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Paper: Perfect Hash Families with Few Functions

Authors:
Simon R. Blackburn
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URL: http://eprint.iacr.org/2003/017
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Abstract: An {\em $(s;n,q,t)$-perfect hash family} is a set of functions $\phi_1,\phi_2,\ldots ,\phi_s$ from a set $V$ of cardinality $n$ to a set $F$ of cardinality $q$ with the property that every $t$-subset of $V$ is injectively mapped into $F$ by at least one of the functions $\phi_i$. The paper shows that the maximum value $n_{s,t}(q)$ that $n$ can take for fixed $s$ and $t$ has a leading term that is linear in $q$ if and only if $t>s$. Moreover, for any $s$ and $t$ such that $t>s$, the paper shows how to calculate the coefficient of this linear leading term; this coefficient is explicitly calculated in some cases. As part of this process, new classes of good perfect hash families are constructed.
BibTeX
@misc{eprint-2003-11735,
  title={Perfect Hash Families with Few Functions},
  booktitle={IACR Eprint archive},
  keywords={combinatorial cryptography},
  url={http://eprint.iacr.org/2003/017},
  note={ s.blackburn@rhul.ac.uk 12080 received 28 Jan 2003},
  author={Simon R. Blackburn},
  year=2003
}