Combination of Sharing Matrix and Image Encryption for Lossless $(k,n)$ -Secret Image Sharing

This paper first introduces a <inline-formula> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula>-sharing matrix <inline-formula> <tex-math notation="LaTeX">$S^{(k, n)}$ </tex-math></inline-formula> and its generation algorithm. Mathematical analysis is provided to show its potential for secret image sharing. Combining sharing matrix with image encryption, we further propose a lossless <inline-formula> <tex-math notation="LaTeX">$(k,n)$ </tex-math></inline-formula>-secret image sharing scheme (SMIE-SIS). Only with no less than <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> shares, all the ciphertext information and security key can be reconstructed, which results in a lossless recovery of original information. This can be proved by the correctness and security analysis. Performance evaluation and security analysis demonstrate that the proposed SMIE-SIS with arbitrary settings of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> has at least five advantages: 1) it is able to fully recover the original image without any distortion; 2) it has much lower pixel expansion than many existing methods; 3) its computation cost is much lower than the polynomial-based secret image sharing methods; 4) it is able to verify and detect a fake share; and 5) even using the same original image with the same initial settings of parameters, every execution of SMIE-SIS is able to generate completely different secret shares that are unpredictable and non-repetitive. This property offers SMIE-SIS a high level of security to withstand many different attacks.

[1]  Ching-Nung Yang,et al.  Property Analysis of XOR-Based Visual Cryptography , 2014, IEEE Transactions on Circuits and Systems for Video Technology.

[2]  Yicong Zhou,et al.  Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents , 2018, IEEE Transactions on Cybernetics.

[3]  Yicong Zhou,et al.  Image encryption using a new parametric switching chaotic system , 2013, Signal Process..

[4]  Young-Chang Hou,et al.  Progressive Visual Cryptography With Unexpanded Shares , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

[5]  Jinhu Lu,et al.  On Cryptanalysis of Fridrich's chaotic image encryption scheme , 2016, ArXiv.

[6]  Chengqing Li,et al.  Cracking a hierarchical chaotic image encryption algorithm based on permutation , 2015, Signal Process..

[7]  Ljupco Kocarev,et al.  Discrete Lyapunov Exponent and Resistance to Differential Cryptanalysis , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Jun-jie Chen,et al.  A chaos-based digital image encryption scheme with an improved diffusion strategy. , 2012, Optics express.

[9]  Robert H. Deng,et al.  Key-Aggregate Cryptosystem for Scalable Data Sharing in Cloud Storage , 2014, IEEE Transactions on Parallel and Distributed Systems.

[10]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[11]  Pei-Ling Chiu,et al.  Digital Image Sharing by Diverse Image Media , 2014, IEEE Transactions on Information Forensics and Security.

[12]  Peng Li,et al.  Improvements of a two-in-one image secret sharing scheme based on gray mixing model , 2012, J. Vis. Commun. Image Represent..

[13]  Yicong Zhou,et al.  Cascade Chaotic System With Applications , 2015, IEEE Transactions on Cybernetics.

[14]  Ja-Chen Lin,et al.  Secret Image Sharing: a Boolean-Operations-Based Approach Combining Benefits of Polynomial-Based and Fast Approaches , 2009, Int. J. Pattern Recognit. Artif. Intell..

[15]  Ching-Nung Yang,et al.  Optimal Contrast Grayscale Visual Cryptography Schemes With Reversing , 2013, IEEE Transactions on Information Forensics and Security.

[16]  Wei Sun,et al.  Extended Capabilities for XOR-Based Visual Cryptography , 2014, IEEE Transactions on Information Forensics and Security.

[17]  Yicong Zhou,et al.  2D Sine Logistic modulation map for image encryption , 2015, Inf. Sci..

[18]  Yicong Zhou,et al.  Dynamic Parameter-Control Chaotic System , 2016, IEEE Transactions on Cybernetics.

[19]  Wei-Ho Chung,et al.  A Probabilistic Model of $(t,n)$ Visual Cryptography Scheme With Dynamic Group , 2012, IEEE Transactions on Information Forensics and Security.

[20]  S. Li,et al.  Cryptographic requirements for chaotic secure communications , 2003, nlin/0311039.

[21]  Zhi Zhou,et al.  Halftone visual cryptography , 2006, IEEE Transactions on Image Processing.

