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This article corresponds to an extensive review of Quantum Computers. We chose to consider topics relevant to quantum computing, such as machine learning, and the deepening of other issues related to cybersecurity. We introduce the reader to the basic concepts of quantum computing so that they can easily understand the terms mentioned in this review. We analyze different state of the art articles, and we give a summary of the contributions made. Finally, we conclude with the analysis of the bibliography, the research centers, the current state of the art, surprising results and conclusions.

Professor Bill Buchanan OBE FRSE considers the impact of advancements in quantum computing on cryptography and explores the methods available for safeguarding data. [ABSTRACT FROM AUTHOR]

Quantum secure direct communication (QSDC) can directly transmit secret messages through quantum channel without keys. Device-independent (DI) QSDC guarantees the message security relying only on the observation of the Bell-inequality violation, but not on any detailed description or trust of the devices’ inner workings. Compared with conventional QSDC, DI-QSDC has relatively low secret message capacity. To increase DI-QSDC’s secret messages capacity, we propose a high-capacity DI-QSDC protocol based on the hyper-encoding technique. The total message leakage rate of our DI-QSDC protocol only relies on the most robust degree of freedom. We provide the numerical simulation of its secret message capacity altered with the communication distance. Our work serves as an important step toward the further development of DI-QSDC systems.

The leading countries across the world have entered the race to develop quantum technologies that will enable them to ensure their continued economic prosperity. Among these technologies, a special place is occupied by quantum communication, which is designed to ensure information security in an era where a quantum computer is capable of compromising a number of cryptography algorithms. In this article, this new digital technology includes quantum key distribution and encryption methods that are cryptographically resistant to a quantum computer. The study does not consider the regulation of the quantum communication sub-technology, the so-called “quantum internet,” due to the technical limitations of the existing equipment. The authors note that their predictions about the cryptographic strength of encryption algorithms are based solely on modern knowledge about the capabilities of quantum computing and do not take into account its hidden potential, for example, in terms of cryptanalysis information systems based on a machine learning model generated by a quantum computer. Currently, the only data protection system that is not subject to quantum threats is the technology of quantum key distribution. In today’s information and digital age, information security systems are an important element of critical infrastructure. Given the importance of these technologies, different states use different methods to regulate this field. This article puts forward and substantiates the hypothesis that the implementation of a combination of regulatory legal acts could have a greater positive impact on the development of quantum communication and ensure an acceptable level of information security in the post-quantum era. The analysis showed that a significant number of states and interstate associations are conducting research in this area, relying only on investment growth. This strategy has prevented any country from achieving the competencies of the People’s Republic of China. The authors also analyzed the methods of legal support used by China, Russia, and other countries in the field of quantum communication, which made it possible to identify a model of legal regulation of quantum communication that stimulates this technology’s development.

Abstract The quantum communication channel is considered to be eavesdropped when the signal Quantum Bit Error Rate (QBER) exceeds a defined theoretical limit and is thus considered a figure of merit parameter for assessing the security of a quantum channel. This work presents a general mathematical model considering device imperfections and various sources of errors for estimating signal QBER in polarisation encoded satellite‐based QKD systems. QBER performance for satellite‐to‐ground downlink scenarios has been investigated for multiple sky brightness conditions (day time and night time operations), two operating wavebands: 800 and 1550 nm as well as for different quantum transmitter and quantum receiver architectures. Further, a novel QBER estimation analysis for inter‐satellite QKD links has also been presented. The estimation results obtained from the developed model have been validated against and found in good agreement with the measured results of the only reported satellite‐to‐ground QKD experiments till date. The presented QBER modelling and analysis will aid in system engineering and efficient design of future satellite‐based QKD systems.

The field of computing is about to undergo a revolution thanks to quantum computing, a ground-breaking innovation based on the ideas of quantum physics. The enormous implications and potential that quantum computing has for cloud computing are explored in this publication. We examine the difficulties faced by current cryptography systems as well as prospective improvements in fields like machine learning, simulations, and data security as we delve into the basic alterations in computing paradigms. Additionally, we go over the revolutionary possibilities for cloud computing, such as the creation of quantum-safe cloud security solutions, hybrid computing models, and quantum cloud services.

