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On the Size of Monotone Span Programs

  • Ventzislav Nikov
  • Svetla Nikova
  • Bart Preneel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3352)

Abstract

Span programs provide a linear algebraic model of computation. Monotone span programs (MSP) correspond to linear secret sharing schemes. This paper studies the properties of monotone span programs related to their size. Using the results of van Dijk (connecting codes and MSPs) and a construction for a dual monotone span program proposed by Cramer and Fehr we prove a non-trivial upper bound for the size of monotone span programs. By combining the concept of critical families with the dual monotone span program construction of Cramer and Fehr we improve the known lower bound with a constant factor, showing that the lower bound for the size of monotone span programs should be approximately twice as large. Finally, we extend the result of van Dijk showing that for any MSP there exists a dual MSP such that the corresponding codes are dual.

Keywords

Linear Span Access Structure Secret Sharing Scheme Recombination Vector Parity Check Matrix 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ventzislav Nikov
    • 1
  • Svetla Nikova
    • 2
  • Bart Preneel
    • 2
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department Electrical Engineering, ESAT/COSICKatholieke Universiteit LeuvenHeverlee-LeuvenBelgium

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