How to compress encrypted data effectively and reconstruct it in a high quality way is a challenging research problem in the cloud computing environment. The challenge mainly comes from the encryption by cloud users

which masks statistical characteristics of cover data and thus makes the compression of encrypted data in the cloud side unable to fully exploit the statistical characteristics in a traditional way. Based on the fitness evaluation of statistical models in characterizing wavelet coefficients

a new compression scheme is proposed on encrypted grey images

which leverages the statistic model and rate distortion optimization. The coarsest subband and the other wavelet subbands generated through lifting wavelet decomposition of grey image are encrypted by stream and permutation ciphers

respectively. They are then compressed in lossless and lossy ways

respectively. The receiver finally performs the inverse operations to reconstruct the original image. As sufficient tests show that the Cauchy distribution can well characterize wavelet coefficients

the Cauchy distribution is adopt to represent wavelet subbands. Via this statistical model

the ratedistortion theory is further used to derive optimal quantization steps for lossy compression. Experimental results show that the proposed algorithm can obtain better compressing efficiency and reconstruction quality. Also

it is significantly better than other permutationbased prior arts

and it is comparable to or even better than the conventional JPEG compression algorithm.