Analysis of Three (k, n) Secret Sharing Methods and Development of a (4, n) Method with Valid Participant Authentication, Error Detection, and 100% Repairing of Multiple Damages

The aim of this thesis is the analysis of three secret sharing methods and development of a new method having better features. We work on Yuan’s and Chang-Chen-Wang’s methods; the latter one is enhanced. Yuan proposed two methods which use least significant bits of each pixel that is easiest way to hide a secret black-white image into multiple grayscale cover images by ± 1 operation that is difficult to detect. They are (n, n) as allowing to restore the secret from n covers out of n covers; their (2, 3) only modification is also proposed by Yuan. Chang-Chen-Wang Secret grayscale image Sharing between several grayscale cover images with Authentication and Remedy method (SSAR) has participant authentication and damaged pixels repairing properties while Yuan’s methods have not these features. We implemented the algorithms and conducted experiments on them getting Peak Signal to Noise Ratio (PSNR) and Structural Similarity values similar to those obtained in the papers of Yuan and Chang-Chen-Wang. We show that SSAR may fail under made assumption of uniqueness of the covers’ identifiers, is not able fake participant recognizing, and has limited by five bits out of eight (62.5%) repairing ability of one corrupted pixel. Error and fake participant detection ability is supported by 4-bit hash value. The SSAR method is (3, n) as allowing to restore a secret from any three of n cover images. We correct assumptions on the uniqueness of the identifiers so that SSAR works now correctly and propose (4, n) SSAR enhancement, SSAR-E, allowing 100% exact restoration of a corrupted pixel by the use of any four out of n covers, and recognizing a fake participant with the help of cryptographic hash functions, which have 5-bit values that allows better error detection. Also by the use of special permutation having only one loop including all the secret image pixels, SSAR-E is able restoring all the secret image damaged pixels having just one correct pixel left. The performance and size of cover images for SSAR-E are the same as for SSAR. Keywords: Secret sharing, grayscale images, steganography, authentication, repairing