# American Institute of Mathematical Sciences

August  2013, 7(3): 311-317. doi: 10.3934/amc.2013.7.311

## Average complexities of access structures on five participants

 1 Department of Mathematics, Iran University of Science and Technology, Tehran, Iran, Iran

Received  July 2012 Revised  July 2013 Published  July 2013

In this paper, we consider the 12 access structures on five participants for which determining the exact values of the average complexities remained as open problems in Jackson and Martin's paper [6]. We establish the exact values of the average complexities of these access structures.
Citation: Motahhareh Gharahi, Massoud Hadian Dehkordi. Average complexities of access structures on five participants. Advances in Mathematics of Communications, 2013, 7 (3) : 311-317. doi: 10.3934/amc.2013.7.311
##### References:
 [1] C. Blundo, A. De Santis, D. R. Stinson and U. Vaccaro, Graph decompositions and secret sharing schemes,, J. Cryptol., 8 (1995), 39. doi: 10.1007/BF00204801. Google Scholar [2] R. M. Capocelli, A. De Santis, L. Gargano and U. Vaccaro, On the size of shares of secret sharing schemes,, J. Cryptol., 6 (1993), 157. Google Scholar [3] T. M. Cover and J. A. Thomas, "Elements of Information Theory,'' $2^{nd}$ edition,, Wiley, (2006). Google Scholar [4] L. Csirmaz, The size of a share must be large,, J. Cryptol., 10 (1997), 223. doi: 10.1007/s001459900029. Google Scholar [5] W.-A. Jackson and K. M. Martin, Geometric secret sharing schemes and their duals,, Des. Codes Cryptogr., 4 (1994), 83. doi: 10.1007/BF01388562. Google Scholar [6] W.-A. Jackson and K. M. Martin, Perfect secret sharing schemes on five participants,, Des. Codes Cryptogr., 9 (1996), 267. doi: 10.1007/BF00129769. Google Scholar [7] J. Martí-Farré and C. Padró, On Secret Sharing Schemes, Matroids and Polymatroids,, J. Math. Cryptol., 4 (2010), 95. doi: 10.1515/JMC.2010.004. Google Scholar [8] C. Padró and G. Sáez, Lower bounds on the information rate of secret sharing schemes with homogeneous access structure,, Inform. Process. Lett., 83 (2002), 345. doi: 10.1016/S0020-0190(02)00213-2. Google Scholar [9] C. Padró and L. Vázquez, Finding lower bounds on the complexity of secret sharing schemes by linear programming,, in, (2010), 344. doi: 10.1007/978-3-642-12200-2_31. Google Scholar

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##### References:
 [1] C. Blundo, A. De Santis, D. R. Stinson and U. Vaccaro, Graph decompositions and secret sharing schemes,, J. Cryptol., 8 (1995), 39. doi: 10.1007/BF00204801. Google Scholar [2] R. M. Capocelli, A. De Santis, L. Gargano and U. Vaccaro, On the size of shares of secret sharing schemes,, J. Cryptol., 6 (1993), 157. Google Scholar [3] T. M. Cover and J. A. Thomas, "Elements of Information Theory,'' $2^{nd}$ edition,, Wiley, (2006). Google Scholar [4] L. Csirmaz, The size of a share must be large,, J. Cryptol., 10 (1997), 223. doi: 10.1007/s001459900029. Google Scholar [5] W.-A. Jackson and K. M. Martin, Geometric secret sharing schemes and their duals,, Des. Codes Cryptogr., 4 (1994), 83. doi: 10.1007/BF01388562. Google Scholar [6] W.-A. Jackson and K. M. Martin, Perfect secret sharing schemes on five participants,, Des. Codes Cryptogr., 9 (1996), 267. doi: 10.1007/BF00129769. Google Scholar [7] J. Martí-Farré and C. Padró, On Secret Sharing Schemes, Matroids and Polymatroids,, J. Math. Cryptol., 4 (2010), 95. doi: 10.1515/JMC.2010.004. Google Scholar [8] C. Padró and G. Sáez, Lower bounds on the information rate of secret sharing schemes with homogeneous access structure,, Inform. Process. Lett., 83 (2002), 345. doi: 10.1016/S0020-0190(02)00213-2. Google Scholar [9] C. Padró and L. Vázquez, Finding lower bounds on the complexity of secret sharing schemes by linear programming,, in, (2010), 344. doi: 10.1007/978-3-642-12200-2_31. Google Scholar
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