We examine the Amplitude-Encoding (AE) case of the Double Random Phase Encoding (DRPE) technique. A cost function is the function we use to evaluate an attempted decryption with our original input image. For systems with a relatively small key-space we can evaluate the output of every key to get an overall idea of the spread of these keys in key-space. However for larger systems this is not practical. Based on a normalised root mean squared cost function we wish to identify expressions for the mean and variance of the output (decrypted) intensity for a sample set of keys in a large system (256x256 pixels).