UNIVERSALLY IDEAL SECRET-SHARING SCHEMES

Given a set of parties {1,...,n), an access structure is a monotone co llection of subsets of the parties. For a certain domain of secrets, a secret-sharing scheme for an access structure is a method for a deale r to distribute shares to the parties. These shares enable subsets in the access structure to reconstruct the secret, while subsets not in t he access structure get no information about the secret. A secret-shar ing scheme is ideal if the domains of the shares are the same as the d omain of the secrets. An access structure is universally ideal if ther e exists an ideal secret-sharing scheme for it over every finite domai n of secrets. An obvious necessary condition for an access structure t o be universally ideal is to be ideal over the binary and ternary doma ins of secrets. In this work, we prove that this condition is also suf ficient. We also show that being ideal over just one of the two domain s does not suffice for universally ideal access structures. Finally, w e give an exact characterization for each of these two conditions.