A well-known technique for optical image encryption is the double random phase encoding (DRPE) technique, which uses two random phase masks (RPMs), one RPM at the input plane of the encryption system and the other RPM at the Fourier plane of the optical system, in order to obtain the encrypted image. In this work, we propose to use tilted planes for the Fourier and the output planes of the optical DRPE encryption system with the purpose of adding two new security keys, which are the angles of the tilted planes. The optical diffraction on a tilted plane is computed using the angular spectrum of plane waves and the coordinate rotation in the Fourier domain. The tilted distributions at the intermediate and output planes of the optical DRPE encryption system are the second RPM and the encrypted image, respectively. The angles of the tilted planes allow improvement to the security of the encrypted image. We perform several numerical simulations with the purpose of demonstrating the validity and feasibility of the proposed image encryption system.