The Quantum Key Distribution (QKD) network approach has emerged as a promising solution and has garnered significant interest across various domains. QKD networks can be broadly categorized into two main types: those based on measurement-device-dependent (MDD) protocols and those based on measurement-device-independent (MDI) protocols. A novel network scheme is proposed combining these two protocols to guarantee end-to-end secure communication. It comprises two interconnected networks — the first uses a measurement-device-dependent protocol to connect routers with nearby nodes, while the second employs a measurement-device-independent protocol to interconnect the routers. In the first network, the process begins with Alice (Router) generating two types of weak quantum signals — the first has intensity, frequency and polarization or phase randomly varied, while the second with different delay times. Alice randomly transmits either signal states carrying information or decoy states with varying properties to the receivers (Bobs) over the quantum channels. She also sends a synchronization signal along with the quantum signals. At the receiver end, the synchronization pulse timestamps the incoming quantum signals. Each Bob then randomly shifts the frequencies of the received signals and measures their phase/polarization of the first signal and measures the delay times of the second signal. The secret key is derived by combining the frequency, the delay time and the phase/polarization information of the quantum signals, resulting in longer key lengths. Encoding information across multiple degrees of freedom enables extended key generation for secure communication. However, between the routers, MDI-QKD protocols are used to securely share the keys. This hybrid approach aims to ensure secure end-to-end communication across the network. [ABSTRACT FROM AUTHOR]

Quantum computing provides a revolution in computational competences, leveraging the principles of quantum mechanics to process data in fundamentally novel ways. This paper explores the profound implications of quantum computing on cryptography, focusing on the vulnerabilities it introduces to classical encryption methods such as RSA and ECC, and the emergence of quantum-resistant algorithms. We review the core principles of quantum mechanics, including superposition and entanglement, which underpin quantum computing and cryptography. Additionally, we examine quantum encryption algorithms, particularly Quantum Key Distribution (QKD) protocols and post-quantum cryptographic methods, highlighting their potential to secure communications in the quantum era. This analysis emphasizes the urgent need for developing robust quantum-resistant cryptographic solutions to safeguard sensitive information against the imminent threats posed by advancing quantum technologies. [ABSTRACT FROM AUTHOR]

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10 − 1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km. [ABSTRACT FROM AUTHOR]

In the digital age, securing data and ensuring communication confidentiality are paramount, highlighting the crucial role of public key cryptography. Traditional algorithms like RSA, while secure, have limitations due to their long key lengths and computational intensity, making them less suitable for resource-constrained environments. Elliptic Curve Cryptography (ECC) is favored for its compact keys and strong security but faces new challenges with quantum computing. To address this, we introduce Enhanced Elliptic Curve Cryptography (EECC), an algorithm that enhances security and efficiency. EECC uses secure elliptic curves, an advanced random number generator, optimized key lengths, and quantum-resistant mechanisms to fortify against quantum threats. Both theoretical analysis and empirical tests show EECC's effectiveness in thwarting attacks and improving encryption and decryption speeds, affirming its value in modern secure communications and data protection. [ABSTRACT FROM AUTHOR]

Quantum private comparison (QPC) represents a cryptographic approach that enables two parties to determine whether their confidential data are equivalent, without disclosing the actual values. Most existing QPC protocols utilizing single photons or Bell states are considered highly feasible, but they suffer from inefficiency. To address this issue, we present a novel QPC protocol that capitalizes on the entanglement property of Bell states and local operations to meet the requirements of efficiency. In the proposed protocol, two participants with private inputs perform local operations on shared Bell states received from a semi-honest third party (STP). Afterward, the modified qubits are returned to the STP, who can then determine the equality of the private inputs and relay the results to the participants. A simulation on the IBM Quantum Cloud Platform confirmed the feasibility of our protocol, and a security analysis further demonstrated that the STP and both participants were unable to learn anything about the individual private inputs. In comparison to other QPC protocols, our proposed solution offers superior performance in terms of efficiency. [ABSTRACT FROM AUTHOR]

To address the potential threat to the power grid industry posed by quantum computers and ensure the security of bidirectional communication in smart grids, it is imperative to develop quantum-safe authentication protocols. This paper proposes a semi-quantum bidirectional authentication protocol between a control center (CC) and a neighboring gateway (NG). This method uses single photons to facilitate communication between the CC and the NG. Security analysis demonstrates that the protocol can effectively resist common attack methods, including double CNOT attacks, impersonation attacks, interception-measurement-retransmission attacks, and entanglement-measurement attacks. Comparisons with other protocols reveal that this protocol has significant advantages, making it more appealing and practical for real-world applications. Finally, by simulating the protocol on the IBM quantum simulator, this protocol not only validates the theoretical framework but also confirms the practical feasibility of the protocol. [ABSTRACT FROM AUTHOR]

This study develops a technology analysis to detect technological trajectories in quantum computing that can lay the foundation of a quantum industry. Study design considers data of 10,089 scientific products in 'quantum computing' over 1989–2020 period and 19,266 scientific products in 'quantum computer' over 1967–2020 period to cover all scientific production in this research field; a complementary analysis considers 8,505 patents over 1977–2020 in 'quantum computing' and 9,792 patents in 'quantum computer' over 1985–2020 period. Models of technological evolution applied here show main technological trajectories in quantum computing and computer and their rates of growth that suggest path-breaking directions in quantum technology, such as quantum optics, quantum information, quantum algorithms, quantum entanglement, quantum communication and quantum cryptography. Findings here provide information to extend the knowledge in the evolution of quantum computing and computers to support the management of these new technologies and R&D investments towards innovations generating industrial, economic and social change. [ABSTRACT FROM AUTHOR]

