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On a Bound of Cover-Free Families

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Abstract

In this paper, we use refined Stirling formulas to determine a bound of cover-free families given by Stinson et al. [31].

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References

  1. P. R. Beesack, Improvement of Stirling formula by elementary methods, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No., Vol. 271–301 (1969) pp. 17–21.

    Google Scholar 

  2. D. Boneh and J. Shaw, Collusion-secure fingerprinting for digital data, IEEE Tran. Information Theory, Vol. 44 (1998) pp. 1897–1905. (Lecture Notes in Computer Science, Vol. 963 (1995) pp. 452–465 (Crypto '95).)

    Google Scholar 

  3. P. Buchner, Bemerkungen zur Strlinshen formel, Elem. Math., Vol. 6 (1951) pp. 8–11.

    Google Scholar 

  4. K. A. Bush, W. T. Federer, H. Pesotan and D. Raghavarao, New combinatorial designs and their application to group testing, Journal of Statistical Planning and Inference, Vol. 10 (1984) pp. 335–343.

    Google Scholar 

  5. B. Chor, A. Fiat and M. Naor, Tracing traitors. In Advances in Cryptology-Crypto '94, Lecture Notes in Computer Science, Vol. 839 (1994) pp. 480–491.

    Google Scholar 

  6. B. Chor, A. Fiat, M. Naor and B. Pinkas, Tracing traitors, IEEE Transactions on Information Theory, Vol. 46 (2000) pp. 893–910.

    Google Scholar 

  7. A. G. Dyachkov and V. V. Rykov, Bounds on the length of disjunctive codes, Problemy Peredachi Informatsii, Vol. 18 (1982) pp. 7–13 [Russian].

    Google Scholar 

  8. A. G. Dyachkov, V. V. Rykov and A. M. Rashad, Superimposed distance codes, Problems of Control and Information Theory, Vol. 18 (1989) pp. 237–250.

    Google Scholar 

  9. M. Dyer, T. Fenner, A. Frieze and A. Thomason, On key storage in secure networks, J. Cryptology, Vol. 8 (1995) pp. 189–200.

    Google Scholar 

  10. K. Engel, Interval packing and covering in the boolean lattice, Combin. Probab. Comput., Vol. 5 (1996) pp. 373–384.

    Google Scholar 

  11. P. Erdös, P. Frankl and Z. Füredi, Families of finite sets in which no set is covered by the union of two others, Journal of Combinatorial Theory A, Vol. 33 (1982) pp. 158–166.

    Google Scholar 

  12. P. Erdös, P. Frankl and Z. Füredi, Families of finite sets in which no set is covered by the union of r others, Israel Journal of Mathematics, Vol. 51 (1985) pp. 75–89.

    Google Scholar 

  13. Z. Füredi, On r-cover-free families, Journal of Combinatorial Theory A, Vol. 73 (1996) pp. 172–173.

    Google Scholar 

  14. E. Gafni, J. Staddon and Y. L. Yin, Efficient methods for integrating traceability and broadcast encryption. In Advances in Cryptology-Crypto '99, Lecture Notes in Computer Science, Vol. 1666 (1999) pp. 372–387.

    Google Scholar 

  15. J. A. Garay, J. Staddon and A. Wool, Long-lived broadcast encryption. In Advances in Cryptology-Crypto' 00, Lecture Notes in Computer Science, Vol. 1880 (2000) pp. 335–353.

    Google Scholar 

  16. H. D. L. Hollmann, J. H. van Lint, J. P. Linnartz and L. M. G. M. Tolhuizen, On codes with the identifiable parent property, Journal of Combinatorial Theory A, Vol. 82 (1998) pp. 121–133.

    Google Scholar 

  17. F. K. Hwang and V. T. Sós, Non-adaptive hypergeometric group testing, Studia Sci. Math. Hungar, Vol. 22 (1987) pp. 257–263.

    Google Scholar 

  18. W. H. Kautz and R. C. Singleton, Nonrandom binary superimposed codes, IEEE Trans. Inform. Theory, Vol. 10 (1964) pp. 363–377.

    Google Scholar 

  19. E. Knill, W. J. Bruno and D. C. Torney, Non-adaptive group testing in the presence of error, Discrete Appl. Math., Vol. 88 (1998) pp. 261–290.

    Google Scholar 

  20. J. Köner and M. Lucertini, Compressing inconsistent data, IEEE Tran. Information Theory, Vol. 40 (1994) pp. 706–715.

    Google Scholar 

  21. R. Kumar, S. Rajagopalan and A. Sahai, Coding constructions for blacklisting problems without computational assumptions. In Advances in Cryptology-Crypto '99, Lecture Notes in Computer Science, Vol. 1666 (1999) pp. 609–623.

    Google Scholar 

  22. C. J. Mitchell and F. C. Piper, Key storage in secure networks, Discrete Applied Mathematics, Vol. 21 (1988) pp. 215–228.

    Google Scholar 

  23. K. A. S. Quinn, Bounds for key distribution patterns. Journal of Cryptology, Vol. 12 (1989) pp. 227–240

    Google Scholar 

  24. M. Ruszinkó, On the upper bound of the size of the r-cover-free families, Journal of Combinatorial Theory A, Vol. 66 (1994) pp. 302–310.

  25. R. Safavi-Naini and H. Wang, New results on multi-receiver authentication codes. In Advances in Cryptology-Eurocrypt '98, Lecture Notes in Computer Science, Vol. 1438 (1998) pp. 527–541.

    Google Scholar 

  26. J. N. Staddon, D. R. Stinson and R. Wei, Combinatorial properties of frameproof and traceability codes, IEEE Tran. Information Theory, Vol. 47 (2001) pp. 1042–1049.

    Google Scholar 

  27. D. R. Stinson, Tran van Trung and R. Wei, Secure frameproof codes, key distribution patterns, group testing algorithms and related structures, Journal of Statistical Planning and Inference, Vol. 86 (2000) pp. 595–617.

    Google Scholar 

  28. D. R. Stinson and R. Wei, Combinatorial properties and constructions of traceability schemes and frameproof codes, SIAM Journal on Discrete Mathematics, Vol. 11 (1998) pp. 41–53.

    Google Scholar 

  29. D. R. Stinson and R. Wei, Key preassigned traceability schemes for broadcast encryption. In Selected Areas in Cryptology-SAC '98, Lecture Notes in Computer Science, Vol. 1556 (1999) pp. 144–156.

    Google Scholar 

  30. D. R. Stinson and R. Wei, Generalized cover-free families, Discret Math., Vol. 279 (2004) pp. 463–479

    Google Scholar 

  31. D. R. Stinson, R. Wei and L. Zhu, Some new bounds for cover-free families, J. Combin. Theory A, Vol. 90 (2000) pp. 224–234.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Suzhou, 215006, China

    X. Ma

  2. Department of Computer Science, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada

    R. Wei

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  1. X. Ma
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  2. R. Wei
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Ma, X., Wei, R. On a Bound of Cover-Free Families. Designs, Codes and Cryptography 32, 303–321 (2004). https://doi.org/10.1023/B:DESI.0000029231.44423.43

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  • DOI: https://doi.org/10.1023/B:DESI.0000029231.44423.43

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