We report on the numerical computation of the Lyapunov exponents and the Kolmogorov-Sinai entropy for a three-dimensional, dilute, random Lorentz gas both in equilibrium and in nonequilibrium steady states. In our method the phase- and tangent-space dynamics are treated exactly. Furthermore, we propose a highly efficient stochastic technique for the computation of Lyapunov spectra of dilute systems. Our results are in excellent agreement with analytical results of Latz, van Beijeren, and Dorfman [preceding Letter, Phys.Rev.Lett.{ital 78}, 207 (1997)]. {copyright} {ital 1997} {ital The American Physical Society}