Constructions and Properties of General ( k, n ) Block-Based Progressive Visual Cryptography

Recently, Hou and others introduced a (2, n) block-based progressive visual cryptographic scheme (BPVCS) in which image blocks can be gradually recovered step by step. In Hou and others' (2, n)-BPVCS, a secret image is subdivided into n non-overlapping image blocks. When t (2 <= t <= n) participants stack their shadow images, all the image blocks associated with these t participants will be recovered. However, Hou and others' scheme is only a simple 2-out-of-n case. In this paper, we discuss a general (k, n)-BPVCS for any k and n. Our main contribution is to give two constructions (Construction 1 and Construction 2) of this general (k, n)-BPVCS. Also, we theoretically prove that both constructions satisfy a threshold property and progressive recovery of the proposed (k, n)-BPVCS. For k = 2, Construction 1 is reduced to Hon and others' (2, n)-BPVCS.