Progressive Secret Image Sharing Using Multiplicative Primitive Irreducible Polynomials
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Wu, Xiaotian
Wang, Xinyue
Chen, Bing
Xia, Zhihua
Yang, Ching-Nung
Yan, Wei Qi
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Institute of Electrical and Electronics Engineers (IEEE)
Abstract
Progressive secret image sharing (PSIS) encodes a secret into n shadows, enabling the secret to be gradually revealed as more shared data becomes available. However, current techniques suffer from non-uniform progressive recovery and inferior visual quality of low-level decoded images. To address these issues, we combine multiplicative primitive irreducible polynomials with polynomial ring Chinese Remainder Theorem (CRT) to establish a PSIS. A method with 2 progressive levels is presented, where two polynomials f1(α) and f2(α) determine a main polynomial F(α) = f1(α) × f2(α). A (k – 1)-degree polynomial over (mod F(α)) is constructed for shadow generation. The secret can be losslessly recovered by Lagrange interpolation over (mod F(α)), or gradually recovered through modified shadows using Lagrange interpolation and polynomial ring CRT. The scheme is further extended to t progressive levels, and a bit rearrangement technique is devised to enhance progressive recovery performance. Experiments and comparisons illustrate the effectiveness of the proposed technique, including uniform progressive recovery and superior low-level image quality.
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0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, Artificial Intelligence & Image Processing, 4006 Communications engineering, 4009 Electronics, sensors and digital hardware, 4603 Computer vision and multimedia computation, Secret sharing, Secret image sharing, Chinese Remainder Theorem, Polynomial ring, Progressive recovery
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IEEE Transactions on Circuits and Systems for Video Technology, ISSN: 1051-8215 (Print); 1558-2205 (Online), Institute of Electrical and Electronics Engineers (IEEE), 1-1. doi: 10.1109/tcsvt.2026.3704601
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This article has been accepted for publication in IEEE Transactions on Circuits and Systems for Video Technology. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TCSVT.2026.3704601