It is well known that many of the traditional cryptographic schemes (like RSA and DH) will be vulnerable when scalable quantum computers will be available. However, quantum cryptographic protocols can provide unconditional security. One such protocol for quantum key distribution (QKD) is coherent one way (COW) protocol which is realized often because of ease of implementation, though the security proof is still an open problem. In the present work, we report experimental realization of an optical fiber based COW protocol for QKD in the telecom wavelength (1550 nm) where the attenuation in the optical fiber is minimum. A laser of 1550 nm wavelength, attenuator and intensity modulator is used for the generation of pulses having average photon number 0.5 and repetition rate of 500 MHz. The experiment is performed over 40, 80 and 120 km of optical fiber and several experimental parameters like disclose rate, compression ratio, dead time and excess bias voltage of the detector are varied for all the cases (i.e., for 40, 80 and 120 km distances) to observe their impact on the final key rate. Specifically, it is observed that there is a linear increase in the key rate as we decrease compression ratio or disclose rate. The key rate obtains its maximum value for least permitted values of disclose rate, compression ratio and dead time. It seems to remain stable for various values of excess bias voltage. While changing various parameters, we have maintained the quantum bit error rate (QBER) below 6% (5%) for distance ≥ 120 km ( ≤ 120 km). The key rate obtained is also found to remain stable over time. Experimental results obtained here are also compared with the earlier realizations of the COW QKD protocol. Further, to emulate key rate at intermediate distances and at a distance larger than 120 km, an attenuator of 5 dB loss is used which can be treated as equivalent to ∼ 25 km of the optical fiber used in the present implementation. This has made the present implementation equivalent to the realization of COW QKD upto ∼ 145 km. [ABSTRACT FROM AUTHOR]

In this paper, the authors present a technique for developing a secure messaging service called "CryptoMess" which utilizes the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) algorithm for secure key exchange and the Advanced Encryption Standard (AES) to protect message content in communication. In addition, the authors have incorporated the Falcon post-quantum digital signature technology to ensure the integrity and authenticity of communications between the sender and the recipient. The novel post-quantum cryptographic algorithms utilized by the authors are still under consideration in the competition to select cryptosystems for use in quantum computing systems organized by the NIST Standards Institute. As a result, the messaging program "CryptoMess" is able to exchange messages between users, providing safety, security, integrity, and authenticity. The authors have included modern post-quantum cryptography techniques, such as the Falcon digital signature system, to guarantee that the product operates safely. The program has a transmitting rate of approximately 209–261 ms and a receiving rate of approximately 168–206 ms. The message signing time is about 260 ms, and the message verification speed is approximately 185 ms. Key generation time is about 741 ms, key encapsulation time is about 1.454 ms, and key decapsulation time is about 1.921 ms. The source code of the "CryptoMess" communications program has been analyzed and tested by the authors using the Fortify Static Code Analyzer tool to ensure that the product has been created safely and securely. [ABSTRACT FROM AUTHOR]

The discrete-logarithm problem and related problems are important in public-key cryptography; however, these problems can be reduced to the hidden-subgroup problem (HSP) of an abelian group, for which efficient quantum algorithms exist. This paper more broadly regards these problems as semigroup-action problems (SAPs) on different modules. The results prove that if the action on a module is injective or the cardinality of the hidden subgroup's least generating set is less than or equal to that of the ring's least generating set, the corresponding SAP on the module can be reduced to the HSP of an abelian group in polynomial time; therefore, most cryptosystems based on the SAP on a module cannot resist quantum cryptanalysis. The results are applicable to the discrete-logarithm problem and matrix-action problem on a group, along with other SAPs on a module. Such reduction is not be found for the SAP on the semi-module. The cryptographic systems based on SAPs on some semi-modules are likely to resist quantum attacks. [ABSTRACT FROM AUTHOR]

With the rapid development of quantum computing technology, the traditional cryptosystem will face a significant threat. It is an urgent security issue to study the security impact of quantum computing on classical cryptosystems and provide reliable cryptographic primitives for the post-quantum era. A powerful way to solve this problem is to quantize the classical cryptanalysis tools and use the improved versions for cryptanalysis. In this paper, we propose a quantum Zero-correlation analysis algorithm based on the Bernstein–Vazirani and Grover algorithms. It can find zero-correlation linear hulls for Feistel and SPN structures. We prove the correctness of the algorithm and analyze its complexity. Compared with the classical algorithms, the proposed quantum algorithm has significant advantages when the number of encryption rounds of block ciphers is large. Moreover, compared with the existing quantum Zero-correlation linear analysis, the proposed algorithm is more efficient and does not depend on the algebraic characteristics of the target cipher, which makes the algorithm has more flexible application scenarios. With the development of quantum computers, we discuss the threat of quantum cryptanalysis algorithms to classical security. [ABSTRACT FROM AUTHOR]

