A high capacity message embedding in encrypted HEVC video is proposed in this paper. The challenges addressed in this paper include keeping the encrypted video compliant with standardized decoders, correctly decrypting the video and finally, correctly extracting the message bits. The message embedding is achieved by altering the values of reference picture indices and motion vectors which results in scrambled video. Sixteen picture references are used in this work and therefore, combined with alteration of motion vectors, a maximum of six message bits can be embedded per coding unit. Motion vectors are altered by swapping their x and y components and/or changing their signs. This is achieved with full compliance with the HEVC video syntax. To extract message bits, an authorized decoder builds a classification model per video sequence and uses it for predicting the true values of the reference indices and motion vectors. As such, message bits are extracted and the video is correctly reconstructed to its unscrambled state. Coding units that result in misclassification are identified at the encoder and excluded from message embedding. This results in slightly lower embedding rates but ensures accurate video reconstruction. Using nine video sequences of various resolutions that are compressed using four different quantization parameters, the experimental results revealed that the true average message embedding rate is 2.7 bits per coding unit or 173 kbit/s. This is achieved with accurate video reconstruction at the expense of increasing the bitrate of the encoder by 3%. Comparison with existing work shows that the proposed solution is superior in terms of embedding capacity whilst reducing the excessive bitrate of the encoder.