THE COMPUTATIONAL-COMPLEXITY OF UNIVERSAL HASHING

Any implementation of Carter-Wegman universal hashing from n-bit strings to m-bit strings requires a time-space tradeoff of TS=OMEGA(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; OMEGA(log n) parallel time bound on a CREW PRAM; and exponential size for constant-depth circuits.