General Constructions for Threshold Multiple-Secret Visual Cryptographic Schemes
Shyong Jian Shyu, Hung-Wei Jiang · IEEE Transactions on Information Forensics and Security · 2013
A conventional threshold (kout ofn) visual secret sharing scheme encodes one secret imagePintontransparencies (called shares) such that any group ofktransparencies revealsPwhen they are superimposed, while that of less thankones cannot. We define and develop general constructions for threshold multiple-secret visual cryptographic schemes (MVCSs) that are capable of encodingssecret imagesP1,P2,...,Psintonshares such that any group of less thankshares obtains none of the secrets, while 1) each group ofk,k+1,...,nshares revealsP1,P2, ...,Ps, respectively, when superimposed, referred to as (k,n,s)-MVCS wheres=n-k+1; or 2) each group ofushares reveals P(ru) whereru∈ {0,1,2,...,s} (ru=0 indicates no secret can be seen),k≤u≤nand 2 ≤s≤n-k+1, referred to as (k,n,s,R)-MVCS in whichR=(rk,rk+1, ...,rn) is called the revealing list. We adopt the skills of linear programming to model (k,n,s) - and (k,n,s,R) -MVCSs as integer linear programs which minimize the pixel expansions under all necessary constraints. The pixel expansions of different problem scales are explored, which have never been reported in the literature. Our constructions are novel and flexible. They can be easily customized to cope with various kinds of MVCSs.