ABSTRACTThis work proposes a novel scheme of commutative reversible data hiding and encryption. In encryption part, the gray values of two neighboring pixels are masked by same pseudo‐random bits. In data‐hiding part, the additional data are embedded into various bit planes with a reversible manner, and a parameter optimization method based on a capacity–distortion criterion is used to ensure a good performance. Because the data space used for accommodating the additional data is not affected by the encryption operation, the data embedded in plain/encrypted domain can be extracted from encrypted/plain domain, and the way of insertion/extraction of additional data in plain domain is same as that in encrypted domain. Furthermore, the original image can be recovered without any error from an image containing additional data. Copyright © 2013 John Wiley & Sons, Ltd.