A new asymmetric cryptosystem using Schur decomposition in gyrator transform (GT) domain is introduced. In this approach, the color image to be encoded is first dissociated into red, green and blue channels and then modulated by multiplying three different random phase masks. The three modulated color channels are combined into one gray image by using convolution. The convoluted image is gyrator transformed. The gyrator spectrum is then amplitude- and phase-truncated. The asymmetric decryption phase keys for red, green and blue channels are generated digitally during the encryption process. The phase-truncated image is divided into U and T parts by Schur decomposition. Finally, U and T parts are independently gyrator transformed to obtain two encoded images, which can be assigned to a joint authorized user (or two authorized users). GT evades optical alignment problems. The Schur decomposition represents an intermediate step in SVD decomposition, and thus requires less number of computations. The multiplication order of Schur decomposition, three transformation angles of GT, and three asymmetric keys are regarded as decryption keys, which boost the degree of security against existing attacks. The proposed encryption process can be carried out digitally, while the decryption process can be realized optically. Numerical simulations prove the validity and security of the proposed approach.