Hierarchical secret image sharing scheme in compressed sensing

Abstract Secret image sharing (SIS) is a technique of protecting the secret images from an unauthorized access through the generation of few shares or shadow images and serves various purposes such as multi-party computation, threshold cryptography, access control etc. Some of these applications demand hierarchical access based SIS scheme with flexible shadow size adaptive to the available transmission bandwidth. To this aim, share/shadow image generation (with reduced size) is considered here as a sparse signal (secret) reconstruction problem as is done in compressed sensing or compressive sampling (CS). A prediction error (PE) matrix is formed for the secret image which then undergoes sub-sampling followed by its partitioning into two sets of shares: one mandatory share (MS) and ‘ n ’ number of general shares (GSs) thus form an integrated framework of CS and Shamir’s ( k , n )-threshold secret sharing scheme. The contribution of the MS and at least ‘ k ’ number of GSs are essential to reconstruct the secret image. The change in the number of CS measurements leads to the flexibility in share size adaptive to transmission bandwidth and offers a progressive quality access control along with relative changes in unauthorized decoding probability. A large set of simulation results show the average decoding quality of the secret images with PSNR values of 31.4 dB and 35.7 dB for 10% and 30% measurements, respectively.

[1]  Ching-Nung Yang,et al.  Generalized random grids-based threshold visual cryptography with meaningful shares , 2015, Signal Processing.

[2]  Chien-Chang Chen,et al.  Weighted modulated secret image sharing method , 2009, J. Electronic Imaging.

[3]  Chih-Fong Tsai,et al.  A privilege-based visual secret sharing model , 2015, J. Vis. Commun. Image Represent..

[4]  Ching-Nung Yang,et al.  Constructions and properties of k out of n scalable secret image sharing , 2010 .

[5]  Ching-Nung Yang,et al.  A general (k, n) scalable secret image sharing scheme with the smooth scalability , 2011, J. Syst. Softw..

[6]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[7]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[8]  Ja-Chen Lin,et al.  Secret image sharing , 2002, Comput. Graph..

[9]  Santi P. Maity,et al.  An image-in-image communication scheme using secret sharing and M-ary spread spectrum watermarking , 2017 .

[10]  Shih-Chieh Wei,et al.  A technique for sharing a digital image , 2015, Comput. Stand. Interfaces.

[11]  Ching-Nung Yang,et al.  Steganography and authentication in image sharing without parity bits , 2012 .

[12]  Moni Naor,et al.  Visual Cryptography , 1994, Encyclopedia of Multimedia.

[13]  Ziba Eslami,et al.  Secret image sharing scheme with hierarchical threshold access structure , 2014, J. Vis. Commun. Image Represent..

[14]  Ching-Nung Yang,et al.  Essential secret image sharing scheme with different importance of shadows , 2013, J. Vis. Commun. Image Represent..

[15]  Aswin C. Sankaranarayanan,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[16]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[17]  B. Sklar,et al.  Rayleigh fading channels in mobile digital communication systems Part I: Characterization , 1997, IEEE Commun. Mag..

[18]  Ja-Chen Lin,et al.  Fast-weighted secret image sharing , 2009 .

[19]  Lin Cai,et al.  Transmission Control for Compressive Sensing Video over Wireless Channel , 2013, IEEE Transactions on Wireless Communications.

[20]  Shyong Jian Shyu,et al.  Weighted Threshold Secret Image Sharing , 2009, PSIVT.

[21]  Peng Li,et al.  Reducing shadow size in essential secret image sharing by conjunctive hierarchical approach , 2015, Signal Process. Image Commun..

[22]  Peng Li,et al.  Essential secret image sharing scheme with the same size of shadows , 2016, Digit. Signal Process..

[23]  Tamir Tassa,et al.  Hierarchical Threshold Secret Sharing , 2004, Journal of Cryptology.

[24]  Chin-Chen Chang,et al.  A hierarchical threshold secret image sharing , 2012, Pattern Recognit. Lett..

[25]  Wei Li,et al.  A multilevel image thresholding segmentation algorithm based on two-dimensional K-L divergence and modified particle swarm optimization , 2016, Appl. Soft Comput..

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

[27]  Chin-Chen Chang,et al.  A novel real-time and progressive secret image sharing with flexible shadows based on compressive sensing , 2014, Signal Process. Image Commun..

[28]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.