Secret image sharing in encrypted domain based on chaos theory and Chinese Remainder Theorem

Abstract

The increasing reliance on digital images emphasizes the need for stronger security. While encryption offers protection, it remains vulnerable to single points of failure or attack. Secret Image Sharing in the Encrypted Domain (SIS-ED) improves security by combining encryption with secret sharing, addressing issues like image leakage and unauthorized reconstruction. This paper proposes a new (n,n)-threshold SIS-ED scheme based on chaos theory and the Chinese Remainder Theorem (CRT) to enhance image protection in practical applications. In the sharing stage, a chaos-based cryptosystem scrambles the pixels of the secret image, disrupting spatial correlations. The scrambled image is split into n one-dimensional vectors, which undergo pixel fusion process. The n-tuple bytes are encoded into a single unique number using CRT with a set of mutually coprime numbers greater than 255, ensuring full reversibility and lossless recovery. The resulting (8n + 1)-bit numbers are converted to binary and split into 8-bit chunks to form a byte vector of encoded image. A random byte sequence generated by a chaotic function (Logistic map) is XORed with this vector to add additional perturbation to the encoded image. The perturbed image is then divided into n shares for distribution. In the recovery stage, pixel separation is performed by solving linear congruence equations using modular arithmetic. The proposed SIS-ED framework enables perfect data reconstruction, eliminating the need for random pixel expansion and producing compressed, more compact shares. Experiments validate the effectiveness and robust cryptographic properties of the approach.