With the development of cloud server, reversible data hiding in encrypted domain has received widespread attention for management of encrypted media. Most of existing reversible data hiding methods are based on stream ciphers, which are mainly concerned with data storage security. While homomorphic ciphers focus on data processing security, which is popular in cloud and other third-party platforms. Reversible data hiding with homomorphic cryptography has been an active topic in the research filed. In this paper, we propose a new lossless data hiding method based on homomorphic cryptosystem. After a content owner generates encrypted media with homomorphic ciphers, a data hider embeds secret data by establishing a mapping between secret bits and losslessly modifying encrypted media. At the receiver side, the embedded data is extracted from encrypted domain with a little auxiliary message. And original media is recovered by directly decrypting marked encrypted media. During the embedding process, the modification of encrypted media does not change the corresponding original media owing to homomorphic and probabilistic properties. Thus, no distortion is introduced in the whole procedures of data embedding. And directly decrypted media containing embedded data is the same as the original media. Meanwhile, the proposed method achieves a high embedding rate through efficient mapping and skillful use of expanded pixel values. The experimental results show that compared with state-of-the-art methods, the proposed method has higher embedding rate without distortion.