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Journal of Optimization in Soft Computing (JOSC) بهينه سازي در محاسبات نرم

Energy‑Driven Quantum Audio Watermarking Using Synergistic Wavelet and Cosine Transforms with Quantum k‑Means Clustering

Masoumeh Ebri, Mohammad Mosleh, Mohsen Yoosefi Nejad, Mohammad Kheyrandish, Amin Mehranzadeh

Published May 31, 2026• 0 citations
Publisher

Abstract

Abstract. This paper presents an energy-aware quantum audio watermarking framework that exploits quantum signal transformations and clustering techniques to achieve robust and imperceptible watermark embedding. The proposed method integrates the Quantum Discrete Wavelet Transform (QDWT), Quantum Discrete Cosine Transform (QDCT), quantum k-means (Q-means) clustering, and a dynamic XOR-based embedding mechanism. The host audio signal is segmented into frames and analyzed in the quantum transform domain to extract joint time–frequency features. Based on the transform-domain energy characteristics and clustering outcomes, perceptually tolerant embedding regions are adaptively identified using predefined energy thresholds. Watermark insertion is performed through quantum-controlled XOR operations, where the embedding depth is dynamically selected according to the energy level of each audio segment. This energy-driven strategy ensures minimal perceptual distortion while enhancing robustness against signal processing attacks. Experimental evaluations demonstrate that the proposed method consistently outperforms conventional LSB-based watermarking schemes, achieving high transparency with signal-to-noise ratio (SNR) values exceeding 60 dB and strong robustness with bit error rates (BER) below 0.1 under various qubit-flip noise and zero-attack scenarios. These results confirm the effectiveness of the proposed framework in preserving audio quality while maintaining reliable watermark recovery.

