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.

[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.

[3]

T. M. Cover and J. A. Thomas, "Elements of Information Theory,'' $2^{nd}$ edition,, Wiley, (2006).

[4]

L. Csirmaz, The size of a share must be large,, J. Cryptol., 10 (1997), 223. doi: 10.1007/s001459900029.

[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.

[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.

[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.

[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.

[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.

show all references

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.

[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.

[3]

T. M. Cover and J. A. Thomas, "Elements of Information Theory,'' $2^{nd}$ edition,, Wiley, (2006).

[4]

L. Csirmaz, The size of a share must be large,, J. Cryptol., 10 (1997), 223. doi: 10.1007/s001459900029.

[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.

[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.

[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.

[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.

[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.

[1]

Bagher Bagherpour, Shahrooz Janbaz, Ali Zaghian. Optimal information ratio of secret sharing schemes on Dutch windmill graphs. Advances in Mathematics of Communications, 2019, 13 (1) : 89-99. doi: 10.3934/amc.2019005

[2]

Stefka Bouyuklieva, Zlatko Varbanov. Some connections between self-dual codes, combinatorial designs and secret sharing schemes. Advances in Mathematics of Communications, 2011, 5 (2) : 191-198. doi: 10.3934/amc.2011.5.191

[3]

Ryutaroh Matsumoto. Strongly secure quantum ramp secret sharing constructed from algebraic curves over finite fields. Advances in Mathematics of Communications, 2019, 13 (1) : 1-10. doi: 10.3934/amc.2019001

[4]

Valentin Afraimovich, Maurice Courbage, Lev Glebsky. Directional complexity and entropy for lift mappings. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3385-3401. doi: 10.3934/dcdsb.2015.20.3385

[5]

Erik M. Bollt, Joseph D. Skufca, Stephen J . McGregor. Control entropy: A complexity measure for nonstationary signals. Mathematical Biosciences & Engineering, 2009, 6 (1) : 1-25. doi: 10.3934/mbe.2009.6.1

[6]

Eitan Tadmor. Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4579-4598. doi: 10.3934/dcds.2016.36.4579

[7]

Matthew Bourque, T. E. S. Raghavan. Policy improvement for perfect information additive reward and additive transition stochastic games with discounted and average payoffs. Journal of Dynamics & Games, 2014, 1 (3) : 347-361. doi: 10.3934/jdg.2014.1.347

[8]

Bin Li, Hai Huyen Dam, Antonio Cantoni. A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 297-304. doi: 10.3934/naco.2016012

[9]

Yonggui Zhu, Yuying Shi, Bin Zhang, Xinyan Yu. Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing. Inverse Problems & Imaging, 2014, 8 (3) : 925-937. doi: 10.3934/ipi.2014.8.925

[10]

Suxiang He, Pan Zhang, Xiao Hu, Rong Hu. A sample average approximation method based on a D-gap function for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 977-987. doi: 10.3934/jimo.2014.10.977

[11]

Mingzheng Wang, M. Montaz Ali, Guihua Lin. Sample average approximation method for stochastic complementarity problems with applications to supply chain supernetworks. Journal of Industrial & Management Optimization, 2011, 7 (2) : 317-345. doi: 10.3934/jimo.2011.7.317

[12]

Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4569-4577. doi: 10.3934/dcds.2016.36.4569

[13]

Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399

[14]

Nan Li, Song Wang, Shuhua Zhang. Pricing options on investment project contraction and ownership transfer using a finite volume scheme and an interior penalty method. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-20. doi: 10.3934/jimo.2019006

[15]

Tomáš Roubíček. Thermodynamics of perfect plasticity. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 193-214. doi: 10.3934/dcdss.2013.6.193

[16]

Olof Heden. A survey of perfect codes. Advances in Mathematics of Communications, 2008, 2 (2) : 223-247. doi: 10.3934/amc.2008.2.223

[17]

Pavel Bachurin, Konstantin Khanin, Jens Marklof, Alexander Plakhov. Perfect retroreflectors and billiard dynamics. Journal of Modern Dynamics, 2011, 5 (1) : 33-48. doi: 10.3934/jmd.2011.5.33

[18]

Marcela Mejía, J. Urías. An asymptotically perfect pseudorandom generator. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 115-126. doi: 10.3934/dcds.2001.7.115

[19]

Stefano Galatolo. Orbit complexity and data compression. Discrete & Continuous Dynamical Systems - A, 2001, 7 (3) : 477-486. doi: 10.3934/dcds.2001.7.477

[20]

Valentin Afraimovich, Lev Glebsky, Rosendo Vazquez. Measures related to metric complexity. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1299-1309. doi: 10.3934/dcds.2010.28.1299

2017 Impact Factor: 0.564

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]