On the Isolation of a Common Secret

  • Don Beaver
  • Stuart Haber
  • Peter Winkler
Part of the Algorithms and Combinatorics book series (AC, volume 14)


Two parties are said to “share a secret” if there is a question to which only they know the answer. Since possession of a shared secret allows them to communicate a bit between them over an open channel without revealing the value of the bit, shared secrets are fundamental in cryptology.

We consider below the problem of when two parties with shared knowledge can use that knowledge to establish, over an open channel, a shared secret. There are no issues of complexity or probability; the parties are not assumed to be limited in computing power, and secrecy is judged only relative to certainty, not probability. In this context the issues become purely combinatorial and in fact lead to some curious results in graph theory.

Applications are indicated in the game of bridge, and for a problem involving two sheriffs, eight suspects and a lynch mob.


Communication Protocol Shared Secret Incidence Graph True Edge Fano Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Zs. Baranyai, On the factorization of the complete uniform hypergraph, Infinite and finite sets (Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I (1975) 91–108.Google Scholar
  2. 2.
    M. Fischer, M. Paterson, and C. Rackoff, Secret bit transmission using a random deal of cards, Distributed Computing and Cryptography, American Mathematical Society (1991) 173–181.Google Scholar
  3. 3.
    M. Fischer and R. Wright, Multiparty secret key exchange using a random deal of cards, Proceedings of CRYPTO ’91, Springer-Verlag Lecture Notes in Computer Science, Vol 576 (1992) 141–155.Google Scholar
  4. 4.
    P. Winkler, Cryptologic techniques in bidding and defense (Parts I, II, III, IV), Bridge Magazine (April-July 1981) 148–149, 186–187, 226–227, 12–13.Google Scholar
  5. 5.
    P. Winkler, The advent of cryptology in the game of bridge, Cryptologia, vol. 7 (1983) 327–332.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Don Beaver
    • 1
  • Stuart Haber
    • 2
  • Peter Winkler
    • 3
  1. 1.Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Surety Technologies Inc. and BellcoreMorristownUSA
  3. 3.AT&T Bell LaboratoriesMurray HillUSA

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