Joseph T. Yun, Eli Lifton, Eunseo Lee, Y. M. Yun · 11 authors
The rapid advancements in quantum computing present significant threats to existing encryption standards and internet security. Simultaneously, the advent of Web 3.0 marks a transformative era in internet history, emphasizing enhanced data security, decentralization, and user ownership. This white paper introduces the W3ID, an abbreviation of Web3 standard meeting universal digital ID, which is a Universal Digital Identity (UDI) model designed to meet Web3 standards while addressing vulnerabilities posed by quantum computing. W3ID innovatively generates secure Digital Object Identifiers (DOIs) tailored for the decentralized Web 3.0 ecosystem. Additionally, W3ID employs a dual-key system for secure authentication, enhancing both public and private verification mechanisms. To further enhance encryption strength and authentication integrity in the quantum computing era, W3ID incorporates an advanced security mechanism. By requiring quadruple application of SHA-256, with consecutive matches for validation, the system expands the number of possibilities to 256^4, which is approximately 4.3 billion times the current SHA-256 capacity. This dramatic increase in computational complexity ensures that even advanced quantum computing systems would face significant challenges in executing brute-force attacks. W3ID redefines digital identity standards for Web 3.0 and the quantum computing era, setting a new benchmark for security, scalability, and decentralization in the global digital twin ecosystem.
Bit commitment is a fundamental cryptographic primitive and a cornerstone for numerous two-party cryptographic protocols, including zero-knowledge proofs. However, it has been proven that unconditionally secure bit commitment, both classical and quantum, is impossible. In this work, we demonstrate that imposing a restriction on the committing party to perform only separable operations enables secure quantum bit commitment schemes. Specifically, we prove that in any perfectly hiding bit commitment protocol, an honestly-committing party limited to separable operations will be detected with high probability if they attempt to alter their commitment. To illustrate our findings, we present an example protocol.
Non-interactive zero-knowledge (NIZK) proof systems are a cornerstone of modern cryptography, but their security has received little attention in the quantum settings. Motivated by improving our understanding of this fundamental primitive against quantum adversaries, we propose a new definition of security against quantum adversary. Specifically, we define the notion of quantum simulation soundness (SS-NIZK), that allows the adversary to access the simulator in superposition. We show a separation between post-quantum and quantum security of SS-NIZK, and prove that Sahaiâs construction for SS-NIZK (in the CRS model) can be made quantumly-simulation-sound. As an immediate application of our new notion, we prove the security of the Naor-Yung paradigm in the quantum settings, with respect to a strong quantum IND-CCA security notion. This provides the quantum analogue of the classical dual key approach to prove the security of encryption schemes. Along the way, we introduce a new notion of quantum-query advantage functions, which may be used as a general framework to show classical/quantum separation for other cryptographic primitives, and it may be of independent interest.
With the rapid development of quantum computers, proofs of quantumness have recently become an interesting and intriguing research direction. However, in all current schemes for proofs of quantumness, quantum provers almost invariably face the risk of being maliciously exploited by classical verifiers. In fact, through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. In other words, malicious verifiers can break some schemes (that quantum provers are not aware of) through interaction with quantum provers. All this is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness. To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent any malicious verifier from exploiting quantum advantage. Interestingly, we find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes. Due to some technical reason, it appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. Intuitively, this helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof. Specifically, the two principle proofs of quantumness schemes: Shor's factoring-based scheme and learning with errors-based scheme in [Brakerski et al, FOCS, 2018], can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Notably, the zero-knowledge proofs of quantumness can be viewed as an enhanced security notion for proofs of quantumness. To prevent malicious verifiers from exploiting the quantum device's capabilities or knowledge, it is advisable to transition existing proofs of quantumness schemes to this framework whenever feasible.
