We present the results of applying data compression techniques to encrypted three-dimensional (3D) objects. The objects are captured using phase-shift digital holography and encrypted using a random phase mask in the Fresnel domain. Both the amplitude and the phase of our 3D objects are encrypted using this technique. The advantage of a digital representation of the optical wavefronts is that they can be processed and transmitted using conventional means. Arbitrary views of the 3D objects are decrypted and reconstructed using digital propagation. Compression is applied to the encrypted digital holograms prior to transmission. Degradation due to lossy quantization compression is measured in the reconstruction domain. Finally, we use a speedup metric to validate that our compression techniques are viable for time-critical 3D imaging applications. Our techniques are suitable for a range of secure 3D object storage and transmission applications.