The hybrid input-output algorithm, error reduction algorithm, and combinations of both phase retrieval algorithms are applied to perform ciphertext-only attacks on linear canonical transform (LCT)-based amplitude encoding double-random-phase encryption (DRPE) systems. Special cases of LCT-based DRPE systems, i.e., Fourier-transform-based, fractional-Fourier-transform-based, and Fresnel-transform-based DRPE, can also be successfully attacked using the method proposed. Numerical simulations are performed to demonstrate the efficacy of the proposed attacking method.