  In this paper we compute the values of the p-adic multiple polylogarithms of
depth two at roots of unity. Our method is to solve the fundamental
differential equation satisfied by the crystalline frobenius morphism using
rigid analytic methods. The main result could be thought of as a computation in
the p-adic theory of higher cyclotomy. We expect the result to be useful in
proving non-vanishing results since it gives quite explicit formulas.
