Compressive Sensing (CS), which makes it possible to reduce the amount of data and thereby greatly simplify the sensor system has become a very important research area. In this method, data is compressed before measurements whereas data is first measured and then compressed in the current technology. This approach leads to reducing the number of sensors. In this study, simultaneous compressive sensing and optical cryptography is developed as a new approach for encryption and decryption of signals and images. In the current work, CS is achieved with the orthogonal matching pursuit (OMP) algorithm. Then, the CS-OMP algorithm is combined with the double random phase/amplitude encyrption (DRPAE) method to achieve both compression and encyrption of data. In order to achieve high security, the keys used in DRPAE are transmitted to the receiver by an asymmetric cryptography method, such as the RSA method. Thus, the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPAE is a symmetric optical encyrption method. In this approach, the use of the detection matrix in CS also protects DRPAE phase/amplitude keys against well-known attacks which no longer function. The data size is also decreased.