We discuss an acceleration mechanism of charged particles in the presence of elliptically or linearly polarized electromagnetic waves at parallel shocks. Such waves are often detected by spacecraft observations in the deep foreshock region of the Earth's bow shock. Under the influence of a circularly polarized electromagnetic wave and an electrostatic shock potential, particles can be accelerated efficiently by gyroresonant surfing, a perpendicular acceleration mechanism due to a combined effect of trapping by the wave and dragging by the electrostatic field. We describe the elliptically or linearly polarized waves as a superposition of two circularly polarized waves with the same phase speed and wavelength, but with the opposite wave polarization. In the presence of such waves, particles are pitch angle diffused, and this leads to smearing of the perpendicular acceleration. However, the particles are efficiently accelerated in the parallel direction owing to exchange of the parallel and the perpendicular kinetic energies, and/or owing to the shock potential. Furthermore, as the wave ellipticity becomes large, because of the strong pitch angle scattering, the particles can be repeatedly accelerated by the gyroresonant surfing. The efficient diffusion both in the pitch angle and in the energy space produces the particle distribution function similar to the so-called diffuse ions associated with the elliptically and linearly polarized waves observed in the foreshock.