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

47 Scopus citations


Any implementation of Carter-Wegman universal hashing from n-bit strings to m-bit 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.

Original languageAmerican English
Title of host publicationProc 22nd Annu ACM Symp Theory Comput
PublisherPubl by ACM
Number of pages9
ISBN (Print)0897913612, 9780897913614
StatePublished - 1990
Externally publishedYes
EventProceedings of the 22nd Annual ACM Symposium on Theory of Computing - Baltimore, MD, USA
Duration: 14 May 199016 May 1990

Publication series

NameProc 22nd Annu ACM Symp Theory Comput


ConferenceProceedings of the 22nd Annual ACM Symposium on Theory of Computing
CityBaltimore, MD, USA


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