Title: On the Size of Monotone Span Programs
Authors: Nikov, V
Nikova, Svetla
Preneel, Bart
Issue Date: 2005
Publisher: Springer-Verlag
Host Document: Lecture Notes in Computer Science vol:3352 pages:252-265
Conference: SCN 2004 date:September 08-10, 2004
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.
ISSN: 0302-9743
Publication status: published
KU Leuven publication type: IC
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics

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