Linear algebraic techniques to construct monochrome visual cryptographic schemes for general access structure and its applications to color images

Abstract

Though the monochrome (black and white) visual cryptography has a very rich literature, a very few papers have been published for the construction of general access structure. In this paper we put forward a method of construction of a strong monochrome visual cryptographic scheme (VCS) for general access structure using linear algebra. As a particular case of general access structure, $$(k,n)$$ ( k , n ) -VCS for $$2 \le k \le n$$ 2 ≤ k ≤ n is obtained. The $$(n,n)$$ ( n , n ) -VCS obtained from the scheme attains the optimal pixel expansion as well as optimal relative contrast. We provide an efficient construction of $$(n-1,n)$$ ( n ? 1 , n ) -VCS. We further extend our monochrome VCS to color VCS for restricted access structures. Finally, we provide some interesting examples that will lead to some future research directions in the area of VCS.