[22]  Shujun Li,et al.  Cryptanalysis of a chaotic image encryption method , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[23]  Yicong Zhou,et al.  Image encryption: Generating visually meaningful encrypted images , 2015, Inf. Sci..

[24]  Yicong Zhou,et al.  A new 1D chaotic system for image encryption , 2014, Signal Process..

[25]  Deepa Kundur,et al.  Distributed Secret Sharing for Discrete Memoryless Networks , 2008, IEEE Transactions on Information Forensics and Security.

[26]  Amir Akhavan,et al.  Cryptanalysis of “an improvement over an image encryption method based on total shuffling” , 2015 .

[27]  Shyong Jian Shyu,et al.  General Constructions for Threshold Multiple-Secret Visual Cryptographic Schemes , 2013, IEEE Transactions on Information Forensics and Security.

[28]  Shih-Chieh Wei,et al.  Random-Grid-Based Visual Cryptography Schemes , 2014, IEEE Transactions on Circuits and Systems for Video Technology.

[29]  Vasif V. Nabiyev,et al.  Polynomial approach in a secret image sharing using quadratic residue , 2009, 2009 24th International Symposium on Computer and Information Sciences.

[30]  Yicong Zhou,et al.  Binary-block embedding for reversible data hiding in encrypted images , 2017, Signal Process..

[31]  Chin-Chen Chang,et al.  Secret Image Sharing Using Quadratic Residues , 2007, Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2007).

[32]  Verónica Fernández Mármol,et al.  On the inadequacy of the logistic map for cryptographic applications , 2008, 0805.4355.

[33]  Yehuda Lindell,et al.  Introduction to Modern Cryptography , 2004 .

[34]  Wei Sun,et al.  Generalized Random Grid and Its Applications in Visual Cryptography , 2013, IEEE Transactions on Information Forensics and Security.

[35]  Gonzalo Álvarez,et al.  Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems , 2003, Int. J. Bifurc. Chaos.

[36]  Lein Harn,et al.  Group Authentication , 2013, IEEE Transactions on Computers.

[37]  Pei-Ling Chiu,et al.  Image Size Invariant Visual Cryptography for General Access Structures Subject to Display Quality Constraints , 2013, IEEE Transactions on Image Processing.

[38]  Alfredo De Santis,et al.  On the Relation of Random Grid and Deterministic Visual Cryptography , 2014, IEEE Trans. Inf. Forensics Secur..

[39]  Heung-Kyu Lee,et al.  Color Extended Visual Cryptography Using Error Diffusion , 2011, IEEE Transactions on Image Processing.

[40]  Mitsugu Iwamoto.  A Weak Security Notion for Visual Secret Sharing Schemes , 2012, IEEE Transactions on Information Forensics and Security.

[41]  Kaoru Kurosawa.  General Error Decodable Secret Sharing Scheme and Its Application , 2011, IEEE Transactions on Information Theory.

[42]  Che-Wei Lee,et al.  A Secret-Sharing-Based Method for Authentication of Grayscale Document Images via the Use of the PNG Image With a Data Repair Capability , 2012, IEEE Transactions on Image Processing.

[43]  Mithun V Mhatre,et al.  Key-Aggregate Cryptosystem for Scalable Data Sharing in Cloud Storage- A Review , 2015 .

[44]  Pei-Ling Chiu,et al.  Sharing Visual Secrets in Single Image Random Dot Stereograms , 2014, IEEE Transactions on Image Processing.

[45]  Shyong Jian Shyu.  Visual Cryptograms of Random Grids for General Access Structures , 2013, IEEE Transactions on Circuits and Systems for Video Technology.

[46]  Chuankun Wu,et al.  Embedded Extended Visual Cryptography Schemes , 2011, IEEE Transactions on Information Forensics and Security.

[47]  Giovanni Di Crescenzo,et al.  Halftone Visual Cryptography Via Error Diffusion , 2009, IEEE Transactions on Information Forensics and Security.

[48]  Duncan S. Wong,et al.  On Secret Reconstruction in Secret Sharing Schemes , 2008, IEEE Transactions on Information Theory.

[49]  Feng Liu,et al.  Step Construction of Visual Cryptography Schemes , 2010, IEEE Transactions on Information Forensics and Security.