This study proposes a large capacity, reversible, and separable algorithm based on adaptive embedding to address the issues plaguing reversible data hiding in the encrypted images (RDH-EI) algorithms, such as reversibility, low embedding rate, and incomplete separation. An improved Arnold and chaos-based image encryption algorithm is proposed in the image encryption stage, permitting the original image several times using the Arnold matrix and performing pixel diffusion using the generated chaotic sequence. Then, the encrypted image is interpolated with an improved image interpolation algorithm to create the cover image to be embedded with the secret data. The difference between the secret data to be embedded and the maximum value of n-bit data is first calculated in the data embedding stage. Then, an adaptive data embedding method is proposed to embed the secret data into the interpolated pixels, based on the difference and the size of the secret data. Experimental results show that the proposed algorithm is fully reversible, has no additional data and no data overflow, and is separable with all uncorrelated keys. The proposed algorithm has higher image quality at the same embedding rate than others. It is also resistant to histogram and regular singular (RS) steganalysis.INDEX TERMS Encrypted domain, reversible data hiding, adaptive embedding, image interpolation.