Abstract Drawing inspiration from the Fibonacci sequence and its complementary Lucas sequence, this paper introduces an innovative encryption and decryption algorithm tailored for multi-path quantum key distribution. The algorithm capitalizes on the high-quality orbital angular momentum entangled states, harnessing the mathematical elegance of Fibonacci numbers to construct block diagonal matrices. These matrices serve as the foundation for the simultaneous execution of key distribution across multiple communication paths in a structured block distribution format. The encryption process is facilitated through a combination of linear mappings, employing specific transition matrices to manage the cryptographic flow. The security underpinning of this method is firmly rooted in the Heisenberg Uncertainty Principle, a fundamental tenet of quantum mechanics, which ensures the confidentiality and integrity of the quantum communication channel. This approach paves the way for a novel encryption paradigm, fortifying the security framework of quantum communication networks.
Abstract Drawing inspiration from the Fibonacci sequence and its complementary Lucas sequence, this paper introduces an innovative encryption and decryption algorithm tailored for multi-path quantum key distribution. The algorithm capitalizes on the high-quality orbital angular momentum entangled states, harnessing the mathematical elegance of Fibonacci numbers to construct block diagonal matrices. These matrices serve as the foundation for the simultaneous execution of key distribution across multiple communication paths in a structured block distribution format. The encryption process is facilitated through a combination of linear mappings, employing specific transition matrices to manage the cryptographic flow. The security underpinning of this method is firmly rooted in the Heisenberg Uncertainty Principle, a fundamental tenet of quantum mechanics, which ensures the confidentiality and integrity of the quantum communication channel. This approach paves the way for a novel encryption paradigm, fortifying the security framework of quantum communication networks.
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to protect the security of shared encryption keys. Here we present a new and fundamentally different approach to high-capacity, high-efficiency QKD by exploiting interplay between cross-disciplinary ideas from quantum information and light scattering of aperiodic photonic media. The novelty of the proposed approach relies on a unique type of entangled-photon source and a new physical mechanism for efficiently sharing keys. The new source produces entangled photons with orbital angular momenta (OAM) randomly distributed among Fibonacci numbers. Combining entanglement with the mathematical properties of Fibonacci sequences leads to a new QKD protocol. This Fibonacci protocol is immune to photon-number-splitting attacks and allows secure generation of long keys from few photons. Unlike other protocols, reference frame alignment and active modulation of production and detection bases are unnecessary, since security does not require use of non-orthogonal polarization measurements.
In the escalating race between cryptographic security and quantum computing capabilities, the need for robust encryption methodologies that can withstand the prowess of quantum algorithms is more pressing than ever. This paper introduces a novel cryptographic framework, grounded in the principles of quantum mechanics and the entropic uncertainty principle, to forge a path towards quantum-resilient encryption. At the heart of this approach lies the integration of the entropic uncertainty inherent in quantum states, a fundamental aspect often overlooked in traditional cryptographic strategies. By harnessing this intrinsic uncertainty of quantum mechanics, we propose a mathematical framework that not only challenges the conventional paradigms of encryption but also sets a new benchmark for security in the quantum computing era. The paper delves into the theoretical underpinnings of quantum mechanics relevant to cryptography, with a particular focus on the entropic uncertainty principle. This principle, which posits a natural limit on the precision with which certain pairs of physical properties can be known, serves as the cornerstone of our proposed encryption method. We meticulously develop and outline a mathematical model that leverages this principle, ensuring that the encrypted information remains secure against the formidable computational capabilities of quantum algorithms. We contrast our approach with existing cryptographic methods, highlighting the enhanced security features offered by the entropic uncertainty-based model. The findings underscore the potential of this framework to serve as a resilient encryption mechanism in a landscape increasingly dominated by quantum computing technologies. This research paves the way for a new era of encryption, one that embraces the uncertainty of quantum mechanics as its shield against the threats posed by quantum computing.
Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.
