Perfect hash families: Constructions and existence

Robert A. Walker, Charles Colbourn

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


A perfect hash family PHF(N; k, v, t) is an N × k array on v symbols with v ≥ t, in which in every N × t subarray, at least one row is comprised of distinct symbols. Perfect hash families have a wide range of applications in cryptography, particularly to secure frameproof codes, in database management, and indirectly in software interaction testing. New recursive constructions, new direct constructions, and PHFs found using tabu search are provided here. The first general tables of the best known sizes of PHFs are presented; in the process, the known direct and recursive constructions are surveyed.

Original languageEnglish (US)
Pages (from-to)125-150
Number of pages26
JournalJournal of Mathematical Cryptology
Issue number2
StatePublished - Apr 19 2007


  • Interaction testing
  • Perfect hash family
  • Three-term arithmetic progression

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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