Combination of Sharing Matrix and Image Encryption for Lossless $(k,n)$ -Secret Image Sharing

This paper first introduces a (k, n)-sharing matrix S^(k,n) and its generation algorithm. Mathematical analysis is provided to show its potential for secret image sharing. Combining sharing matrix with image encryption, we further propose a lossless (k, n)-secret image sharing scheme (SMIE-SIS). Only with no less than k shares, all the ciphertext information and security key can be reconstructed, which results in a lossless recovery of original information. This can be proved by the correctness and security analysis. Performance evaluation and security analysis demonstrate that the proposed SMIE-SIS with arbitrary settings of k and n has at least five advantages: 1) it is able to fully recover the original image without any distortion; 2) it has much lower pixel expansion than many existing methods; 3) its computation cost is much lower than the polynomial-based secret image sharing methods; 4) it is able to verify and detect a fake share; and 5) even using the same original image with the same initial settings of parameters, every execution of SMIE-SIS is able to generate completely different secret shares that are unpredictable and non-repetitive. This property offers SMIE-SIS a high level of security to withstand many different attacks.

I. Introduction

Secret image sharing is an interesting research topic in multimedia security society. Its function is to encrypt an original image into different shares. Using () or more shares can successfully reconstruct the original image. With less than shares, any information of the original image can not be accessed. This unique and interesting function allows secret image sharing to be used in many fields such as general access structures [1], discrete memoryless network [2], visual authentication and identification [3], [4], data sharing [5], and so on.