k out of k extended visual cryptography scheme by random grids

Author-Highlights•We propose a (k, k)-EVCS by RG, in which each share can have a different content.•Some concepts and tools are developed to analyze RG-based EVCSs.•The visual quality of decoded image and that of share images can be easily traded.

This paper first gives a formal definition of k out of k extended visual cryptography scheme by random grids ((k, k) RG-based EVCS), in which a secret image and k cover images are encoded into k share images in such a way that the k share images show the k cover images individually and the stacking of any k share images will reveal the secret image while from any less than k share images, we can deduce no information about the secret image. Then we present a (k, k) RG-based EVCS that needs neither extra pixel expansion nor any basis matrices (codebook), which are inevitable in conventional solutions of EVCS. In addition, the proposed scheme can easily trade the visual quality of the decoded image with the visual quality of share images by setting a certain parameter in the scheme from small to large. The correctness of the proposed scheme is validated by formal proofs, and its feasibility is demonstrated by computer simulations.