DOI
10.82553/josc.2026.202605311241592

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Abstract. This paper presents an energy-aware quantum audio watermarking framework that exploits quantum signal transformations and clustering techniques to achieve robust and imperceptible watermark embedding. The proposed method integrates the Quantum Discrete Wavelet Transform (QDWT), Quantum Discrete Cosine Transform (QDCT), quantum k-means (Q-means) clustering, and a dynamic XOR-based embedding mechanism. The host audio signal is segmented into frames and analyzed in the quantum transform domain to extract joint time–frequency features. Based on the transform-domain energy characteristics and clustering outcomes, perceptually tolerant embedding regions are adaptively identified using predefined energy thresholds. Watermark insertion is performed through quantum-controlled XOR operations, where the embedding depth is dynamically selected according to the energy level of each audio segment. This energy-driven strategy ensures minimal perceptual distortion while enhancing robustness against signal processing attacks. Experimental evaluations demonstrate that the proposed method consistently outperforms conventional LSB-based watermarking schemes, achieving high transparency with signal-to-noise ratio (SNR) values exceeding 60 dB and strong robustness with bit error rates (BER) below 0.1 under various qubit-flip noise and zero-attack scenarios. These results confirm the effectiveness of the proposed framework in preserving audio quality while maintaining reliable watermark recovery.
The study presented in this work explores the implementation of a watermarking scheme for quantum audio signals based on quantum Discrete Cosine Transformation (qDCT). The qDCT transforms the quantum host audio signal which is encoded as an FRQA (flexible representation of quantum audio) content from time domain to frequency domain and manipulates or modifies the high-frequency positions to embed the quantum watermark audio information into it. The strong energy compaction property of DCT is utilized in this scheme, i.e. after the DCT process to a digital audio, most of the signal information tends to be concentrated in a few low-frequency components and its high-frequency components could record some extra information like watermark audio. Built on the circuit model of quantum computation, the circuit networks to execute the embedding and extraction procedures of qDCT-based watermarking algorithm are designed and simulation-based experiments are conducted to demonstrate their implementation.
Current quantum audio watermarking schemes prioritize robustness but often overlook critical security vulnerabilities, leaving systems exposed to impersonation and unauthorized use. To address this gap, we propose a dual-security mechanism that synergistically integrates joint verification and certification of watermarks, inspired by the paging seal principle. Our framework incorporates Quantum Error Correction (QEC) coding to enhance resilience against qubit errors and malicious tampering. Experimental results show improved performance: the watermark maintains high imperceptible with SNR> 46 dB under increased embedding rates, and achieves a 62.5% reduction in average BER compared to several state-of-the-art methods at a qubit error probability of 0.10. These results suggest that the proposed approach offers enhanced security and robustness, representing a promising direction for secure quantum audio watermarking.
The protection of multimedia information against copying and tampering attacks by unauthorized parties is a challenge nowadays because of the tremendous increase in digital communications. Based on this, this paper presents a quantum blind image watermarking scheme incorporating Improved Novel Enhanced Representation (INEQR) for efficient image encoding, two-dimensional Quantum Discrete Cosine Transform (QDCT) frequency domain processing, and adaptive QIM for watermark embedding. The selection of watermarking parameters in this framework is carried out in a completely secure manner using Quantum Key Distribution (QKD) based on BB84. Simulation work on 30 standard grayscale images shows the strong imperceptibility, achieving PSNR values in the range of 52–58 dB and SSIM values between 0.98 and 0.999. and a more than 95 percent accuracy level in watermark recovery under attacks such as noise, compression attacks, and geometric attacks, thus authenticating PSNR-52– 58 dB and SSIM-0.98–0.999. Robustness analysis performed against signal processing and geometric attacks indicates reliable extraction of watermarks, where the proposed framework attains an extraction accuracy of more than 95% under additive noise and filtering scenarios and moderate robustness against geometric attacks such as rotation and scaling. These indicate that the proposed framework is effective and provides imperceptible blind image watermarks based on the quantum approach.
The protection of multimedia information against copying and tampering attacks by unauthorized parties is a challenge nowadays because of the tremendous increase in digital communications. Based on this, this paper presents a quantum blind image watermarking scheme incorporating Improved Novel Enhanced Representation (INEQR) for efficient image encoding, two-dimensional Quantum Discrete Cosine Transform (QDCT) frequency domain processing, and adaptive QIM for watermark embedding. The selection of watermarking parameters in this framework is carried out in a completely secure manner using Quantum Key Distribution (QKD) based on BB84. Simulation work on 30 standard grayscale images shows the strong imperceptibility, achieving PSNR values in the range of 52–58 dB and SSIM values between 0.98 and 0.999. and a more than 95 percent accuracy level in watermark recovery under attacks such as noise, compression attacks, and geometric attacks, thus authenticating PSNR-52– 58 dB and SSIM-0.98–0.999. Robustness analysis performed against signal processing and geometric attacks indicates reliable extraction of watermarks, where the proposed framework attains an extraction accuracy of more than 95% under additive noise and filtering scenarios and moderate robustness against geometric attacks such as rotation and scaling. These indicate that the proposed framework is effective and provides imperceptible blind image watermarks based on the quantum approach.
Abstract Quantum watermarking is a technique to embed specific information, usually the owner’s identification, into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum watermarking based on quantum wavelet transforms is proposed which includes scrambling, embedding and extracting procedures. The invisibility and robustness performances of the proposed watermarking method is confirmed by simulation technique. The invisibility of the scheme is examined by the peak-signal-to-noise ratio (PSNR) and the histogram calculation. Furthermore the robustness of the scheme is analyzed by the Bit Error Rate (BER) and the Correlation Two-Dimensional (Corr 2-D) calculation. The simulation results indicate that the proposed watermarking scheme indicate not only acceptable visual quality but also a good resistance against different types of attack.
With the rise of quantum computing and the limitations of traditional encryption methods, ensuring secure data transmission in IoT frameworks has become increasingly critical. This work presents a quantum-enhanced hybrid communication system that integrates adaptive audio techniques with quantum image processing. The proposed system operates in three main stages: first, text data is converted into binary format and encoded into quantum circuits using Qiskit; second, the quantum-encoded data is embedded into audio signals using an adaptive Least Significant Bit (LSB) technique; finally, the stego-audio’s robustness is evaluated under simulated IoT network conditions. Unlike conventional approaches, this method offers dual-layer security by combining dynamic audio embedding with quantum-based image representation, making it resistant to both quantum attacks and signal degradation. Experimental results demonstrate strong performance, with a Peak Signal-to-Noise Ratio (PSNR) ranging from 45 to 50 dB, a Bit Error Rate (BER) below 2%, and entropy values exceeding 7.5. These outcomes indicate the system’s effectiveness for secure, quantum-resilient communication in IoT environments with bandwidth and security constraints.