A New Scheme Based on (t,n)-Secret Image Sharing With Steganography Based on Joseph’s Problem and HLR

Saeidi, Zahra; Mashhadi, Samaneh

doi:10.22042/isecure.2025.219355

A New Scheme Based on (t,n)-Secret Image Sharing With Steganography Based on Joseph’s Problem and HLR

Document Type : Research Article

Authors

Zahra Saeidi

Samaneh Mashhadi

Cryptography and Data Security Laboratory, School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran

https://doi.org/10.22042/isecure.2025.219355

Abstract

The paper presents a novel approach to Secret Image Sharing (SIS) that combines (t, n)-threshold schemes with steganography, utilizing Joseph’s problem and Homogeneous Linear Recursion (HLR) to enhance security. The methodology involves dividing a secret image into shadow images, embedding these shadows into cover images using a Least Significant Bit (LSB) method guided by Joseph’s problem. The study aims to increase the security of SIS while maintaining high visual quality in the stego images. The authors validate their approach through various experiments, demonstrating that the proposed method improves Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) compared to existing methods.

Keywords

Joseph’s Problem

Homogeneous Linear Recursion

Secret Image Sharing

Steganography

[1] Shamir Adi. How to share a secret. Commun. ACM, 22:612–613, 1979.
[2] Ali Kanso and Mohammad Ghebleh. An efficient(t, n)–threshold secret image sharing scheme. Multimedia Tools and Applications, 76:16369–16388, 2017.
[3] Chih-Ching Thien and Ja-Chen Lin. Secret image sharing. Computers & Graphics, 26(5):765–770, 2002.
[4] Chang-Chou Lin and Wen-Hsiang Tsai. Secret image sharing with steganography and authentication. Journal of Systems and software, 73(3):405–414, 2004.
[5] Ching-Nung Yang, Chih-Cheng Wu, Yi-Chin Lin, and Cheonshik Kim. Enhanced matrix-based secret image sharing scheme. IEEE Signal Processing Letters, 19(12):789–792, 2012.
[6] Chin-Chen Chang, Yi-Pei Hsieh, and Chia-Hsuan Lin. Sharing secrets in stego images with authentication. Pattern Recognition, 41(10):3130–3137, 2008.
[7] Chin-Chen Chang, Yi-Hui Chen, and Lin-Yi Chuang. Meaningful shadows for image secret sharing with steganography and authentication techniques. J. Inf. Hiding Multim. Signal Process., 5(3):342–352, 2014.
[8] Lizhi Xiong, Xinwei Zhong, Ching-Nung Yang, and Xiao Han. Transform domain-based invertible and lossless secret image sharing with authentication. IEEE Transactions on information Forensics and Security, 16:2912–2925, 2021.
[9] Lizhi Xiong, Xinwei Zhong, and Ching-Nung Yang. Dwt-sisa: a secure and effective discrete wavelet transform-based secret image sharing with authentication. Signal Processing, 173:107571, 2020.
[10] Sara Charoghchi and Samaneh Mashhadi. A secure secret image sharing with steganography and authentication by hamming code (15, 11) for compressed images. Multimedia Tools and Applications, 83(11):31933–31955, 2024.
[11] Zahra Saeidi, Ameneh Yazdi, Samaneh Mashhadi, Masoud Hadian, and Adnan Gutub. High performance image steganography integrating iwt and hamming code within secret sharing. IET Image Processing, 18(1):129–139, 2024.
[12] Samaneh Mashhadi and Zahra Saeedi. A (t, n)-secret image sharing with steganography based on rook polynomial and lwe problem. Multimedia Tools and Applications, 82(25):39077–39097, 2023.
[13] Massoud Hadian Dehkordi and Samaneh Mashhadi. New efficient and practical verifiable multisecret sharing schemes. Information Sciences, 178(9):2262–2274, 2008.
[14] Xiaotian Wu and Ching-Nung Yang. Partial reversible ambtc-based secret image sharing with steganography. Digital Signal Processing, 93:22–33, 2019.
[15] Yan-Xiao Liu, Ching-Nung Yang, Yung-Shun Chou, Song-Yu Wu, and Qin-Dong Sun. Progressive (k, n) secret image sharing scheme with meaningful shadow images by gemd and rgemd. Journal of Visual Communication and Image Representation, 55:766–777, 2018.