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Scientific Reports

Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications

Ahmed A. Abd El‐Latif, Bassem Abd-El-Atty, Mohammed A. Amin, Abdullah M. Iliyasu

Published Feb 6, 2020• 155 citations
Publisher

Abstract

Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. The performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications.

DOI
10.1038/s41598-020-58636-w

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Designing efficient and secure cryptosystems has been a preoccupation for many scientists and engineers for a long time wherein they use chaotic systems to design new cryptosystems. While one dimensional (1-D) chaotic maps possess powerful properties compared to higher dimension ones, they are vulnerable to various attacks due to their small key space, chaotic discontinuous ranges, and degradation in chaotic dynamical behaviours. Moreover, when simulated on a computer, every such chaotic system produces a periodic cycle. Meanwhile, quantum random walks exhibit the potential for deployment in efficient cryptosystem design, which makes it an excellent solution for this problem. In this context, we present a new method for constructing substitution boxes (S-boxes) based on cascaded quantum-inspired quantum walks and chaos inducement. The performance of the proposed S-box scheme is investigated via established S-box evaluation criterion and outcomes suggest that the constructed S-box has significant qualities for viable applications information security. Further, we present an efficient scheme for pseudo-random numbers generation (PRNG) whose sustainability over long periods remedies the periodicity problem associated with traditional cryptographic applications. Furthermore, by combining the two mechanisms, an atypical image encryption scheme is introduced. Simulation results and analysis validate that the proposed image encryption algorithm will offer gains in many cryptographic applications.
The paper proposes a lossless quantum image encryption scheme based on substitution tables (S-box) scrambling, mutation operation and general Arnold transform with keys. First, the key generator builds upon the foundation of SHA-256 hash with plain-image and a random sequence. Its output value is used to yield initial conditions and parameters of the proposed image encryption scheme. Second, the permutation and gray-level encryption architecture is built by discrete Arnold map and quantum chaotic map. Before the permutation of Arnold transform, the pixel value is modified by quantum chaos sequence. In order to get high scrambling and randomness, S-box and mutation operation are exploited in gray-level encryption stage. The combination of linear transformation and nonlinear transformation ensures the complexity of the proposed scheme and avoids harmful periodicity. The simulation shows the cipher-image has a fairly uniform histogram, low correlation coefficients closed to 0, high information entropy closed to 8. The proposed cryptosystem provides 2256 key space and performs fast computational efficiency (speed = 11.920875 Mbit/s). Theoretical analyses and experimental results prove that the proposed scheme has strong resistance to various existing attacks and high level of security.
This paper presents a novel approach to hardware security key generation leveraging the unique properties of quantum chaos. Traditional hardware security key generation methods often rely on pseudo-random number generators (PRNGs) which are susceptible to various attacks. Quantum chaos, arising from the inherent sensitivity to initial conditions in chaotic systems, offers a fundamentally different approach, providing a source of high-quality randomness and inherent robustness. This research details the design and implementation of a hardware system specifically engineered to generate quantum chaotic signals, followed by a method for extracting a cryptographic key based on the statistical characteristics of these signals. The core claim of this work is the generation of hardware security keys with high key authenticity. The key mechanism involves a stable quantum chaos signal generation system combined with statistical key extraction. The resulting keys are expected to demonstrate superior security characteristics compared to those generated by conventional PRNGs. This approach addresses the vulnerabilities inherent in existing hardware security solutions and provides a promising pathway toward more robust and secure key generation. ---
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.
