Abstract:
A (k,n) -threshold visual cryptography scheme ( (k,n) -threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the ``visual'' recovery of the secret image, but by inspecting less that k share one cannot gain any information on the secret image. The ``visual'' recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation.
In this paper we analyze the contrast of the reconstructed image for (k,n) -threshold VCS. We define a canonical form for (k,n) -threshold VCS and we also provide a characterizazion of (k,n) -threshold VCS. We completely characterize contrast optimal (n-1,n) -threshold VCS in canonical form. Moreover, for n\geq 4 , we provide, a contrast optimal (3,n) -threshold VCS in canonical form. We first describe a family of (3,n) -threshold VCS achieving various values of contrast and pixel expansion. Then, we prove an upper bound on the contrast of any (3,n) -threshold VCS and show that a scheme in the described family has optimal contrast. Finally, for k=4,5 we present two schemes with contrast asymptotically equal to 1/64 and 1/256, respectively.