A (k, n) multi-secret image sharing scheme based on Chinese remainder theorem and Arnold cat map

Abstract

A multi-secret image sharing (MSIS) scheme is a procedure to break down secret images into numerous shares and distribute each share to each authorized participant. Most existing ( n , n ) schemes face the problem of all-or-nothing that is all the n shares are required to reconstruct a secret image. If a single share is lost, then the secret image will not be recovered. Moreover, the existing ( k , n ) MSIS schemes either require k consecutive shares or general access structure to recover the secret images. The proposed scheme addresses the previous schemes’ issues. It is based on Arnold cat map, Chinese remainder theorem (CRT), and Boolean operation. It is a ( k , n ) threshold scheme where k is the threshold, and n is the number of participants. Arnold cat map is adopted for the randomization of images, and Boolean operation is used for producing public share images. CRT is utilized for the recovery of images. It has high fault tolerance capability as any of the k participants can submit their shares to reconstruct images and consume less computational time due to employing the modular method. Moreover, it can withstand differential as well as statistical attacks.