To maintain the security of the image encryption and to protect the image from intruders, a new asymmetric cryptosystem based on fractional Hartley Transform (FrHT) and the Arnold transform (AT) is proposed. AT is a method of image cropping and edging in which pixels of the image are reorganized. In this cryptosystem we have used AT so as to extent the information content of the two original images onto the encrypted images so as to increase the safety of the encoded images. We have even used Structured Phase Mask (SPM) and Hybrid Mask (HM) as the encryption keys. The original image is first multiplied with the SPM and HM and then transformed with direct and inverse fractional Hartley transform so as to obtain the encrypted image. The fractional orders of the FrHT and the parameters of the AT correspond to the keys of encryption and decryption methods. If both the keys are correctly used only then the original image would be retrieved. Recommended method helps in strengthening the safety of DRPE by growing the key space and the number of parameters and the method is robust against various attacks. By using MATLAB 8.3.0.52 (R2014a) we calculate the strength of the recommended cryptosystem. A set of simulated results shows the power of the proposed asymmetric cryptosystem.