Cheating immune k-out-of-n block-based progressive visual cryptography

Abstract

Hou et al. introduced a (2, n) block-based progressive visual cryptographic scheme (BPVCS). In (2, n)-BPVCS, a secret image is subdivided into n non-overlapped image blocks. When t (2 ≤ t ≤ n) participants stack their shadow images, the image blocks belonged to these t participants will be recovered. Unfortunately, Hou et al.’s (2, n)-BPVCS suffers from the cheating problem. Additionally, Hou et al.’s scheme is only suitable for 2-out-of-n case, i.e., (k, n)-BPVCS where k = 2. In this paper, we propose a cheating immune (k, n)-BPVCS for k>2. The main contribution of our paper is that the proposed (k, n)-BPVCS is not only cheating immune, but also suitable for general k-out-of-n threshold, where k and n are integers with 2 ≤ k ≤ n. Theoretical analysis demonstrates that our scheme still holds progressive recovery and security, and meantime has cheating immune capability.