The rapid growth in the storage and transmission of visual data across communication, sensing, and decision-making systems requires image encryption methods that are both computationally efficient and resilient against quantum-enabled adversaries. Classical chaotic encryption offers desirable properties such as sensitivity, unpredictability, and large key spaces, but its practical use is limited by restricted chaotic ranges, and conventional confusion–diffusion mechanisms often fail to eliminate structural redundancies in images. This thesis furthers the field by developing novel chaotic and gate-efficient quantum image encryption architectures. First, it introduces a new cosine-modulated polynomial chaotic map and validates its dynamical and statistical suitability for cryptographic key generation. Second, it designs lightweight yet effective chaotic primitives, including the Single-Round Single S-Box (SRSS) confusion mechanism and the featureaware diffusion scheme (PermutEx) that address the limitations in breaking correlation and maintaining efficiency. Third, these components are integrated into a complete endto- end chaos-based encryption framework that combines feature-driven segmentation, adaptive permutation, and dynamic confusion, demonstrating strong security across entropy, correlation, and differential metrics. Finally, the thesis advances two quantum image encryption architectures, i.e., a chaos-enhanced quantum image encryption framework that strengthens quantum confusion and diffusion mechanisms, and a gate-efficient architecture that reduces circuit depth and multi-qubit operations while retaining robust security. The proposed architectures achieve improved computational efficiency compared to existing chaos-based and quantum image encryption techniques, by reducing redundant operations, minimising circuit depth, and enabling lightweight yet effective confusion-diffusion processes. Consequently, this thesis provides a way forward for advancing image encryption by integrating chaotic and quantum approaches, offering practical steps for protecting visual data in the post-quantum era.
Generating high-quality random numbers is essential for cryptography, statistical simulations, and cybersecurity. While pseudo-random number generators (PRNGs) are computationally efficient, their deterministic nature introduces potential security vulnerabilities. Recent research has explored chaotic systems as entropy sources due to their sensitivity to initial conditions-a key property for randomness generation. An emerging direction involves leveraging chaos in quantum systems. This paper proposes a quantum-inspired PRNG based on the Quantum Kicked Rotor (QKR), a well-known model in quantum chaos exhibiting complex dynamics such as dynamical localization. The method simulates the QKR and extracts pseudo-random sequences through momentum basis measurements. The generated sequences are evaluated for statistical quality, including the NIST 800-22 standard, which passed all 15 test. The sequences exhibit strong non-periodicity, a critical property for secure cryptographic applications. The proposed approach combines the unpredictability of quantum chaos with the scalability of classical simulation, offering a practical and efficient alternative for secure random number generation.
The recent advances in digital services such as telehealth, video conferencing, military imaging, and video surveillance require highly reliable, secure storage and transmission of multimedia images and video. Specifically, video surveillance systems are commonly adopted for real-time event detection and video analytics. The video captured by video surveillance cameras often holds personal information, which requires privacy protection. Unlike text, digital images and video frames have many special properties, for instance, pixel correlations, textures, and huge size, which results in conventional cryptosystems like AES, data encryption standard (DES), etc., being appropriate for performing image encryption tasks as they possess very low efficiency when the data size is large. Chaotic cryptosystem has recommended a proficient approach for performing multimedia encryption with special characteristics like randomness and dynamic behavior. Though chaotic cryptosystem provides better security, these frameworks are vulnerable to cryptanalytic attacks with high computation machines. Thus, the recent advancement of quantum methodologies for quantum information processing has gained popularity in many fields such as information security, video processing, etc. 204 In this work, an attempt was made to investigate the proficiency of quantum cryptography in the field of secure video surveillance applications. To ensure the privacy of surveillance video, the proposed framework presented a novel Quantum based video cryptosystem for encrypting the digital video frames. Initially, the video frames are converted into quantum qubit frames by processing the pixel values. Next, to guarantee the secrecy of digital video information, the qubit planes are encrypted by utilizing series of quantum gates such as swap gate, controlled not gate, Toffoli gate and Hadamard gates under confusion and diffusion phases. The secrecy of digital video frames is reinforced by utilizing plain image-based quantum chaos for secret key generation. The traditional chaotic maps are quantized to obtain the quantumbased random sequences and these random sequences are further utilized to construct the secret keys for performing encryption and decryption operation. The numerical simulations and security analysis prove that the proposed system ensures secure video surveillance against cryptanalytic attacks. Also, the proposed quantum-based secure video surveillance system has ensured the effectiveness of quantum image processing in real-time video surveillance applications.