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We propose a phase-only asymmetric optical cryptosystem based on random modulus decomposition (RMD). The cryptosystem is presented for effectively improving the capacity to resist various attacks, including the attack of iterative algorithms. On the one hand, RMD and phase encoding are combined to remove the constraints that can be used in the attacking process. On the other hand, the security keys (geometrical parameters) introduced by Fresnel transform can increase the key variety and enlarge the key space simultaneously. Numerical simulation results demonstrate the strong feasibility, security and robustness of the proposed cryptosystem. This cryptosystem will open up many new opportunities in the application fields of optical encryption and authentication. [ABSTRACT FROM AUTHOR]