Requirements for Group Independent Linear Threshold Secret Sharing Schemes

  • Brian King
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2384)


In a t out of n threshold scheme, any subset of t or more participants can compute the secret key k, while subsets of t − 1 or less participants cannot compute k. Some schemes are designed for specific algebraic structures, for example finite fields. Whereas other schemes can be used with any finite abelian group. In[24], the definition of group independent sharing schemes was introduced. In this paper, we develop bounds for group independent t out of n threshold schemes. The bounds will be lower bounds which discuss how many subshares are required to achieve a group independent linear threshold scheme. In particular, we will show that our bounds for the n − 1 out of n threshold schemes are tight for infinitely many n.


secret sharing linear secret sharing threshold cryptography group independent linear threshold schemes monotone span programs and bounds on share size 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Brian King
    • 1
  1. 1.IUPUI campusPurdue School of Engineering and TechnologyUSA

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