A Note on Multiple Secret Sharing Using Chinese Remainder Theorem and Exclusive-OR

This paper reviews the former existing scheme on <inline-formula> <tex-math notation="LaTeX">$(n,n)$ </tex-math></inline-formula>-multiple secret sharing (MSS) for color images along with its slight limitation. This scheme generates a set of <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> shared images from a set of <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> secret images using the Chinese remainder theorem (CRT) and Boolean exclusive-OR (XOR) operation. This scheme works well if the number of secret images <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is even number. However, the former scheme has a slight problem while the number of secret images <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is an odd number. This paper proposes a new technique to overcome this problem by introducing symmetric and transferred masking coefficients to generate a set of shared images. To further improve the security level of the proposed method, a set of secret images is first transformed with hyperchaotic scrambling method before generating shared images. The security of the proposed <inline-formula> <tex-math notation="LaTeX">$(n,n)$ </tex-math></inline-formula>-MSS can also be increased by merging a shared color image into 2-D matrix representation. As documented in the experimental results, the proposed method offers a promising result on <inline-formula> <tex-math notation="LaTeX">$(n,n)$ </tex-math></inline-formula>-MSS scheme regardless of the number of secret images <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is odd or even number. In addition, the proposed method outperforms the former existing <inline-formula> <tex-math notation="LaTeX">$(n,n)$ </tex-math></inline-formula>-MSS schemes in terms of quantitative measurements.

[1]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[2]  Jen-Bang Feng,et al.  A new multi-secret images sharing scheme using Largrange's interpolation , 2005, J. Syst. Softw..

[3]  Tzungher Chen,et al.  Efficient multi-secret image sharing based on Boolean operations , 2011, Signal Process..

[4]  Chin-Chen Chang,et al.  A multi-threshold secret image sharing scheme based on MSP , 2012, Pattern Recognit. Lett..

[5]  Xiangde Zhang,et al.  A novel image encryption-compression scheme using hyper-chaos and Chinese remainder theorem , 2013, Signal Process. Image Commun..

[6]  Chien-Chang Chen,et al.  A secure Boolean-based multi-secret image sharing scheme , 2014, J. Syst. Softw..

[7]  Jing-Ming Guo,et al.  False-positive-free SVD-based image watermarking , 2014, J. Vis. Commun. Image Represent..

[8]  Mingchu Li,et al.  A multi-threshold secret image sharing scheme based on the generalized Chinese reminder theorem , 2015, Multimedia Tools and Applications.

[9]  Hedieh Sajedi,et al.  Steganalysis based on steganography pattern discovery , 2016, J. Inf. Secur. Appl..

[10]  Ching-Nung Yang,et al.  Enhanced Boolean-based multi secret image sharing scheme , 2016, J. Syst. Softw..

[11]  Heri Prasetyo,et al.  False-positive-free GSVD-based image watermarking for copyright protection , 2016, 2016 International Symposium on Electronics and Smart Devices (ISESD).

[12]  Neeta Nain,et al.  A novel approach for sharing multiple color images by employing Chinese Remainder Theorem , 2017, J. Vis. Commun. Image Represent..

[13]  Millie Pant,et al.  Multipurpose image watermarking in the domain of DWT based on SVD and ABC , 2017, Pattern Recognit. Lett..

[14]  Dilip Kumar Yadav,et al.  A minesweeper game-based steganography scheme , 2017, J. Inf. Secur. Appl..

[15]  Yang Liu,et al.  Secure and robust digital image watermarking scheme using logistic and RSA encryption , 2018, Expert Syst. Appl..

[16]  Yuefeng Ji,et al.  Multi-bit wavelength coding phase-shift-keying optical steganography based on amplified spontaneous emission noise , 2018 .

[17]  Chi-Man Pun,et al.  Reversible data-hiding in encrypted images by redundant space transfer , 2018, Inf. Sci..

[18]  Sungyoung Lee,et al.  Selective bit embedding scheme for robust blind color image watermarking , 2018, Inf. Sci..

[19]  Jian Weng,et al.  Adopting secret sharing for reversible data hiding in encrypted images , 2018, Signal Process..

[20]  Fouad Khelifi,et al.  On the security of a stream cipher in reversible data hiding schemes operating in the encrypted domain , 2018, Signal Process..

[21]  Santi P. Maity,et al.  Hierarchical secret image sharing scheme in compressed sensing , 2018, Signal Process. Image Commun..