A cheating immune (k, n) visual cryptography scheme by using the rotation of shares

Abstract

Since Noar and Shamir introduced visual cryptography scheme (VCS), the cheating problem of VCS has absorbed much attention of scholars. The current researches on cheating immune have one or more of these serious disadvantages: (1) each share has extra pixel expansion, (2) some methods need extra verification shares to determine the share is genuine or not, (3) some schemes require a higher encryption/decryption overhead, and (4) the authentication procedure needs a trusted third party. In order to establish a novel cheating immune visual cryptography scheme (CIVCS) without pixel expansion, this paper generates n original shares by using random grid based visual cryptography scheme (RG-based VCS) and stamps authentication patterns on original shares to obtain verifiable shares, where the authentication patterns are three adjacent and non-intersect concentric solid black rings. In authentication phase, the authentication patterns can be revealed respectively by stacking any two verifiable shares in several ways, including rotating one of the two shares by $90^{\circ }$, $180^{\circ }$, and $270^{\circ }$ counterclockwise. The main contribution of this paper is that we propose a novel CIVCS without the above deficiencies. Furthermore, experimental results and theoretical proofs are provided for illustrating the effectiveness of the proposed CIVCS.