In the increasing number of system approaches published in the field of optical encryption, the security level of the system is evaluated by qualitative and empirical methods. To quantify the security of the optical system, we propose to use the equivalent of the key length routinely used in algorithmic encryption. We provide a calculation method of the number of independent keys and deduce the binary key length for optical data encryption. We then investigate and optimize the key length of the combined phase- and amplitude-modulated key encryption in the holographic storage environment, which is one of the promising solutions for the security enhancement of single- and double-random phase-encoding encryption and storage systems. We show that a substantial growth of the key length can be achieved by optimized phase and amplitude modulation compared to phase-only encryption. We also provide experimental confirmation of the model results.
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