(3, n)-visual secret sharing scheme with unexpanded shares

Visual secret sharing scheme (VSSS) is a method to encode a secret image into n noise-like shadow images called shares. Decryption is possible by overlapping an adequate number (say, t) of shares. The hidden secret message will be naturally revealed and can be decoded by the human visual system (HVS) without the necessity of any complicated computation or replacement algorithms. Moreover, no knowledge of sophisticated cryptographic techniques is needed for the encryption and decryption processes. However, the secret image will be invisible if the number of stacked shares is less than t. This is so called (t, n)-threshold visual cryptography scheme ((t, n)-VCS). The greatest advantage of this decryption process is that neither complex computations nor any knowledge about VCS are needed. It is a simple and safe secret sharing method for the decoding of secret images when computer-resources are lacking. (3, n)-threshold visual secret sharing scheme ((3, n)-VSSS) is a special case of (t, n)-VSSS. In previous related (t, n)-VSSS researches, their sharing schemes are mostly an individual work of a specific t, however, they are not making an analysis whether this scheme is the best candidate for that specific t. Besides, the common drawbacks of the related researches include complex design method, poor black-white contrast of the restored image, and expanded pixels. In order to solve the above problems, we used combinatics to design a novel (3, n)-VSSS with unexpanded shares, and to analyze the visual effects with different parameters setting. We found that randomly selecting n/4 (resp. 3n/4) positions in each column of the dispatching matrix ML₁ (resp. ML₀) and filling them with a value of 1 can generate the best contrast when any 3 shares are stacked together; while randomly selecting 1 (resp. n-1) positions in each column of the dispatching matrix ML₁ (resp. ML₀) and filling them with a value of 1 can generate the best contrast when all n shares are stacked together. Theoretical analysis shows that our black-white contrast (visual effect) in the restored image will converge to 1/16 when the number of participators approximated to infinite (n → ∞), and this is the optimum result in (3, n)-VSSS. Compared to other related researches, this study has the following advantages: (1) the design concept is simple and easy to implement; (2) the black-white contrast of the restored image is better than other related (3, n)-VSSS researches; (3) the transparencies (shares) are the same size as the secret image.