Quantum reversible circuits for audio watermarking based on echo hiding technique

Watermarking is the process of embedding information into a host signal, and it’s a significant process when it enters into the copyright protection or digital works. In the near future, quantum computing will be developed and therefore the protection of quantum data will be a vital issue. This paper proposes a novel quantum reversible realization of echo hiding-based audio watermarking in the quantum representation of digital signal (QRDS). In the embedding process, according to watermark qubits, some echo frames are generated by modifying time and amplitude qubits of host audio frames. Then, a watermarked quantum audio signal is obtained; as a sum on quantum host and quantum echo audio signals. The proposed extraction phase is carried out in non-blind manner. For this purpose, a calculation is carried out on each frame of host audio signal, in which, the given frame is embedded with |0〉 and |1〉, separately, the sum of the absolute values of differences between corresponding frame of received watermarked quantum audio signal and these two calculated frames is computed. The lower sum of absolute differences indicates the correct embedded qubit in the corresponding frame. The embedding and extraction processes are implemented using quantum reversible circuits, on nanoscale. The proposed scheme has a payload of 512 at SNR = 60.31. The simulation results show that the proposed scheme has high robustness against quantum signal processing attacks.