Visual multiple secret sharing based upon turning and flipping

The secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies (called shares) in the form of rectangles, which reveal the secret image to the human visual system when they are superimposed. Recently, visual secret sharing schemes involving multiple secrets have attracted much attention. By adopting rotations on one of the two encoded circle shares, more than two secrets could be shared. Yet, the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones. In this paper, we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares. Specifically, we define some operations onto a transparency based upon turning over or flipping around. Then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share, whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations. The proposed schemes, which solidly elaborate the relationship between the encoded shares and the shared secrets, broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically.