As an interdisciplinary research between watermarking and cryptography, privacy-aware reversible watermarking permits a party to entrust the task of embedding watermarks to a cloud service provider without compromising information privacy. The early development of schemes were primarily based upon traditional symmetric-key cryptosystems, which involve an extra implementation cost of key exchange. Although recent research attentions were drawn to schemes compatible with asymmetric-key cryptosystems, there were notable limitations in the practical aspects. In particular, the host signal must either be enciphered in a redundant way or be pre-processed prior to encryption, which would largely limit the storage efficiency and scheme universality. To relax the restrictions, we propose a novel research paradigm and devise different schemes compatible with different homomorphic cryptosystems. In the proposed schemes, the encoding function is recognised as an operation of adding noise, whereas the decoding function is perceived as a corresponding denoising process. Both online and offline contentadaptive predictors are developed to assist watermark decoding for various operational requirements. A three-way trade-off between the capacity, fidelity and reversibility is analysed mathematically and empirically. It is shown that the proposed schemes achieve the state-the-art performance.