  The class of the two-loop massless crossed boxes, with light-like external
legs, is the final unresolved issue in the program of computing the scattering
amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order.
  In this paper, we describe an algorithm for the tensor reduction of such
diagrams. After connecting tensor integrals to scalar ones with arbitrary
powers of propagators in higher dimensions, we derive recurrence relations from
integration-by-parts and Lorentz-invariance identities, that allow us to write
the scalar integrals as a combination of two master crossed boxes plus
simpler-topology diagrams.
  We derive the system of differential equations that the two master integrals
satisfy using two different methods, and we use one of these equations to
express the second master integral as a function of the first one, already
known in the literature. We then give the analytic expansion of the second
master integral as a function of epsilon=(4-D)/2, where D is the space-time
dimension, up to order O(epsilon^0).
