An efficient protocol for unconditionally secure secret key exchange
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Multiparty Secret Key Exchange Using a Random Deal of Cards
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Dealing necessary and sufficient numbers of cards for sharing a one-bit secret key
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Necessary and Sufficient Numbers of Cards for Sharing Secret Keys on Hierarchical Groups
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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We propose the problem of how to transmit an information-theoretically secure bit using random deals of cards among players in hierarchical groups and a computationally unlimited eavesdropper. A player in the highest group wants to send players in lower groups a secret bit which is secure from the eavesdropper and some other players. We formalize this problem and design protocols for constructing secret key exchange spanning trees on hierarchical groups. For each protocol we give sufficient conditions to successfully construct a secret key exchange spanning tree for the hand sizes of the players and the eavesdropper.