Because of gigantic specialized headways in communication and media, there is a requirement for web correspondence in various areas such as military, medicinal, and e-administration. To take into account this need for data security, a reversible data-hiding algorithm in an encrypted domain for absolute moment block truncation coding (AMBTC)-compressed images is proposed. To secure the content of the cover image, firstly an AMBTC compressed image is encrypted through homomorphic encryption and then a binary secret message in base₄ numeral framework is embedded at embeddable pixel values of the AMBTC-compressed image without occurrence of any overflow problem. The embedding rate can be additionally improved with no disintegration of the visual nature of the cover image. Highlights of the proposed algorithm are elimination of the overflow problem during data embedding in cover image and yielding a peak signal-to-noise ratio (PSNR) value of infinite decibels. The cover image and stego image are indistinguishable from one another. Visual quality of the stego images obtained through the proposed method is superior to all the other compared methods. The experimental results reveal that, with regard to the embedding rate and PSNR value for all test images, the proposed algorithm performed superior to other ones.