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Quantum-resistant image encryption using 2D Henon map with a three-qubit entanglement-based QKD protocol

Durra Tarannum, Md. Abu Syed, Bipash Kumar Biswas, Mahdy Rahman Chowdhury

Published Nov 11, 2025• 0 citations
Publisher

Abstract

Safeguarding image confidentiality is a crucial communication concern due to the valuable information that must remain inaccessible to unauthorized users. However, the imminent emergence of quantum computers has introduced pressing security concerns to current cryptography. This paper proposes a quantum-resistant cryptosystem integrating a three-qubit entanglement-based Quantum Key Distribution protocol with a chaotic Henon map to develop an image transmission system resilient to classical and quantum adversaries. This QKD employs bidirectional qubit transmission to entangle three qubits, resulting in a quantum-secured key that is double that of the E91 protocol and demonstrates exceptional eavesdropper detection capabilities via the CHSH inequality violation. A 2D Henon map is utilized to address the intrinsic vulnerabilities related to key size and security in one-dimensional logistic maps. The expanded key generates a more complex sequence employing the Henon map, ensuring the utmost security of the encryption by integrating the chaotic randomness with the cryptographic properties embedded in entanglement. The findings from various security assessments indicate that the proposed encryption is both reliable and effective. It exhibits robust resistance to differential analysis, showing NPCR at 99.6% and UACI near 50%. A colossal 10220 key space thwarts brute-force attempts, while near-zero correlation and uniform pixel-intensity distribution confirm strong statistical security, highlighting the advantages of quantum–classical cryptography protocols.

