New constructions for perfect hash families and related structures using combinatorial designs and codes

Journal of Combinatorial Designs

Volumn 8, Issue 3, 2000, Pages 189-200

  Stinson, D R ^a   Wei, R ^a   Zhu, L ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b SOOCHOW UNIVERSITY   (China)

Author keywords

Orthogonal arrays; Perfect hash families; Separating hash families

Indexed keywords

EID: 0039591714     PISSN: 10638539     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1520-6610(2000)8:3<189::AID-JCD4>3.0.CO;2-A     Document Type: Article

References (24)

1. N. Alon, Explicit construction of exponential sized families of k-independent sets, Discrete Math. 58 (1986), 191-193.
2. M. Atici, Hash families: recursive constructions and applications to cryptography, PhD thesis, University of Nebraska, 1996.
3. M. Atici, S. S. Magliveras, D. R. Stinson, and W.-D. Wei, Some recursive constructions for perfect hash families. J. Combin. Designs 4 (1996), 353-363.
4. M. Atici, D. R. Stinson, and R. Wei, A new practical algorithm for the construction of a perfect hash function, J. Combin. Math. Combin. Comput., to appear.
5. J. Bierbrauer, Construction of orthogonal arrays, J. Statist. Plan. Infer. 56 (1996), 39-47.
6. J. Bierbrauer, T. Johansson, G. Kabatiansky, and B. Smeets. On families of hash functions via geometric codes and concatenation, Proceedings of CRYPTO 93, Lecture Notes in Computer Science, 773 (1994), 331-342.
7. S. R. Blackburn, "Combinatorics and threshold cryptograpy" Combinatorial designs and their applications, Chapman and Hall Research Notes in Mathematics, 403 (1999), 49-70.
8. S. R. Blackburn. Personal communication.
9. S. R. Blackburn and P. R. Wild, Optimal linear perfect hash families, J. Combin. Theory A 83 (1998), 233-250.
10. K. A. Bush, W. T. Federer, H. Pesotan, and D. Raghavarao, New combinatorial designs and their application to group testing, J Statist. Plan. Infer. 10 (1984) 355-343.
11. C. J. Colbourn and J. H. Dinitz, CRC Handbook of Combinatorial Designs, CRC Press, Inc., 1996.
12. M. Dyer, T. Fenner, A. Frieze, and A. Thomason, On key storage in secure networks, J. Cryptology 8 (1995), 189-200.
13. P. Erdös, P. Frankl and Z. Füredi, Families of finite sets in which no set is covered by the union of two others, J. Combin. Theory A 33 (1982), 158-166.
14. P. Erdös, P. Frankl, and Z. Füredi, Families of finite sets in which no set is covered by the union of r others. Israel J. Math. 51 (1985), 75-89.
15. A. D. Friedman, R. L. Graham, and J. D. Ullman, Universal single transition time asynchronous state assignments, IEEE Trans. Comput. 18 (1969), 541-547.
16. Z. Füredi, On r-cover-free families, J. Combin. Theory A 73 (1996), 172-173.
17. H.-D. Gronau, and R. C. Mullin, On super-simple 2-(vυ, 4, λ) designs, J. Combin. Math. Combin. Comput. 11 (1992), 113-121.
18. F. K. Hwang and V. T. Sós, Non-adaptive hypergeometric group testing, Studia Sci. Math. Hungar. 22 (1987), 257-263.
19. K. Mehlhorn, Data structures and algorithms 1: sorting and searching, Springer-Verlag, Berlin, 1984.
20. W. H. Kautz and R. C. Singleton, Nonrandom binary superimposed codes, IEEE Trans. Inform. Theory 10 (1964), 363-37 7.
21. C. J. Mitchell and F. C. Piper, Key storage in secure networks, Disc. Appl. Math. 21 (1988), 215-228.
22. G. L. Mullen and J. Shiue, A simple construction for orthogonal Latin rectangles, J. Combin. Math. Combin. Comput. 9 (1991), 161-166.
23. D. R. Stinson and T. van Trung, Some new results on key distribution patterns and broadcast encryption, Designs, Codes, Crypt. 14 (1998), 261-279.
24. D. R. Stinson, T. van Trung, and R. Wei. Secure frameproof codes, key distribution patterns, group testing algorithms and related structures, J. Statist. Plan. Infer., to appear.