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

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.  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

[1]

Jie Li, Xiangdong Ye, Tao Yu. Mean equicontinuity, complexity and applications. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 359-393. doi: 10.3934/dcds.2020167

[2]

Shengxin Zhu, Tongxiang Gu, Xingping Liu. AIMS: Average information matrix splitting. Mathematical Foundations of Computing, 2020, 3 (4) : 301-308. doi: 10.3934/mfc.2020012

[3]

Timothy Chumley, Renato Feres. Entropy production in random billiards. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1319-1346. doi: 10.3934/dcds.2020319

[4]

Bing Gao, Rui Gao. On fair entropy of the tent family. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021017

[5]

Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020165

[6]

Håkon Hoel, Gaukhar Shaimerdenova, Raúl Tempone. Multilevel Ensemble Kalman Filtering based on a sample average of independent EnKF estimators. Foundations of Data Science, 2020, 2 (4) : 351-390. doi: 10.3934/fods.2020017

[7]

Yunping Jiang. Global graph of metric entropy on expanding Blaschke products. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1469-1482. doi: 10.3934/dcds.2020325

[8]

Matania Ben–Artzi, Joseph Falcovitz, Jiequan Li. The convergence of the GRP scheme. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 1-27. doi: 10.3934/dcds.2009.23.1

[9]

Zi Xu, Siwen Wang, Jinjin Huang. An efficient low complexity algorithm for box-constrained weighted maximin dispersion problem. Journal of Industrial & Management Optimization, 2021, 17 (2) : 971-979. doi: 10.3934/jimo.2020007

[10]

Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 217-256. doi: 10.3934/dcds.2020217

[11]

Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020465

[12]

François Dubois. Third order equivalent equation of lattice Boltzmann scheme. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 221-248. doi: 10.3934/dcds.2009.23.221

[13]

Russell Ricks. The unique measure of maximal entropy for a compact rank one locally CAT(0) space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 507-523. doi: 10.3934/dcds.2020266

[14]

Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100

[15]

Jintai Ding, Zheng Zhang, Joshua Deaton. The singularity attack to the multivariate signature scheme HIMQ-3. Advances in Mathematics of Communications, 2021, 15 (1) : 65-72. doi: 10.3934/amc.2020043

[16]

Karan Khathuria, Joachim Rosenthal, Violetta Weger. Encryption scheme based on expanded Reed-Solomon codes. Advances in Mathematics of Communications, 2021, 15 (2) : 207-218. doi: 10.3934/amc.2020053

[17]

Franck Davhys Reval Langa, Morgan Pierre. A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 653-676. doi: 10.3934/dcdss.2020353

[18]

Matúš Tibenský, Angela Handlovičová. Convergence analysis of the discrete duality finite volume scheme for the regularised Heston model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1181-1195. doi: 10.3934/dcdss.2020226

[19]

Magdalena Foryś-Krawiec, Jiří Kupka, Piotr Oprocha, Xueting Tian. On entropy of $ \Phi $-irregular and $ \Phi $-level sets in maps with the shadowing property. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1271-1296. doi: 10.3934/dcds.2020317

[20]

Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013

2019 Impact Factor: 0.734

Metrics

  • PDF downloads (46)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]