  We study a secret sharing problem with three secrets where the secrets are
allowed to be related to each other, i.e., only certain combinations of the
three secrets are permitted. The dealer produces three shares such that every
pair of shares reveals a unique secret and reveals nothing about the other two
secrets, other than what can be inferred from the revealed secret. For the case
of binary secrets, we exactly determine the minimum amount of randomness
required by the dealer, for each possible set of permitted combinations. Our
characterization is based on new lower and upper bounds.