DOI
10.1063/5.0281728

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Safeguarding image confidentiality is a crucial communication concern due to the valuable information that must remain inaccessible to unauthorized users. However, the imminent emergence of quantum computers has introduced pressing security concerns to current cryptography. This paper proposes a quantum-resistant cryptosystem integrating a three-qubit entanglement-based Quantum Key Distribution protocol with a chaotic Henon map to develop an image transmission system resilient to classical and quantum adversaries. This QKD employs bidirectional qubit transmission to entangle three qubits, resulting in a quantum-secured key that is double that of the E91 protocol and demonstrates exceptional eavesdropper detection capabilities via the CHSH inequality violation. A 2D Henon map is utilized to address the intrinsic vulnerabilities related to key size and security in one-dimensional logistic maps. The expanded key generates a more complex sequence employing the Henon map, ensuring the utmost security of the encryption by integrating the chaotic randomness with the cryptographic properties embedded in entanglement. The findings from various security assessments indicate that the proposed encryption is both reliable and effective. It exhibits robust resistance to differential analysis, showing NPCR at 99.6% and UACI near 50%. A colossal 10220 key space thwarts brute-force attempts, while near-zero correlation and uniform pixel-intensity distribution confirm strong statistical security, highlighting the advantages of quantum–classical cryptography protocols.
ABSTRACT The emergence of quantum computing has introduced unprecedented security challenges to conventional cryptographic systems, particularly in the domain of classical communications. Our research addresses these challenges by creatively combining quantum key distribution (QKD), specifically the E91 protocol, with logistic chaotic maps to establish a secure image transmission scheme. Our approach utilises the pseudo‐randomness of chaotic systems alongside the security mechanisms inherent in quantum entanglement‐based protocols. This framework leverages the E91 protocol for secure quantum key distribution to generate identical key pairs at both ends, followed by chaos encryption using the key as a basis for the parameters. This framework utilises the E91 protocol for secure quantum key distribution, leveraging maximally entangled pairs and CHSH inequality tests to detect eavesdropping and potential double‐agent attacks by identifying nonentangled qubits, therefore maintaining key confidentiality. Furthermore, through quantitative simulations, we demonstrate the effectiveness of this scheme through key space and key sensitivity analysis, histogram analysis, information entropy analysis, execution time analysis, and differential attack analysis in end‐to‐end encryption. The results indicate a significant improvement in encryption and decryption efficiency, showcasing the scheme's potential as a viable solution against the vulnerabilities posed by quantum computing advancements. Our research offers a novel perspective on a critical aspect of cybersecurity applications across healthcare, defence, finance, and beyond in the realm of secure quantum communication.
Secure image transmission is increasingly vital in the digital era, especially against emerging quantum threats. This study proposes a hybrid image encryption scheme that integrates Quantum Key Distribution (QKD) using the BB84 protocol with a combination of 7-dimensional (7D) and 2-dimensional (2D) hyperchaotic systems to achieve robust security. The BB84 protocol facilitates quantum-assisted key exchange, ensuring resistance to eavesdropping, while the hyperchaotic systems provide high entropy and complex randomness, utilized in a layered permutation-substitution encryption framework. The initial seeds for chaotic sequences are derived using a SHA-512 hash of both the input image and quantum-generated key, ensuring uniqueness and sensitivity. Experimental validation was conducted using several benchmark images. The information entropy values of the ciphered images reached up to 7.9993, indicating excellent randomness. Differential analysis showed high resistance to small perturbations, with NPCR exceeding 99.61% and UACI averaging around 33.47%, which meet standard security thresholds. Histogram and chi-square tests confirmed the uniform pixel distribution, with chi-square values below 280, satisfying the randomness criterion for 8-bit images. Furthermore, correlation coefficients of adjacent pixels dropped to near zero, evidencing effective decorrelation. The encryption scheme also demonstrated robustness to data loss, as shown by the successful decryption of partially corrupted cipher images. Robustness testing under partial data loss (200×200-pixel blocks) also demonstrated visual recoverability and algorithm resilience. Overall, the proposed BB84-assisted dual-hyperchaotic encryption scheme offers a secure and computationally effective solution for protecting sensitive image data, making it suitable for post-quantum secure communications.
The emergence of quantum computing has introduced unprecedented security challenges to conventional cryptographic systems, particularly in the domain of optical communications. This research addresses these challenges by innovatively combining quantum key distribution (QKD), specifically the E91 protocol, with logistic chaotic maps to establish a secure image transmission scheme. Our approach utilizes the unpredictability of chaotic systems alongside the robust security mechanisms inherent in quantum entanglement. The scheme is further fortified with an eavesdropping detection mechanism based on CHSH inequality, thereby enhancing its resilience against unauthorized access. Through quantitative simulations, we demonstrate the effectiveness of this scheme in encrypting images, achieving high entropy and sensitivity to the original images. The results indicate a significant improvement in encryption and decryption efficiency, showcasing the potential of the scheme as a viable solution against the vulnerabilities posed by quantum computing advancements. Our research offers a novel perspective in secure optical communications, blending the principles of chaos theory with QKD to create a more robust cryptographic framework.
Quantum computing introduces major threats to conventional image encryption methods, especially in medical contexts. This paper addresses these threats by developing a quantum-resistant encryption scheme for medical images. We present a novel framework combining: (1) a novel Mixed Logistic-Ikeda-Henon (MLIH) chaotic map for pseudorandom key generation, (2) quantum image representation using the Novel Enhanced Quantum Representation (NEQR) model, and (3) a two-stage encryption process employing Controlled-Not (CNOT) gate chaining for diffusion and One-Time Pad (OTP) with MLIH-generated keys for confusion. The RGB channels are processed separately through quantum state conversion, CNOT-based diffusion, and keyed confusion before final recombination. To validate practical feasibility, the proposed encryption scheme was implemented on IBM’s 127-qubit ibm_sherbrooke quantum processor, demonstrating real-world feasibility. Experimental validation shows near-ideal entropy (7.9977), superior NPCR (99.97%) and UACI (33.89%) values, and an expansive key space (2 1952 ). The novel MLIH demonstrates a 12.7% improvement in logic gate efficiency compared to conventional chaotic and the image encryption has quantum advantage through parallel CNOT operations. The hardware execution yielded a throughput of 4,500 Circuit Layer Operations Per Second (CLOPS), indicating efficient real-time performance on NISQ devices, Moreover, the echoed cross-resonance (ECR) gate error remained within a median of 1.1 × 10⁻ 2 , supporting reliable circuit execution. The proposed scheme outperforms contemporary quantum and classical encryption approaches in terms of entropy, NPCR, UACI, and key sensitivity, all while maintaining a computational complexity of O(n), ensuring scalability. This study effectively bridges the gap between theoretical quantum security models and real-world implementation on existing NISQ devices, demonstrating resilience against classical statistical and differential attacks, as well as quantum-specific threats such as Grover’s brute-force search and quantum chosen-plaintext attacks. The successful deployment of IBM quantum hardware positions this scheme as a viable solution for secure medical image transmission in quantum-era healthcare systems.
This research introduces a novel cryptographic system that enhances the security of steganographic images by integrating Quantum Key Distribution (QKD) with traditional encryption. Using the E91 QKD protocol, it generates a shared secret key between parties, leveraging quantum entanglement to provide superior protection against eavesdropping. The quantum key is then hashed with the Secure Hash Algorithm (SHA) to produce a fixed-length, high-entropy key for symmetric encryption . The Advanced Encryption Standard (AES) is employed to encrypt steganographic images, which conceal critical data within digital images, adding an extra layer of security through obscurity. Experiments with images of varying resolutions (64 × 64 to 512 × 512 pixels) show consistent encryption performance. The encrypted images exhibit high randomness, with an average entropy of 7.9929. Differential attack resilience is demonstrated by a Number of Pixels Change Rate (NPCR) averaging 99.6928% and a Unified Average Changing Intensity (UACI) of 56.1549%. The average E91 protocol key generation time is 5.78 s with a key rate of 7.43 bps. Encryption and decryption times for test images are 0.00149 and 0.00175 s, respectively. This research combines quantum and classical cryptography with steganography, providing a robust security framework highly resistant to both quantum and classical threats.
Quantum security improves cryptographic protocols by applying quantum mechanics principles, assuring resistance to both quantum and conventional computer attacks. This work addresses these issues by integrating Quantum Key Distribution (QKD) utilizing the E91 method with Multi-Layer Chaotic Encryption, which employs a variety of patterns to detect eavesdropping, resulting in a highly secure image-transmission architecture. The method leverages entropy calculations to determine the unpredictability and integrity of encrypted and decrypted pictures, guaranteeing strong security. Extensive statistical scenarios illustrate the framework's effectiveness in image encryption while preserving high entropy and sensitivity to the original visuals. The findings indicate significant improvement in encryption and decryption performance, demonstrating the framework's potential as a robust response to weaknesses introduced by advances in quantum computing. Several metrics, such as Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Normalized Cross-Correlation (NCC), Bit Error Rate (BER), entropy values for original, encrypted, and decrypted images, and the correlation between original and decrypted images, validate the framework's effectiveness. The combination of QKD with Multi-Layer Chaotic Encryption provides a scalable and resilient technique to secure image communication. As quantum computing advances, this framework offers a future-proof approach for defining secure communication protocols in crucial sectors such as medical treatment, forensic computing, and national security, where information confidentiality is valuable.