Penrose tiling for visual secret sharing
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Penrose tiling for visual secret sharing Xuehu Yan1,2
· Wei Qi Yan3 · Lintao Liu1,2 · Yuliang Lu1,2
Received: 26 December 2019 / Revised: 1 August 2020 / Accepted: 6 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Visual secret sharing (VSS) has the advantage that the decryption is based on our human visual system without participation of any computational devices. However, traditional VSS schemes are only for sharing raster images with regard to pixels, which lead to that the secret image will be aliased when enlarged and its pixels are shared in rectangular way only. In this paper, we will introduce a VSS scheme for vectorized images based on Penrose tiling. Penrose tiling is with the merits of vectorization and nonperiodicity. These properties are applied to the proposed scheme so as to share those vectorized images; the basic unit of secret sharing could be any graphical shapes instead of pixels or rectangular regions only in the traditional methods. Our experiments show the effectiveness of the proposed scheme. Keywords Image sharing · Visual secret sharing · Penrose tiling · Vector image
1 Introduction Image sharing schemes split a secret image into several shares, a.k.a., shadows or shadow images, which are then distributed to corresponding participants for the secret restoration. Moreover, image sharing for (k, n)-threshold is loss-tolerant, i.e., the secret can be decrypted even if n − k shares are lost. Therefore, image secret sharing can be applied to many scenarios, e.g., access control, password transmission [38], key management, digital watermarking [9, 25, 34, 35, 39, 48], identity authentication [4, 18, 49], and distributive storage in cloud computing [2, 17, 33, 50]. As well known, digital images are a special form of data, in which each binary pixel is represented by using one bit of a byte, thus image secret sharing is easily to be generalized for secret sharing. The principle of secret sharing chiefly includes polynomial-based method [19, 30], visual secret sharing (VSS) [5, 26, 37], i.e., visual cryptography (VC), etc. [1, 12, 16, 43]. Xuehu Yan
[email protected] 1
National University of Defense Technology, Hefei 230037, China
2
Anhui Province Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China
3
Auckland University of Technology, Auckland 1142, New Zealand
Multimedia Tools and Applications
To decrypt the secret for the case of (k, n)-threshold, Shamir proposed the first polynomial-based secret sharing [30] through constructing a k − 1 degree polynomial to output n shares, which are then distributed to n participants. When any k or more shares are collected, the secret could be reconstructed by using Lagrange’s interpolation, more information of the polynomial-based secret sharing is available from matrix theory. Following Shamir’s work, the improved schemes were put forward [20, 22, 44] based on the theory of polynomials. The key advantage of this polynomial-based secret sharing is the decryp
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