NDLI: Combinatorial solutions providing improved security for the generalized Russian cards problem

Content Provider	Springer Nature Link
Author	Swanson, C. M. Stinson, D. R.
Copyright Year	2012
Abstract	We present the first formal mathematical presentation of the generalized Russian cards problem, and provide rigorous security definitions that capture both basic and extended versions of weak and perfect security notions. In the generalized Russian cards problem, three players, Alice, Bob, and Cathy, are dealt a deck of $$n$$ cards, each given $$a$$ , $$b$$ , and $$c$$ cards, respectively. The goal is for Alice and Bob to learn each other’s hands via public communication, without Cathy learning the fate of any particular card. The basic idea is that Alice announces a set of possible hands she might hold, and Bob, using knowledge of his own hand, should be able to learn Alice’s cards from this announcement, but Cathy should not. Using a combinatorial approach, we are able to give a nice characterization of informative strategies (i.e., strategies allowing Bob to learn Alice’s hand), having optimal communication complexity, namely the set of possible hands Alice announces must be equivalent to a large set of $$t-(n, a, 1)$$ -designs, where $$t=a-c$$ . We also provide some interesting necessary conditions for certain types of deals to be simultaneously informative and secure. That is, for deals satisfying $$c = a-d$$ for some $$d \ge 2$$ , where $$b \ge d-1$$ and the strategy is assumed to satisfy a strong version of security (namely perfect $$(d-1)$$ -security), we show that $$a = d+1$$ and hence $$c=1$$ . We also give a precise characterization of informative and perfectly $$(d-1)$$ -secure deals of the form $$(d+1, b, 1)$$ satisfying $$b \ge d-1$$ involving $$d-(n, d+1, 1)$$ -designs.
Ending Page	367
Page Count	23
Starting Page	345
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	2
Volume Number	72
Language	English
Publisher	Springer US
Publisher Date	2012-11-13
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Information and Communication, Circuits Protocols Data Structures, Cryptology and Information Theory Discrete Mathematics in Computer Science Data Encryption Russian cards problem Coding and Information Theory Block designs Cryptography Combinatorics Information-theoretic cryptography Combinatorial designs
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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