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 - Publ by ACM
T2 - Proceedings of the 22nd Annual ACM Symposium on Theory of Computing
Y2 - 14 May 1990 through 16 May 1990
ER -