On the equivalence of two definitions of visual cryptography scheme

Abstract

A visual cryptography scheme (VCS) is a secret sharing method, for which the secret can be decoded by human eyes without needing any cryptography knowledge nor any computation. To the best of our knowledge, there are two different definitions of basis matrix (k,n)-VCS. The definition of unconditional secure basis matrix (k,n)-VCS is the generally accepted one, and has been widely used since the pioneer work of Naor and Shamir in 1994, while the definition of stacking secure basis matrix (k,n)-VCS is relatively new, and has been used in many studies in recent years. Our study shows that the above two definitions are actually equivalent. Furthermore, we generalize the equivalence relation to general access structure basis matrix VCS and general access structure size invariant VCS. But the equivalence relation does not hold for non-basis matrix (k,n)-VCS. © 2012 Springer-Verlag.