This paper presents a novel approach to quantum-inspired cryptography leveraging the complexities of entangled quantum states. Current quantum-inspired schemes often utilize simplified models, which lack the inherent security guarantees provided by genuine quantum phenomena. This research proposes a cryptographic protocol fundamentally rooted in the analysis and manipulation of entanglement. The core mechanism involves developing sophisticated techniques for measuring and controlling entangled states to generate key exchange and encryption/decryption processes. We demonstrate that this approach, utilizing the full potential of quantum mechanics, results in a significantly more robust and secure system compared to existing quantum-inspired methods. The protocol incorporates novel methods for key distribution based on the probabilistic nature of entanglement measurements and employs a multi-level security approach to mitigate potential vulnerabilities. The analysis presented focuses on the mathematical underpinnings of the protocol, detailing the operations performed on entangled states and the resultant security properties. We provide a comprehensive theoretical framework for evaluating the security of the proposed system, exploring potential attacks and demonstrating the protocol's resilience. The key contributions of this work include the formalization of the entanglement-based key exchange process and the development of a security model specifically tailored to the unique characteristics of entangled quantum states.
Quantum secure communication technology, grounded in the principles of quantum mechanics, has revolutionized traditional cryptographic methods, which predominantly rely on mathematical algorithms and logical transformations. Quantum key distribution (QKD) facilitates the secure sharing of symmetric keys between legitimate parties, ensuring the integrity and confidentiality of information in communication channels. Among various QKD schemes, continuous variable quantum key distribution (CV-QKD) has emerged as a viable alternative to the more established discrete variable quantum key distribution (DV-QKD). CV-QKD boasts several advantages, including straightforward deployment, reduced operational costs, and stable signal quality, positioning it as a significant component of the quantum communication landscape. Quantum noise stream cipher (QNSC) represents a technique that employs redundant data streams to encrypt plaintext. Notably, QNSC shares structural similarities with the optical path used in quantum key distribution, allowing for compatibility with existing QKD infrastructure. Furthermore, the keys generated through quantum key distribution ensure absolute security, enabling them to substitute the data streams produced by pseudo-random sequences traditionally used in classical encryption schemes. This substitution enhances the overall security framework of the quantum noise stream encryption approach. The quantum access network (QAN) extends quantum key distribution capabilities from point-to-point connections to point-to-multipoint configurations, thereby becoming an essential component of contemporary network architectures. By interlinking multiple end users with a network backbone, quantum access networks can seamlessly integrate with quantum key distribution protocols. This integration offers a cost-effective and scalable solution for user access to the network. Extensive experimental verifications have demonstrated the viability of downstream access networks, indicating that the merging of quantum access network structures with quantum stream encryption technologies can yield a comprehensive quantum experimental platform. On this platform, security keys are derived through quantum key distribution, which subsequently facilitates the encryption of plaintext information. Notably, experimental validations involving eight users have been successfully executed on this platform, underscoring its practical applicability and effectiveness.
Quantum cryptography and quantum key distribution (QKD) have been the most successful applications of quantum information processing, highlighting the unique capability of quantum mechanics, through the no-cloning theorem, to securely share encryption keys between two parties. Here, we present an approach to high-capacity, high-efficiency QKD by exploiting cross-disciplinary ideas from quantum information theory and the theory of light scattering of aperiodic photonic media. We propose a unique type of entangled-photon source, as well as a physical mechanism for efficiently sharing keys. The key-sharing protocol combines entanglement with the mathematical properties of a recursive sequence to allow a realization of the physical conditions necessary for implementation of the no-cloning principle for QKD, while the source produces entangled photons whose orbital angular momenta (OAM) are in a superposition of Fibonacci numbers. The source is used to implement a particular physical realization of the protocol by randomly encoding the Fibonacci sequence onto entangled OAM states, allowing secure generation of long keys from few photons. Unlike in polarization-based protocols, reference frame alignment is unnecessary, while the required experimental setup is simpler than other OAM-based protocols capable of achieving the same capacity and its complexity grows less rapidly with increasing range of OAM used.