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Compression of encrypted data is possible by using distributed source coding. In this paper, we consider the encryption, followed by lossless compression of gray scale and color images. We propose to apply encryption on the prediction errors instead of directly applying on the images and use distributed source coding for compressing the cipher texts. The simulation results show that by using the proposed technique comparable compression gains, with compression ratios varying from 1.5 to 2.5 can be achieved despite encryption.