The area-time complexity of the greatest common divisor problem: a lower bound

We use multiple “information-flow barriers” to show that any VLSI chip which computes the greatest common divisor (GCD) of two n-bit binary integers requires area A and time T satisfying AT 2 = Ω(n 2) . Our result implies that, with respect to VLSI area-time bounds, computing the GCD can be no easier than multiplication. As a corollary we have AT=Ω( n). This bound is best possible, as is shown by a practical design of Brent and Kung for a systolic binary GCD chip.