The joint transform correlator (JTC) is a classical optical architecture, recently associated with interesting applications in optical security. In addition, multiplexing is a tactic associated with optical encrypting mechanisms that provide security for multiple users. However, experimental constraints arise when we intend to reproduce a diffuser shifting multiplexing option. This is due to the invariance to lateral shifts under a JTC setup. To overcome this problem, we propose a setup modification that allows its use under a multiplexing approach. Instead of placing the encrypting mask in contact with the input JTC plane, we use the actual optical Fourier transform of a diffuser projected over the entrance plane of the JTC. We present a theoretical explanation, along with computer simulations and experimental results, that support our proposal.