A Probabilistic Model of $(t,n)$ Visual Cryptography Scheme With Dynamic Group

The (t, n) visual cryptography (VC) is a secret sharing scheme where a secret image is encoded into n transparencies, and the stacking of any t out of n transparencies reveals the secret image. The stacking of t - 1 or fewer transparencies is unable to extract any information about the secret. We discuss the additions and deletions of users in a dynamic user group. To reduce the overhead of generating and distributing transparencies in user changes, this paper proposes a (t, n) VC scheme with unlimited n based on the probabilistic model. The proposed scheme allows n to change dynamically in order to include new transparencies without regenerating and redistributing the original transparencies. Specifically, an extended VC scheme based on basis matrices and a probabilistic model is proposed. An equation is derived from the fundamental definitions of the (t, n) VC scheme, and then the (t, ∞) VC scheme achieving maximal contrast can be designed by using the derived equation. The maximal contrasts with t = 2 to 6 are explicitly solved in this paper.