An Optimal Class of Symmetric Key Generation Systems

  • Rolf Blom
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 209)


It is sometimes required that user pairs in a network share secret information to be used for mutual identification or as a key in a cipher system. If the network is large it becomes impractical or even impossible to store all keys securely at the users. A natural solution then is to supply each user with a relatively small amount of secret data from which he can derive all his keys. A scheme for this purpose will be presented and we call such a scheme a symmetric key generation system (SKGS). However, as all keys will be generated from a small amount of data, dependencies between keys will exist. Therefore by cooperation, users in the system might be able to decrease their uncertainty about keys they should not have access to.

The objective of this paper is to present a class of SKGS for which the amount of secret information needed by each user to generate his keys is the least possible while at the same time a certain minimum number of users have to cooperate to resolve the uncertainty of unknown keys.


  1. (1).
    R. Blom, “An optimal class of symmetric key generation systems”, Report LiTH-ISY-I-0641, Linköping University, 1984.Google Scholar
  2. (2).
    F.J. MacWilliams and N.J.A. Sloane, The Theory of error correcting codes, North-Holland, New York, 1977.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Rolf Blom
    • 1
  1. 1.Ericsson Radio Systems ABStockholmSweden

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