In this paper, a novel reversible data hiding algorithm for encrypted images is proposed.In encryption phase, chaotic sequence is used to encrypt the original image.Then the least significant bits (LSBs) of pixels in encrypted image are losslessly compressed to make space for secret data.With auxiliary bit stream, the lossless compression is realized by Hamming distance calculation between the LSBs stream and auxiliary stream.In receiving terminal, the operation is flexibole, that is it meets the requirement of separation.With the encryption key, a receiver can get access to the marked decrypted image which is similar to the original one.With data-hiding key, the receiver can successfully extract secret data from the encrypted image.With both keys, the receiver can get secret data and the exactly original image.Compared with existing methods, experiments show the feasibility and efficiency of the proposed method,especially in aspect of embedding capacity, embedding quality and error-free recovery with increasing payload.