As an emerging imaging technique, computational ghost imaging (CGI) has its unique application in image encryption. However, the long imaging time and high requirement of transmitting data, both in the size of data and vulnerability of lossy compression, limit its application in the practical communications. Using discrete cosine transform to sparse bucket signals of CGI, we here propose a method by transforming the bucket signals from the sensing matrix domain to the space domain, enhancing the ability of the bucket signals (i.e., encrypted image) to resist the lossy compression. Based on the principle of CGI, we first propose to use gradient descent to find an orthogonal matrix as the encryption key, then test the performance of our method at different quality factors and undersampling rates. Both simulations and experimental results demonstrate that our encryption method shows great resistance to the traditional lossy compression methods and has good performance in the undersampling conditions. Our method provides a convenient way to transmit the bucket signals of CGI by the format that involves lossy compression and thus camouflages itself while significantly reducing the amount of data being transmitted.