We present a unified fast scattering algorithm for dielectric random rough surfaces that asymptotically reduces to the perfect electric conductor (PEC) case when the loss tangent grows extremely large. The Coifman wavelets are employed to implement Galerkin's procedure in the method of moments (MoM). The Coiflets-based surface integral equations (IEs) consist of both the tangential and normal components of electromagnetic fields as unknowns. The inherited mathematical superiority, e.g., local multiresolution analysis and high regularity with Holder index 1.449 in smoothness, allows efficiently implementing both electric field IE and magnetic field IE. Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well-conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. In addition, a semianalytical expression of the tapered-wave carried power is derived, which speeds up computations of the normalization factor of scattering coefficients. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems, namely, matrix condition numbers are kept small and solutions are stable under extremely large loss tangent, where normal components of $H$ -field and tangential $E$ -field have vanished. Compared with the previous publications and laboratory measurements, good agreement is observed.