$k$ Out of $n$ Region Incrementing Scheme in Visual Cryptography

Recently, Wang introduced a novel (2,
n
) region incrementing visual cryptographic scheme (RIVCS), which can gradually reconstruct secrets in a single image with multiple security levels. In RIVCS, the secret image is subdivided into multiple regions in such a way that any
t
shadow images, where 2 ≤
t
≤
n
, can be used to reveal the (
t
-1) th region. However, Wang's scheme suffers from the incorrect-color problem, which the colors of reconstructed images may be reversed (i.e., the black and white are reversed). If the color of text is also the secret information, the incorrect-color problem will compromise the secret. Additionally, Wang's scheme is only suitable for the 2-out-of-
n
case, i.e., (
k
,
n
)-RIVCS where
k
=2. In this paper, we propose a general (
k
,
n
)-RIVCS, where
k
and
n
are any integers, that is able to reveal correct colors of all regions. This paper has made three main contributions: 1) our scheme is a general (
k
,
n
)-RIVCS, where
k
and
n
can be any integers; 2) the incorrect-color problem is solved; and 3) our (
k
,
n
)-RIVCS is theoretically proven to satisfy the security and contrast conditions.