The current blockchain systems lack the ability to resist quantum computing attacks. This puts the confidentiality and integrity of data in blockchain-based data sharing at risk. The security of data sharing faces the new challenges. In this paper, a blockchain data sharing scheme based on quantum re-encryption is proposed. The presented scheme uses quantum key and unitary matrix to encrypt data for two times. It ensures data sharing between the data owner and the data accessor without revealing the owner's private key. Moreover, it utilizes a quantum hash function based on controlled alternate quantum walks to compute quantum hash value. The obtained hash value has higher randomness, collision resistance and input sensitivity. Additionally, this method combines on-chain and off-chain storage. The combined storage method effectively alleviates the storage pressure on the blockchain. Finally, the security of the proposed scheme is analyzed. The results show that this scheme ensures the integrity, confidentiality and non-tampering of the shared data. At the same time, it protects the security of data owner's private keys. [ABSTRACT FROM AUTHOR]

This paper simulated the operation of vacuum state and single decoy state protocols in the BB84 and SARG04 QKD schemes by utilizing the features of the commercial ID-3000 QKD system. Numerical modeling identified an optimal signal-to-decoy state ratio of 0.95:0.05 and an intensity of μ=0.85 for the signal state and ν1=0.05 for the decoy state, ensuring the highest key generation rate and a secure distance of up to 50 km. These protocols were validated experimentally over various transmission distances with standard telecom fiber, using the ID-3000 QKD system in a conventional bi-directional plug-and-play setup. Simulations predicted secure key rates of 1.2 × 105 bits/s for SARG04 and 8.5 × 104 bits/s for BB84 at 10 km, with secure distances of 45 km and 35 km, respectively. The experimental results confirmed these predictions, showing a 30% higher key rate and 20% longer secure distance compared to non-decoy methods. The SARG04 protocol surpassed BB84 in key rate and secure distance, highlighting the twophoton component's role in key generation. This study concludes that the decoy-state method significantly enhances key generation rates and secure distances, optimizing QKD protocols for secure quantum communication. [ABSTRACT FROM AUTHOR]

This paper introduced a novel semiring structure involving nonnegative integers, where operations depended on the comparison of the magnitudes of decimal digit sums. Consequently, a corresponding matrix semiring can be established on this commutative semiring. We showed that the 3-satisfiability problem can be polynomial-time reduced to solving systems of quadratic polynomial equations over this semiring. We proposed a key exchange protocol based on this matrix semiring, with its security relying on the two-sided digital circulant matrix action problem over this semiring. This scheme provides a novel cryptographic primitive for post-quantum cryptography. [ABSTRACT FROM AUTHOR]

Password-based authentication is one of the most prevailing access control mechanism. Typical password-authenticated key exchange (PAKE) protocols are single-server settings and are therefore vulnerable to server compromise attack. To defend against such attack, multi-server PAKE schemes have been advanced, but most of which are built on non-quantum-secure hardness assumptions. Lattice-based cryptosystems are regarded as the most promising one for post-quantum eara by NIST, while the known multi-server password-based authentication solution over lattices achieves merely key transport and is public key infrastructure (PKI)-based, resulting in low efficiency and poor deployability. In this work, we resort to distributed smooth projective hash function (SPHF) to bridge the gap between multi-server PAKE protocol and quantum-security. We first design an exact SPHF and derive the first distributed SPHF over lattices by leveraging the additive homomorphic property of the strong learning with errors (LWE) problem. In particular, the relevant parameters of the public key encryption (PKE) scheme it predicates on are identified, thus eliminating the influence of incomplete lattice homomorphism on the correctness of our SPHFs. Pertinent lattice-based multi-server PAKE protocols are further proposed on both transparent and non-transparent transmission modes by integrating our distributed SPHF into the multi-server framework of Raimondo and Gennaro (EUROCRYPT'03). Our PAKE constructions are able to resist both quantum and sever compromise attacks as well as avoid the expensive cryptographic primitives, including non-interactive zero knowledge (NIZK) proofs, signature/verification, secret sharing and fully homomorphic encryption. Experimental results demonstrate that our SPHFs and PAKE protocols offer better efficiency. [ABSTRACT FROM AUTHOR]

