the （k, k）-PVCS.

关键词： probabilistic visual cryptography visual cryptography visual secret sharing.

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On the Relation of Random Grid and Deterministic visual cryptography

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2014年第4期9卷 653-665页

作者： De Prisco, Roberto De Santis, Alfredo Univ Salerno Dipartimento Informat I-84084 Fisciano Italy

visual cryptography is a special type of secret sharing. Two models of visual cryptography have been independently studied: 1) deterministic visual cryptography, introduced by Naor and Shamir, and 2) random grid visual cryptography, introduced by Kafri and Keren. In this paper, we show that there is a strict relation between these two models. In particular, we show that to any random grid scheme corresponds a deterministic scheme and vice versa. This allows us to use results known in a model also in the other model. By exploiting the (many) results known in the deterministic model, we are able to improve several schemes and to provide many upper bounds for the random grid model and by exploiting some results known for the random grid model, we are also able to provide new schemes for the deterministic model. A side effect of this paper is that future new results for any one of the two models should not ignore, and in fact be compared with, the results known in the other model.

关键词： cryptography visual secret sharing random grids probabilistic visual cryptography

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