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The complexity of the graph access structures on six participants

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Abstract

In this paper, we deal with determining the exact values for the complexity of the five graph access structures on six participants, which remained as open problems in van Dijk’s paper (Des Codes Cryptogr 6:143–169, 1995). We prove that the complexity for each of the five graph access structures is equal to 7/4.

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References

  1. Blundo C., De Santis A., Stinson D.R., Vaccaro U.: Graph decompositions and secret sharing schemes. J. Cryptol 8, 39–64 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blundo C., De Santis A., De Simone R., Vaccaro U.: Tight bounds on the information rate of secret sharing schemes. Des. Codes Cryptogr 11, 107–122 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brickell E.F., Davenport D.M.: On the classification of ideal secret sharing schemes. J. Cryptol 4, 123–134 (1991)

    MATH  Google Scholar 

  4. Capocelli R.M., De Santis A., Gargano L., Vaccaro U.: On the size of shares of secret sharing schemes. J. Cryptol 6, 157–168 (1993)

    Article  MATH  Google Scholar 

  5. Cover T.M., Thomas J.A.: Elements of information theory, 2nd edn. Wiley, New York (2006)

    MATH  Google Scholar 

  6. Csirmaz L.: The size of a share must be large. J. Cryptol. 10, 223–231 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Padró C., Vázquez L.: Finding lower bounds on the complexity of secret sharing schemes by linear programming. Ninth Latin American theoretical informatics symposium, LATIN 2010, Lecture notes in computer science–6034, 344355 (2010)

    Google Scholar 

  8. Stinson D.R.: An explication of secret sharing schemes. Des. Codes Cryptogr 2, 357–390 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun H.M., Chen B.L.: Weighted decomposition construction for perfect secret sharing schemes. Comput. Math. Appl 43, 877–887 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. van Dijk M.: On the information rate of perfect secret sharing schemes. Des. Codes Cryptogr 6, 143–169 (1995)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Massoud Hadian Dehkordi.

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Communicated by D. Jungnickel.

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Gharahi, M., Hadian Dehkordi, M. The complexity of the graph access structures on six participants. Des. Codes Cryptogr. 67, 169–173 (2013). https://doi.org/10.1007/s10623-011-9592-z

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  • DOI: https://doi.org/10.1007/s10623-011-9592-z

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