With the development of cloud computing, the growth in information technology has led to serious security issues. For this reason, a lot of multimedia files are stored in encrypted forms. Methods of reversible data hiding in encrypted images (RDHEI) have been designed to provide authentication and integrity in the encrypted domain. The original image is firstly encrypted to ensure confidentiality, by making the content unreadable. A secret message is then embedded in the encrypted image, without the need of the encryption key or any access to the clear content. The challenge lies in finding the best trade-off between embedding capacity and quality of the reconstructed image. In 2008, Puech et al. suggested using the AES algorithm to encrypt an original image and to embed one bit in each block of 16 pixels (payload = 0.0625 bpp) [12]. During the decryption phase, the original image is reconstructed by measuring the standard deviation into each block. In this paper, we propose an improvement to this method, by performing an adaptive local entropy measurement. We can achieve a larger payload without altering the recovered image quality. Our obtained results are very good and better than most of the modern state-of-the-art methods, whilst offering an improved security level with the use of the AES algorithm, defined as the encryption standard by the NIST.