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Geometric Shared Secret and/or Shared Control Schemes

  • Gustavus J. Simmons
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 537)

Abstract

A shared secret scheme is normally specified in terms of a desired security, Pd, and a concurrence scheme, Γ. The concurrence scheme (aka access structure) identifies subsets of participants (also called trustees or shareholders) each of which should be able to cooperatively recover the secret and/or initiate the controlled action. The security requirement is expressed as the maximum acceptable probability, Pd, that the secret can be exposed or the controlled action initiated by a collection of persons that doesn’t include at least one of the authorized subsets identified in the concurrence scheme. A concurrence scheme is said to be monotone if every set of participants that includes one or more sets from Γ is also able to recover the secret. The closure of Γ, denoted by \( \hat \Gamma \) is the collection of all supersets (not necessarily proper) of the sets in Γ, i.e., the collection of all sets of participants that can recover the secret and/or initiate the controlled action. A shared secret scheme implementing a concurrence scheme Γ is said to be perfect if the probability of recovering the secret is the same for every set, C, of participants: C\( \hat \Gamma \). Since, in particular, C could consist of only nonparticipants, i.e., of persons with no insider information about the secret, the probability, P, of an unauthorized recovery of the secret in a perfect scheme is just the probability of being able to “guess” the secret using only public information about Γ and the shared secret scheme implementing Γ: P ≤ Ptd.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Gustavus J. Simmons
    • 1
  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

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