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Abstract

Using a random deal of cards to players and a computationally unlimited eavesdropper, all players wish to share a one-bit secret key which is informationtheoretically secure from the eavesdropper. This can be done by a protocol to make several pairs of players share one-bit secret keys so that all these pairs form a tree over players. In this paper we obtain a necessary and sufficient condition on the number of cards for the existence of such a protocol.

A Distributed Computing Perspective of Unconditionally Secure Information Transmission in Russian Cards Problems

“…This protocol is later improved in [39], where a detail and clear analysis is presenting, showing that the improved transformation protocol establishes an n-bit secret key exchange for a signature (a, b; e) if and only if Ψ (a, b; e) ≥ n, Ψ a function which is approximately proportional to d, where d is the number of distinct cards in the deck. For key set protocols, Fischer and Wright show that A and B can share a bit if and only if a + b ≥ c + 2, this is reported in [46] (journal version of [45]), where a characterization for the signatures that are solvable by key set protocols is presented, and observe that actually the transformation protocol of Fischer and Wright [28] can deal with a case that is not solvable by key set, namely (3, 2; 4). All this is for randomized protocols, the only case of deterministic protocols that we are aware of is Fischer, Paterson and Rackoff [26], where they give a protocol for secret bit transmission, and show it works if c ≤ min(a, b)/3.…”

“…The idea that card games could be used to achieve security in the presence of computationally unbounded adversaries proposed by Peter Winkler [55] led to an active research line e.g. [26,27,28,29,39,44,45,46,55]. It motivated Fischer and Wright [28] to consider card games, where A, B, C draw cards from a deck D of n cards, as specified by a signature (a, b, c), with n = a + b + c + r. Nobody gets r cards, while A gets a cards, B gets b cards, and C gets c cards.…”