Progressive Secret Image Sharing Using Multiplicative Primitive Irreducible Polynomials

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.