Fully Incrementing Visual Cryptography From a Succinct Non-Monotonic Structure

Visual cryptography (VC) is a variant form of secret sharing. In general threshold setting, the k-out-of-n VC allows that, in a set of n participants, any k can recover and reconstruct the secret by stacking their shares. Recently, the notion of multiple-secret VC has been introduced to embed multiple secrets. Region incrementing visual cryptography (RIVC) is referred to as a new type of multi-secret VC. RIVC defines s layers and takes s secrets, and then embeds each secret into each layer. The layers are defined by the number of participants; for example, let two secrets and two layers be S 2 , S 3 and L 2 , L 3 in two-out-of-three RIVC, where any two participants in L 2 can recover S 2 and three in L 3 can recover S 2 , S 3 . However, there is another multi-secret VC, called fully incrementing visual cryptography (FIVC), which also has the layers, but only one secret Si will reveal in one layer Li. In this paper, our stating point is to propose a new notion of non-monotonic visual cryptography (NVC) for human vision system as a primitive to construct FIVC. We first present an ideal construction of simple NVC, which relies on a slightly unreasonable assumption. Based on the simple NVC, we show a few methods to extend the functionality for complicated cases of NVC. Then, the generic construction is presented as a systematic manner to eliminate the above-mentioned assumption. Finally, we formally introduce a transformation NVC-to-FIVC algorithm, which takes NVC as input and then produce a construction of FIVC. Also, show a demonstration the NVC-to-RIVC algorithm, and analyze some properties regarding NVC. We believe that the notion of NVC can potentially find other applications and is of independent interest.