A recursive construction for perfect hash families

Charles Colbourn, Alan C H Ling

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

A known recursive construction for perfect hash families multiplies the number of factors by q, where q is the largest prime power not exceeding the number of symbols. This is generalized to permit multiplication of the number of factors by powers of q; it is also improved upon by restricting the structure of the ingredient designs. For a perfect hash family of strength t, it may be possible to order its rows so that, for each ℓ ≤ t, the first Σ i=2 N i rows form a perfect hash family of strength ℓ. This 'matroshka' ordering underlies a sometimes substantial reduction in the number of rows generated by the recursive construction. Perfect hash families with useful matroshka orderings are generated using linear orthogonal arrays, and with an effective one-row-at-a-time greedy algorithm.

Original languageEnglish (US)
Pages (from-to)291-306
Number of pages16
JournalJournal of Mathematical Cryptology
Volume3
Issue number4
DOIs
StatePublished - Dec 1 2009

Keywords

  • Distributing hash family
  • Orthogonal array
  • Perfect hash family

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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