The computational complexity of universal hashing

Yishay Mansour*, Noam Nisan, Prasoon Tiwari

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


Summary form only given. Any implementation of Carter-Wegman universal hashing from n-b strings to m-b strings requires a time-space tradeoff of TS = Ω(nm). The bound holds in the general Boolean branching program model, and thus in essentially any model of computation. As a corollary, computing a + b × c in any field F requires a quadratic time-space tradeoff, and the bound holds for any representation of the elements of the field. Other lower bounds on the complexity of any implementation of universal hashing are given as well: quadratic AT2 bound for VLSI implementation; Ω(log n) parallel time bound on a CREW PRAM; and exponential size for constant depth circuits. The results on VLSI implementation are proved using information transfer bounds derived from the definition of a universal family of hash functions.

Original languageAmerican English
Title of host publicationProc Fifth Annu Struct Complexity Theor
PublisherPubl by IEEE
Number of pages1
ISBN (Print)0818620722
StatePublished - 1990
Externally publishedYes
EventProceedings of the Fifth Annual Structure in Complexity Theory Conference - Barcelona, Spain
Duration: 8 Jul 199011 Jul 1990

Publication series

NameProc Fifth Annu Struct Complexity Theor


ConferenceProceedings of the Fifth Annual Structure in Complexity Theory Conference
CityBarcelona, Spain


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