Quantum computing is a new type of computing that is revolutionizing the kind of computational power at people's disposal, including their cryptography applications. This paper aims at presenting a study of significance of quantum computing in different cryptographic techniques, particularly in Shor's Algorithm, Grover's Algorithm, QKD, and NTRUEncrypt. With the help of existing literature, our paper shows that Shor's Algorithm helps to achieve exponential speed up in integer factorisation, that contributes to less time required to factorise an integer like 15. 23 seconds to 0. This reduces the time for a problem solution to 05 seconds as compared to classical methods. Grover's Algorithm enhances search operations outcomes by a quadratic rate, and the time spent to search 256-element database is reduced from 1. 68 seconds to 0. 45 seconds. QKD protocols proved key distribution and a range of a setup time of 5. 00 seconds for a 128-bit key and key generation rates exceeding 1. 2 kbps. To this end they related NTRUEncrypt, a post-quantum cryptographic algorithm, which demonstrated encryption times of 0. A favourable response time concerns 30 seconds for a 128-bit key and 0. 55 seconds when encrypting a 256-bit key and is highly secure. This study calls for the use of new approaches to middle cryptographic threats and show how secure and efficient cryptographic systems can be maintained in the postquantum world. [ABSTRACT FROM AUTHOR]

The rapidly advancing computational capacity of modern computers is making traditional encryption techniques more and more susceptible in the ever-changing field of cybersecurity. Using the ideas of quantum mechanics, quantum cryptography presents a viable way to improve security by introducing protocols that are impervious to hacking attempts based on classical computation. This paper offers an extensive overview of newly developed quantum cryptography methods intended to protect digital communication against present and potential dangers, such as those originating from quantum computers. The potential of key protocols like post-quantum cryptography and quantum key distribution (QKD) to supplement or replace current encryption techniques is investigated. The report outlines the benefits of quantum cryptography, such as its capacity to safeguard wide-scale networks, its ability to detect eavesdropping in real-time, and its unbreakable encryption. It also covers the real-world difficulties in putting these protocols into practice, like budgetary constraints, infrastructure needs, and technology constraints. This survey highlights the critical necessity to implement quantum cryptography solutions as a foundation for future-proof cybersecurity frameworks as the world draws closer to the era of quantum computing. [ABSTRACT FROM AUTHOR]

Hermite–Korkin–Zolotarev (HKZ) reduction is an important notion of lattice reduction which plays a significant role in number theory (particularly the geometry of numbers), and more recently in coding theory and post-quantum cryptography. In this work, we determine a sharp upper bound on the orthogonality defect of HKZ reduced bases up to dimension 3. Using this result, we determine a general upper bound for the orthogonality defect of HKZ reduced bases of arbitrary rank. This upper bound is sharper than existing bounds in literature, such as the one determined by Lagarias, Lenstra and Schnorr [3]. [ABSTRACT FROM AUTHOR]

A significant topic of contemporary cryptography research and standardization is the development of public key crypto systems that resist attacks from quantum computers. Protocols and applications should start investigating the use of quantumresistant key exchange and encryption to protect the confidentiality of current communications against future quantum computers utilizing post-quantum cryptography for a particular key exchange. Since they operate harder and need fewer steps compared to conventional computers, quantum algorithms are more secure and robust. Attackers who use quantum computers have powerful computing capabilities, and a quantum allows for simple cryptographic system breaking. Security algorithms that are quantum secure are resistant to attacks from conventional, as well as quantum computers. This work has surveyed, summarized, and analysed previous research to provide readers of this study an integrated understanding of quantum cryptography. It also discusses quantum attacks, which could be used in place of more conventional cryptography techniques, such as quantum key distribution, which takes advantage of quantum mechanics' properties to ensure secure exchanges of the secret keys, and various quantum algorithms. With quantum computation becoming a very real threat, this should motivate more people to show an early interest in the future of cryptography. [ABSTRACT FROM AUTHOR]

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 , orthogonal to both | T 〉 and | Ψ 〉. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit | GHZ 〉 and | W 〉 states under evolution by a quantum Heisenberg Hamiltonian. [ABSTRACT FROM AUTHOR]

Recently, an appreciable number of protocols for quantum key distribution (QKD) have been experimentally realized as they are expected to be unconditionally secure. Among these QKD protocols, two protocols of distributed phase reference type [namely, coherent one way (COW) and differential phase shift (DPS) QKD protocols] have undergone rapid experimental developments due to the ease of implementation with the presently available technology. In this work, we have experimentally realized optical fibre based COW and DPS protocols for QKD where weak coherent pulses are used to encode the information. Further, we have analysed the key rates with respect to different parameters such as distance, disclose rate, compression ratio and detector dead time. [ABSTRACT FROM AUTHOR]

