A distributed computing perspective of unconditionally secure information transmission in Russian cards problems

In the generalized Russian cards problem, we have a deck of n cards and three participants, A, B, and C, which receive a, b, and c cards respectively. The signature (a,b,c), where n=a+b+c+r, is known to all three participants. The goal is for A to privately communicate her hand to B via a public announcement, without using a shared secret nor cryptography. Using a deterministic protocol, A decides its announcement based on her hand. Using techniques from coding theory, Johnson graphs, and additive number theory, a novel perspective inspired by distributed computing theory is provided, to analyze the amount of information that A needs to send, while preventing C from learning a single card of her hand. In one extreme, B wants to learn all of A's cards; the novel notion of minimal information protocol is considered, so that, in the other extreme, B wishes to learn something about A's hand.