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TR00-003 | 26th November 1999 00:00

Determining the Optimal Contrast for Secret Sharing Schemes in Visual Cryptography


Authors: Matthias Krause, Hans Ulrich Simon
Publication: 17th January 2000 19:05
Downloads: 1037


This paper shows that the largest possible contrast C(k,n)
in a k-out-of-n secret sharing scheme is approximately
4^(-(k-1)). More precisely, we show that
4^(-(k-1)) <= C_{k,n} <= 4^(-(k-1))}n^k/(n(n-1)...(n-(k-1))).
This implies that the largest possible contrast equals
4^(-(k-1)) in the limit when n approaches infinity.
For large n, the above bounds leave almost no gap. For
values of n that come close to k, we will present
alternative bounds (being tight for n=k). The proofs of
our results proceed by revealing a central relation between
the largest possible contrast in a secret sharing scheme
and the smallest possible approximation error in problems
occuring in Approximation Theory.

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