Abstract Blockchain technology ensures accountability, transparency, and redundancy, but its reliance on publicâkey cryptography makes it vulnerable to quantum computing threats. This article addresses the urgent need for quantumâsafe blockchain solutions by integrating postâquantum cryptography (PQC) into blockchain frameworks. Utilizing algorithms from the NIST PQC standardization process, it is aimed to fortify blockchain security and resilience, particularly for IoT and embedded systems. Despite the importance of PQC, its implementation in blockchain systems tailored for embedded environments remains underexplored. A quantumâsecure blockchain architecture is proposed, evaluating various PQC primitives and optimizing transaction sizes through techniques such as publicâkey recovery for Falcon, achieving up to 17% reduction in transaction size. The analysis identifies Falconâ512 as the most suitable algorithm for quantumâsecure blockchains in computerâbased environments and XMSS as a viable but unsatisfactory stateful alternative. However, for embeddedâbased blockchains, Dilithium demonstrates a higher transactionsâperâsecond (TPS) rate compared to Falcon, primarily due to Falcon's slower signing performance on ARM CPUs. This highlights the signing time as a critical limiting factor within embedded blockchains. Additionally, smart contract functionality is integrated, assessing the impact of PQC on smart contract authentication. The findings demonstrate the feasibility and practicality, paving the way for robust and futureâproof IoT applications.
The field of quantitative finance is constantly seeking new tools to exploit the complexities of the financial markets. With classical computers having limitations, the burgeoning field of quantum computing offers immense computational capabilities. Though Belief Networks have been useful in quantitative finance, their towering computational demands on classical systems limit their efficacy. On the other hand, Bitcoinâs popularity has increased in the last few years due to its unique features, such as decentralization and blockchain. Being relatively new Bitcoinâs market possesses huge potential. Price of the Bitcoin depends upon various economic and market factors, also possesses quite high volatility making traders worried while dealing with it. This project tries explore the potential of quantum computing technologies and Belief networks for developing new long-short Bitcoin trading strategy by leveraging the strengths of both paradigms.
The end-to-end verifiable e-voting system Ordinos [26] is primarily characterized by its tally-hiding property, which ensures that only the actual election result, e. g., the winner of the election, is revealed while the full tally consisting of the aggregated votes stays hidden. Ordinos is an abstract model that guarantees tally-hiding, verifiability and vote privacy if the underlying cryptographic primitives satisfy certain requirements. It uses a multi-party-computation protocol over an additively homomorphic encryption scheme and guarantees active security with zero-knowledge proofs. Ordinos has already been instantiated for several election systems using the Paillier [35] encryption scheme, which can be broken by Shorâs algorithm [41]. The aim of this thesis is to instantiate Ordinos post-quantum secure using a variant of Regevâs LWE-based cryptosystem [39], which is adapted to realize an actively secure threshold encryption scheme over an arbitrary plaintext space. Then a noise analysis of the arithmetic and logical components used in the MPC-protocol of the Paillier instantiation is conducted, and the components are slightly adapted to restrict the noise growth. Additionally, valid zero-knowledge proofs are provided and a concrete instantiation achieving a security level of 128 bits is shown.
The intersection of quantum urbanism and non-fungible tokens (NFTs) offers a new paradigm for remapping urban futures, wherein digital and physical realms merge into dynamic, decentralized ecosystems. This article examines how quantum computing, by applying principles such as superposition and probabilistic optimization, can simulate extremely intricate urban systems, from energy networks to traffic patterns, with unprecedented efficiency. Meanwhile, NFTs are transforming the notion of virtual land ownership, allowing decentralized control and hybrid economies that bypass geographical constraints. By integrating these domains, cities can become vibrant spaces where quantum algorithms optimize virtual land value, and NFT-based platforms democratize urban development. However, this transformation poses fundamental challenges: the energy consumption of quantum-blockchain infrastructures risks compromising sustainability goals, while algorithmic opacity and digital divides risk reproducing historical inequalities in virtual realms. Ethical governance policy and principles must concentrate on renewable energy integration, algorithmic transparency, and fair access to prevent exploitation. Drawing from emergent metaverse economy trials and quantum urban simulations, the paper argues that such a nexus would be capable of driving Sustainable Development Goals (SDGs), namely SDG 9 (innovation), SDG 11 (sustainable cities), and SDG 17 (partnerships) if they are premised on participatory design and cross-sectoral collaboration.
