In this paper, we have proposed an asymmetric optical cryptosystem using polar decomposition and Shearlet transform (ST). Polar decomposition is employed to generate multiple private keys for decryption. Gyrator transform (GT) with angle α, is used for optical propagation. Multi-scale directional property of ST is utilized to get Shearlet coefficients from the complex output after GT. The first coefficient is then replaced by a random phase mask before performing inverse ST. The detailed robustness analysis of the proposed method in terms of various potential attacks, such as, noise, occlusion, brute force, special attack, and plaintext attacks is performed and compared with the traditional asymmetric method. Results are presented to demonstrate the validity and effectiveness of the proposed technique.