This article shows an implementation of quantum cryptography. We introduce the reader to the basic concepts of quantum computing so that they can easily understand the terms mentioned in the implementation related to cybersecurity and quantum key distribution (QKD). We show an application of QKD, where we can see how a spy is easily detected when a message is intercepted. [ABSTRACT FROM AUTHOR]

Nowadays, pairing-based cryptography researchers are looking for new parameters for standard security levels against the new number field sieve tower number field sieve algorithm. Recently, they have suggested new parameters for well-studied pairing-friendly curves with odd embedding degrees five and seven resistant to this attack. In this paper, we define optimal ate pairing on curves using sparse families with embedding degrees five and seven. We also provide details to perform the miller loop and the final exponentiation using addition chain process. Our theoretical results costs indicate that these families of curves offer the best performance in the computation of the optimal ate pairing at the 128-bit security level compared to Cocks–Pinch curves of embedding degrees five and seven. The improvement is about 8 , 8 % and 1 9 % faster than the optimal ate pairing previously computed on Cocks–Pinch curves of embedding degrees five and seven, respectively. [ABSTRACT FROM AUTHOR]

In the modern era of the Internet of Things (IoT), especially with the rapid development of quantum computers, the implementation of postquantum cryptography algorithms in numerous terminals allows them to defend against potential future quantum attack threats. Lattice-based cryptography can withstand quantum computing attacks, making it a viable substitute for the currently prevalent classical public-key cryptography technique. However, the algorithm's significant time complexity places a substantial computational burden on the already resource-limited chip in the IoT terminal. In lattice-based cryptography algorithms, the polynomial multiplication on the finite field is well known as the most time-consuming process. Therefore, investigations into efficient methods for calculating polynomial multiplication are essential for adopting these quantum-resistant lattice-based algorithms on a low-profile IoT terminal. Number theoretic transform (NTT), a variant of fast Fourier transform (FFT), is a technique widely employed to accelerate polynomial multiplication on the finite field to achieve a subquadratic time complexity. This study presents an efficient FPGA-based implementation of number theoretic transform for the CRYSTAL Kyber, a lattice-based public-key cryptography algorithm. Our hybrid design, which supports both forward and inverse NTT, is able run at high frequencies up to 417 MHz on a low-profile Artix7-XC7A100T and achieve a low latency of 1.10 μ s while achieving state-of-the-art hardware efficiency, consuming only 541-LUTs, 680 FFs, and four 18 Kb BRAMs. This is made possible thanks to the newly proposed multilevel pipeline butterfly unit architecture in combination with employing an effective coefficient accessing pattern. [ABSTRACT FROM AUTHOR]

In today's world, where quantum technologies are rapidly evolving, traditional cryptographic systems face serious challenges. Quantum computing has the potential to undermine the foundations of modern cryptographic protocols, such as RSA and ECC, by utilizing algorithms that can break these systems in record time. This article is dedicated to analyzing the impact of quantum technologies on cryptography, as well as the necessity of creating new solutions for information protection. The aim of this research is to assess the current state of post-quantum cryptography and identify new approaches that can ensure reliable information security in the face of quantum advancements. The paper discusses areas such as lattice-based cryptography, code-based cryptography, multivariate cryptography, and hash-based cryptography. The scientific and practical significance of this work lies in its contribution to understanding the challenges faced by contemporary cryptography in the context of quantum computing, and it offers possible solutions to overcome these challenges. The research methodology includes a literature review, analysis of existing cryptographic systems, and evaluation of their resilience to quantum attacks. The main results of the study indicate that lattice-based and code-based approaches demonstrate high resilience to quantum attacks and can be utilized for developing new cryptographic protocols. Additionally, it was found that multivariate cryptography, while showing promising results, requires further research to optimize performance. The conclusions of the research emphasize the importance of a comprehensive approach to information security in the context of quantum progress. The value of this research lies in its contribution to the development of post-quantum cryptography, as it not only identifies current challenges but also proposes new directions for future research. The practical significance of the findings is that the results can be used to develop secure information systems in the context of quantum threats. [ABSTRACT FROM AUTHOR]

In this paper, a new hybrid chaotic-quantum encryption model is investigated aiming to solve the interception trouble of information transmission through insecure environment. In this model, the image encryption method is studied using block diagonal chaotic (BDC) matrix and quantum based private key. The block diagonal chaotic model is designed with structured matrix based on two different nonlinear chaotic sequences and private key bits combined with quantum walks (QWs) path. At sender, the key bits convert to QWs states to increase tamper resistant of quantum key distribution in noisy communication channel. At the receiver side, the received data is retrieved merely by both initial key bits and states as similar as the sender initial key bits and states. If the eavesdropper attempts to measure quantum based private key, the key bits change to different states compared to real sender states and drops the bits eavesdropped in quantum channel. We call the hybrid chaotic image encryption method with private key based on quantum states as chaotic quantum key distribution (CQKD) method. The key space is evaluated using CQKD model rather than chaotic based encryption method without quantum distributed states over impure channels. Considering the sensitivity of block diagonal chaotic-based encryption BDC method with accuracy of 10(−32), the key space is increased from 10 111 to 10 142 × 10 a × f (Δ Φ) × (1 Δ p e ) N e with phase-shifted QWs. It guarantees no information access by attackers considering high security against brute-force attacks and outperforms rather than the conventional chaotic encryption schemes. [ABSTRACT FROM AUTHOR]

