Optical cryptography has attracted extensive interest because of the inherent nature of parallel and multidimensional capability of optical information processing compared with computer cryptography. However, the linear space-invariant (LSI) cryptosystems are easy to be simulated and may be vulnerable to different attacks. To resist attacks, several phasetruncated Fourier transforms based asymmetric cryptosystem are proposed to utilize the nonlinear operations in the LSI system, but they are proved to be vulnerable due to the inherent nature of LSI system. Notice that several works misunderstand the concept of nonlinear operations to the nonlinear systems. But the nonlinear systems are not easy to be achieved. Herein, an optical cryptosystem based on Fourier ptychography (FP) with double random phase masks is proposed. The encryption process cannot be precisely simulated but only by optical experiment due to the vignetting effect, which is linear space-variant (LSV) and can act as an one-way function from the perspective of optics purely and guarantee the security of our system. In addition, the encryption for a high resolution, large field-of-view and complexvalued image is achievable. Optical experiments are presented to prove the validity and the security of the proposed system. Our method would give more insights to separate the optical cryptography from computer cryptography in nature. © 2019 SPIE.