Consider a secret sharing problem with three secrets related to each other, i.e., we allow only certain combinations of the three secrets. A dealer produces three shares such that every pair of share reveals a certain secret and nothing about the other two secrets other than what can be inferred from the revealed secret. We bound the randomness complexity of each possible set of permissible combinations and give randomness-optimal schemes for the same for binary secrets.
This is a joint work with Aayush Rajesh, Varun Narayanan, Manoj Prabhakaran and Vinod Prabhakaran.