Isogeny-based cryptography holds significant promise in the realm of post-quantum cryptography, primarily due to its perceived resilience against attacks from quantum computers, based on our current understanding of the underlying mathematical problems. However, it's essential to acknowledge the dynamic nature of post-quantum cryptography, where ongoing research may yield profound insights or lead to the development of novel cryptographic approaches. This study delves into the analysis of Hessian form curves within the framework of isogeny-based cryptography (IBC). We specifically investigate the computational costs associated with deriving Hessian form curves for constructing sections, particularly when employing compression functions. The square-root Velu method is utilized for handling Hessian form curves, and we introduce a novel formula for calculating the curve's coefficient at a specific point on a Hessian curve. Our results indicate that the operational costs of the Hessian form and the Montgomery curve are comparable. Furthermore, we propose the Hessian-Edwards hybrid model, optimizing Hessian-CSIDH and determining the coefficient for the codomain's curve using Edwards curves. According to our findings, various Isogeny-based cryptosystems can be implemented by leveraging Hessian curves. [ABSTRACT FROM AUTHOR]

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This research aims to establish a secure system for key exchange by using post-quantum cryptography (PQC) schemes in the classic channel of quantum key distribution (QKD). Modern cryptography faces significant threats from quantum computers, which can solve classical problems rapidly. PQC schemes address critical security challenges in QKD, particularly in authentication and encryption, to ensure the reliable communication across quantum and classical channels. The other objective of this study is to balance security and communication speed among various PQC algorithms in different security levels, specifically CRYSTALS-Kyber, CRYSTALS-Dilithium, and Falcon, which are finalists in the National Institute of Standards and Technology (NIST) Post-Quantum Cryptography Standardization project. The quantum channel of QKD is simulated with Qiskit, which is a comprehensive and well-supported tool in the field of quantum computing. By providing a detailed analysis of the performance of these three algorithms with Rivest–Shamir–Adleman (RSA), the results will guide companies and organizations in selecting an optimal combination for their QKD systems to achieve a reliable balance between efficiency and security. Our findings demonstrate that the implemented PQC schemes effectively address security challenges posed by quantum computers, while keeping the the performance similar to RSA. [ABSTRACT FROM AUTHOR]

In the era of the Fourth Industrial Revolution, quantum technology is entering the scene with the promise of radically changing the technological paradigm. Quantum computing, simulation, quantum communications and the combination of this technology with artificial intelligence are opening up new horizons of innovation that could revolutionize various industries. Along with its enormous potential, this technology brings legal, ethical and social challenges that require detailed analysis and an interdisciplinary approach. The industrial deployment of quantum technology entails dilemmas regarding human rights, cyber security and national security, as well as the risk of exacerbating inequality, technological exclusion and algorithmic discrimination. With regard to artificial intelligence enhanced by quantum computing technology, we can speak of a completely new facet of the problem of the opacity of algorithms, which is determined not only by the cognitive limitations of the human mind, but stems from the indefinability of the world described by the laws of quantum mechanics. In light of the above, the thesis can be advanced that the classical approach to the principle of transparency and the postulates of creating algorithms that will clearly present the path to the final result, which are part of the broad current of creating ethical and explainable artificial intelligence, may prove difficult to realize in relation to Quantum AI. In the era of the Fourth Industrial Revolution, we are therefore faced with the challenge of implementing new instruments for testing, certifying and inspecting algorithms, such as tools for analyzing and visualizing the results of quantum algorithms, which will be suited to the specifics of Quantum AI and ensure the ethical correctness of the systems. This article will identify selected areas of application of quantum technology, and thus the potential benefits and risks of quantum technology, and also analyze the need to develop ethical and legal standards that allow for the sustainable and socially responsible development of these disruptive technologies. [ABSTRACT FROM AUTHOR]

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum‐proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum‐proof randomness extractors characterizing the input raw data as min‐entropy sources, it is found that the input raw data generated by a large class of trusted‐device quantum random number generators can be characterized as the so‐called reverse block source. This fact enables us to design improved extractors. Two novel quantum‐proof randomness extractors for reverse block sources that realize real‐time block‐wise extraction are proposed specifically. In comparison with the general min‐entropy randomness extractors, the designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make the design an adequate choice for the real‐time post‐processing of practical quantum random number generators. Applying the extractors to the raw data generated by a widely used quantum random number generator, a simulated extraction speed as high as 300 Gbps is achieved. [ABSTRACT FROM AUTHOR]

