This paper proposes a method to secure Compressive Sensing (CS) streams. It involves protecting part of the measurements with a secret key and inserting code into the remaining measurements. The secret key is generated via a cryptographically secure pseudorandom number generator (CSPRNG) and XORed with the measurements to be inserted. For insertion, we use a reversible data hiding (RDH) scheme, which is a prediction error expansion algorithm modified to match the statistics of CS measurements. The reconstruction from the embedded stream results in a visibly distorted image. The image distortion is controlled by the number of embedded levels. In our tests, embedding on 10 levels results in ≈18 dB distortion for images of $256\times 256$ pixels reconstructed with the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). A particularity of the presented method is on-the-fly insertion, which makes it appropriate for the sequential acquisition of measurements with a single-pixel camera. On-the-fly insertion avoids the buffering of CS measurements for the subsequent standard encryption and generation of a thumbnail image.