Lower Bound for the Communication Complexity of the Russian Cards Problem

Abstract

In this paper it is shown that no public announcement scheme that can be modeled in Dynamic Epistemic Logic (DEL) can solve the Russian Cards Problem (RCP) in one announcement. Since DEL is a general model for any public announcement scheme [11], [3], [6], [21], [12] we conclude that there exist no single announcement solution to the RCP. The proof demonstrates the utility of DEL in proving lower bounds for communication protocols. It is also shown that a general version of RCP has no two announcement solution when the adversary has sufficiently large number of cards.

Combinatorial solutions providing improved security for the generalized Russian cards problem

“…In the case n = 7, there does not exist a large set of STS (7), so we cannot construct an optimal (3, 3, 1)-strategy. However, Example 1.2 provides us with an equitable strategy with m = 10 and γ = 2 that is informative for Bob and perfectly 1-secure against Cathy.…”

“…However, Example 1.2 provides us with an equitable strategy with m = 10 and γ = 2 that is informative for Bob and perfectly 1-secure against Cathy. This is because every announcement in this strategy is an STS (7) and every 3-subset occurs in exactly two announcements. Examples from the literature for this case typically only provide weak 1-security.…”

“…This area of research is especially interesting in terms of possible applications to key generation; see, for example [10,11,12,13,14,17,16,2]. Others are concerned with analyzing variations of the problem using epistemic logic [18,19,20,7]. Duan and Yang [9] and He and Duan [15] consider a special generalization, with n − 1 players each dealt n cards, and one player (the intruder) dealt one card; the authors give an algorithm by which a dealer, acting as a trusted third party, can construct announcements for each player.…”