The multipartite nonlocality provides deep insights into the fundamental feature of quantum mechanics and guarantees different degrees of cryptography security for potential applications in the quantum internet. Verifying multipartite nonlocal correlations is a difficult task. A unified approach is proposed that encompasses all the quantum characteristics of the multipartite correlated system beyond from fully separable to biseparable no‐signaling correlations. A straightforward method is offered to verify general systems by lifting partial nonlocal correlations. This allows to construct a chained Bell inequality, facilitating the unified verification of hierarchic multipartite nonlocalities. The lifting method is finally applied to verify the correlations derived from quantum networks. [ABSTRACT FROM AUTHOR]

The socialist millionaire problem aims to compare the equality of two inputs from two users while keeping their inputs undisclosed to anyone. Quantum private comparison (QPC), whose security relies on the principles of quantum mechanics, can solve this problem and achieve the information-theoretic security of information processing. The current QPC protocols mainly utilize the bitwise XOR operation to implement the comparison, leading to insufficient security. In this paper, we propose a rotation operation-based QPC protocol to solve the socialist millionaire problem, which utilizes Bell states as quantum resources and rotation operations for classical calculations. The proposed protocol only utilizes easy-to-implement technologies such as Bell states, rotation operations, and Bell-basis measurements, making it more practical. The analysis demonstrates that our protocol can meet both the correctness and security requirements. Compared with the existing QPC protocols, our protocol has improved performance in terms of practicability and security. [ABSTRACT FROM AUTHOR]

Summary: The present scenario witnesses "the second quantum revolution," which has enabled the development of revolutionary novel quantum tools. Quantum computing endeavors to establish higher computing standards that can potentially solve complex structures. Post‐quantum cryptography (PQC) has emerged as one of the new domains of cryptography, which is resilient to quantum attacks owing to the revolution in quantum computing. To ensure quantum security, the lattice‐based cryptosystem (LB‐cryptosystem) is one of the promising tools of PQC to address quantum‐based threats. The traditional security algorithms, such as RSA and Diffie–Hellman (DH), are strong enough to resist present security threats. However, it has been predicted that quantum technologies have the capability to break the security of most traditional algorithms whose security is based on prime factorization and DH‐type hard problems. Therefore, research is currently focused on addressing the security and privacy threats by using LB‐cryptosystems to secure various applications, organizations' data, and information infrastructure in the quantum era. The purpose of this article is to investigate recent advances in LB‐cryptosystems that may allow the design of secure models for smart‐grid networks (SGNs) against existing and future quantum attacks. SGNs have been explored as the bi‐directional assimilation of communication in terms of electricity generation, transmission, allocation, and utilization. This survey provides a comprehensive overview of LB‐cryptosystems, as well as their potential applications in securing SGNs. Lastly, the article summarizes the various PQC primitives, NIST selected algorithms, open‐source tools along with their packages, and various PQC industrial initiatives, and also compares traditional cryptographic schemes with other PQC. [ABSTRACT FROM AUTHOR]

Most semi-quantum secret sharing protocols are suitable for the application with three participants. Based on the n-level states, a multiparty semi-quantum secret sharing protocol is proposed. Compared with similar protocols, it has the merits as follows. (1) The dealer only needs to prepare the single photon sequence without using any product state or entangle state. (2) To share a secret, the classical parties need not have the ability of measurement. They only need to reorder the photon sequence and send it to the receiver. (3) The dealer knows nothing about any agent's secret shadow. Therefore, it is infeasible for the dealer to impersonate the classical participant to pool the secret shadow during the secret recovering phase. (4) Theoretically, the qubit efficiency of the proposed protocol is asymptotically 100%. The protocol is secure against famous attacks such as intercept-resend attack, measurement-resend attack and entangle-measure attack. [ABSTRACT FROM AUTHOR]

Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications. [ABSTRACT FROM AUTHOR]

In the face of advancing quantum computing capabilities posing significant threats to current cryptographic protocols, the need for post-quantum cryptography has become increasingly urgent. This paper presents a comprehensive analysis of the performance of various post-quantum cryptographic algorithms specifically applied to digital signatures. It focuses on the implementation and performance analysis of selected algorithms, including CRYSTALS-Dilithium, Falcon, and SPHINCS+, using the liboqs library. Performance tests reveal insights into key pair generation, file signing, and signature verification processes. Comparative tests with the well-known and popular RSA algorithm highlight the trade-offs between security and time efficiency. The results can help to select secure and efficient ciphers for specific 5G/6G services. [ABSTRACT FROM AUTHOR]