TY - GEN

T1 - Computational complexity of universal hashing

AU - Mansour, Yishay

AU - Nisan, Noam

AU - Tiwari, Prasoon

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025106672&partnerID=8YFLogxK

U2 - 10.1145/100216.100246

DO - 10.1145/100216.100246

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AN - SCOPUS:0025106672

SN - 0897913612

SN - 9780897913614

T3 - Proc 22nd Annu ACM Symp Theory Comput

SP - 235

EP - 243

BT - Proc 22nd Annu ACM Symp Theory Comput

PB - Association for Computing Machinery (ACM)

T2 - Proceedings of the 22nd Annual ACM Symposium on Theory of Computing

Y2 - 14 May 1990 through 16 May 1990

ER -