We report a full-vector, three-dimensional, numerical solution of Maxwell's equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. The total scattering cross section is determined using the pseudospectral time domain technique. Specific results reported in this paper indicate that multiply scattered light also contains information that can be extracted by the proposed cross-correlation analysis. On a broader perspective, our results demonstrate the feasibility of accurately determining the optical characteristics of arbitrary, macroscopic random media, including geometries with continuous variations of refractive index. Specifically, our results point toward the new possibilities of tissue optics; by numerically solving Maxwell's equations, the optical properties of tissue structures can be determined unambiguously.