In this work an image encryption-decryption system is developed using Gyrator transform (GT) and Jigsaw transform (JT). The encryption system uses two successive GTs and JTs, in order to convert a real image to a real noisy encrypted image. The decryption system is an inverse system with respect to the encryption system. The real image to be encrypted is preprocessed with the purpose of obtaining a real encrypted image, this real encrypted image has the same size as the original image to be encrypted and it is much more convenient for either its storage or transmission. The JT is applied to eliminate the random phase mask used in many encryption systems based on double random phase mask and to increase the security of the encryption-decryption system proposed in this work. Finally, in order to verify the performance of the encryption-decryption system, a digital algorithm was developed. There are four keys used in the encryption-decryption algorithm, which are constituted by the two GTs rotation angles and the two random permutations used in the JTs; all these keys have to be correct for a proper recovery of the original image in the decryption system.