Blockchain technology has revolutionized secure and decentralized digital transactions. However, the emergence of quantum computing presents a significant threat to traditional cryptographic protocols, particularly public-key encryption mechanisms such as RSA and Elliptic Curve Cryptography (ECC). Quantum computers, leveraging Shorâs and Groverâs algorithms, can efficiently break these encryption schemes, compromising blockchain security. This paper explores quantum-secure blockchain protocols that integrate post-quantum cryptographic (PQC) techniques such as lattice-based, hash-based, and code-based cryptography to resist quantum attacks. Additionally, we evaluate quantum-resistant consensus mechanisms like Quantum-Secure Proof of Stake (QS-PoS) and Quantum-Protected Byzantine Fault Tolerance (Q-BFT). Through simulation-based performance analysis, we demonstrate that quantum-safe blockchain models can achieve robust security while maintaining efficient transaction processing. Our findings suggest that a hybrid approach, combining classical cryptographic elements with post-quantum algorithms, provides the best balance between security, performance, and scalability.
Meenal R Kale, Yousef A. Baker ElâEbiary, L. Sathiya, Vijay Kumar Burugari · 7 authors
Quantum computing is progressing at a fast rate and there is a real threat that classical cryptographic methods can be compromised and therefore impact the security of blockchain networks. All of the ways used to secure blockchain like RivestâShamirâAdleman (RSA), Elliptic Curve Cryptography (ECC) and Secure Hash Algorithm 256-bit (SHA256) are the characteristic of the traditional cryptographic techniques vulnerable to attack by quantum algorithms: Shorâs and Groverâs algorithms: can efficiently break asymmetric encryption and speed up brute force attacks. Because of this vulnerability, there exists a need to develop an advance quantum resilient blockchain framework to protect the decentralized ledgers from the future threats of the quantum. This research proposes Post-Quantum Cryptography (PQC), Quantum Key Distribution (QKD) and Quantum Random Number Generation (QRNG) as a formidable architectural integration, to fortify security of blockchain. Classical encryption is replaced with PQC, QKD with secure key exchange by detecting eavesdropping, and QRNG with improving cryptographic randomness to remove the predictable key vulnerability. Only with a small loss of transaction efficiency, we increase transaction encryption accuracy, key exchange security, and resistance to quantum attacks. In this quantum enhanced blockchain design, the idea is to preserve the decentralization, transparency and security and at the same time overcome the future quantum threat. By going through rigorous analysis and comparative evaluation, we demonstrate that the approach saves blockchain networks from the emerging quantum risks to make sure that the decentralized finance, smart contracts and cross chain transactions.
Adeshina Akin Ajayi, Igba Emmanuel, Adesola Dorcas Soyele, Joy Onma Enyejo
This paper explores the integration of quantum cryptography and blockchain technology to address two pressing challenges: securing financial transactions in Central Bank Digital Currencies (CBDCs) and combating the spread of misinformation during U.S. elections through decentralized social media platforms. As quantum computing advances, traditional encryption methods may become obsolete, posing significant risks to digital financial systems. Quantum cryptography, with its quantum-resistant algorithms, offers enhanced protection for CBDC transactions, ensuring long-term security and privacy. Simultaneously, blockchain-based social media platforms provide a decentralized structure that can prevent the dissemination of false information by ensuring transparency and authenticity through cryptographic verification and consensus mechanisms. These platforms also facilitate decentralized identity management, empowering users to verify content without relying on centralized authorities. By combining quantum cryptographyâs secure framework with blockchainâs decentralized transparency, this dual approach creates a more secure digital ecosystem that not only safeguards financial transactions but also strengthens democratic processes. The paper further addresses the regulatory and technical challenges associated with implementing these technologies and their potential to shape a more secure, transparent, and accountable future.
