Compressive Sensing (CS), which makes it possible to reduce the amount of data and thereby to 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 hybrid optical cryptography is developed as a new approach to handle two important problems in the field of communications, namely, effective and efficient signal processing and secure transmission of information. In this work, CS is achieved with the orthogonal matching pursuit (OMP) algorithm. Then, the CS-OMP algorithm is combined with the double random phase encyrption (DRPE) method to achieve both compression and encyrption of data. In order to achieve high security, the keys used in CS and DRPE are transmitted to the receiver by an asymmetric cryptography method. Thus, the overall cryptographic system is a hybrid optical system (both symmetric and asymmetric) since DRPE is a symmetric optical encyrption method.