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An improved version of Li et al.'s method of reversible data hiding of encrypted images is proposed. The original work partitions the encrypted image into two sets, and only one set is used for data embedding. After carrying out a feasibility analysis, the full embedding strategy is employed. Accordingly, the data embedding capacity is dilated. In addition, the corresponding new fluctuation measurement is designed for the full embedding strategy. The experimental results reveal that the full embedding strategy is effective and also indicate that using the new fluctuation measurement the performance is further augmented. The proposed method outperforms other works in terms of performance.Introduction: Data hiding is a technology to embed imperceptible confidential information into a host media. In some applications, for instance in military or medical image systems, the distortion of the host image caused by data hiding is unacceptable. Therefore, a number of reversible data hiding techniques that possess the property of categorical restoration of the host image after data extraction have been studied recently [1][2][3][4][5][6]. In recent years, application of the reversible technique into the encrypted image has also been published [7][8][9][10][11]. Some of them concentrate on embedding information into the partial unencrypted data of the images [7,8], whereas others embed data directly into the fully encrypted images [9-11], which can better protect the privacy of the image in an open environment such as the cloud environment.In Zhang's method [9], all pixels of the host image are encrypted by a stream cipher, and the additional data are embedded into the divided blocks of the encrypted image. At the receiver side, after image decryption, a fluctuation function is used to measure the smoothness of blocks. Afterwards, according to the fluctuation measurement, the embedded bits can be extracted and the image can be recovered at the same time. Later, Hong et al.[10] made an improvement to Zhang's work using a new block smoothness measurement that considers the pixel correlations in the border of neighbouring blocks. As the improved method was still based on blocks, the limitation and centralisation of local pixels in the block led to unreliability of the fluctuation measurement. Li et al.'s method [11] pointed out this drawback and overcame it by abandoning the idea of block division entirely and using the random diffusion strategy. In addition, accurate prediction is adopted to improve the fluctuation measurement.In [11], the encryption of the host image is achieved by applying a bitwise exclusive-or (XOR) operator to every bit of pixels using an encryption key, as shown in (1)

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