Proposal of an Asymptotically Contrast-Ideal (t, n)- Threshold Visual Secret Sharing Scheme

This paper is concerned with a variation of the (t, n)-threshold visual secret sharing scheme ((t, n)-VSSS for short). In the (t, n)-VSSS a secret image is encrypted to n images called shares. While we can reproduce the secret image by stacking arbitrary t shares, no information is revealed from less than t shares. We consider a new (t, n)-VSSS in which stacking more than t shares enables us to recognize a secret image more clearly than stacking just t shares. In particular, for the cases of t = 2, 3,4, 5 we can prove the existence of basis matrices of the (t, n)-VSSS that almost perfectly reproduces a secret image when all the n shares are stacked if n is sufficiently large