We propose a scheme for authentication of physical keys that are materialized by optical multiple-scattering media. The authentication relies on the optical response of the key when probed by randomly selected coherent states of light, and the use of standard wavefront-shaping techniques that direct the scattered photons coherently to a specific target mode at the output. The quadratures of the electromagnetic field of the scattered light at the target mode are analysed using a homodyne detection scheme, and the acceptance or rejection of the key is decided upon the outcomes of the measurements. The proposed scheme can be implemented with current technology and offers collision resistance and robustness against key cloning.