François Le Gall, Yupan Liu, Harumichi Nishimura, Qisheng Wang
We introduce two models of space-bounded quantum interactive proof systems, QIPL and QIP_{U}L. The QIP_{U}L model, a space-bounded variant of quantum interactive proofs (QIP) introduced by Watrous (CC 2003) and Kitaev and Watrous (STOC 2000), restricts verifier actions to unitary circuits. In contrast, QIPL allows logarithmically many pinching intermediate measurements per verifier action, making it the weakest model that encompasses the classical model of Condon and Ladner (JCSS 1995). We characterize the computational power of QIPL and QIP_{U}L. When the message number m is polynomially bounded, QIP_{U}L â QIPL unless P = NP: - QIPL^HC, a subclass of QIPL defined by a high-concentration condition on yes instances, exactly characterizes NP. - QIP_{U}L is contained in P and contains SACÂč âȘ BQL, where SACÂč denotes problems solvable by classical logarithmic-depth, semi-unbounded fan-in circuits. However, this distinction vanishes when m is constant. Our results further indicate that (pinching) intermediate measurements uniquely impact space-bounded quantum interactive proofs, unlike in space-bounded quantum computation, where BQL = BQ_{U}L. We also introduce space-bounded unitary quantum statistical zero-knowledge (QSZK_{U}L), a specific form of QIP_{U}L proof systems with statistical zero-knowledge against any verifier. This class is a space-bounded variant of quantum statistical zero-knowledge (QSZK) defined by Watrous (SICOMP 2009). We prove that QSZK_{U}L = BQL, implying that the statistical zero-knowledge property negates the computational advantage typically gained from the interaction.
Abstract The healthcare industry frequently handles sensitive and proprietary data, and due to strict privacy regulations, it is often reluctant to share it directly. In todayâs context, Federated Learning (FL) stands out as a crucial remedy, facilitating the rapid advancement of distributed machine learning while effectively managing critical concerns regarding data privacy and governance. The fusion of federated learning and quantum computing represents a groundbreaking interdisciplinary approach with immense potential to revolutionize various industries, from healthcare to finance. In this work, we propose a federated learning framework based on quantum tensor networks (QTNs) that takes advantage of the principles of many-body quantum physics. Currently, there are no known classical tensor networks (TNs) implemented in federated settings. Furthermore, we investigated the effectiveness and feasibility of the proposed framework by conducting a differential privacy analysis to ensure the security of sensitive data across healthcare institutions. Experiments on popular medical image datasets show that the federated quantum tensor network (FedQTNs) model achieved a mean receiver-operator characteristic area under the curve of 91%â98%, outperforming several state-of-the-art federated learning methods. Moreover, QTN models require fewer parameters in FL settings compared to traditional classical models, which often suffer from over-parameterization. This reduction in parameters not only improves the efficiency of the communication process but also significantly decreases data consumption during training. As a result, QTN models facilitate a more effective and resource-efficient approach to training in decentralized environments with limited communication bandwidth. The FedQTN models demonstrate a smaller performance drop even when using strong differential privacy settings, maintaining higher accuracy compared to classical models under similar privacy constraints. Experimental results demonstrate that the quantum federated global model, consisting of highly entangled TN structures, showed better generalization and robustness and achieved higher testing accuracy, surpassing the performance of locally trained clients under unbalanced data distributions among healthcare institutions.
Private set intersection (PSI) has important application value, however, current quantum PSI protocols are either unsuitable for multi-party scenarios or inefficient. Recently, Imran (arXiv: 2303.17196v3 , 2023) proposed two quantum secure multi-party greatest common divisor (GCD) protocols that can be used for PSI, but with the downside of information leakage and resource consumption. In this paper, we propose a novel quantum secure multi-party GCD protocol that has higher security and lower complexity. To hide privacy, each party randomly selects a coefficient within a range determined by his input integer, and with the assistance of a semi-honest third party TP, all parties secretly calculate the linear combination of their inputs under these coefficients. Once enough linear combinations are collected, TP calculates the GCD of these combinations, which is equal to the GCD of all input integers. To verify the honesty of participants, a quantum zero-knowledge proof sub-protocol is designed. Analysis shows that our GCD protocol is correct and has security against malicious attacks. Moreover, its complexity is polynomial level and lower than Imranâs. Furthermore, we demonstrate the scalability of our GCD protocol in private set operations, such as private set intersection, private set intersection cardinality, private multi-set intersection, etc.
The Internet of Medical Things (IoMT) has significantly enhanced the healthcare system by enabling advanced patient monitoring, data analytics, and remote interactions. Given that IoMT devices generate vast amounts of sensitive data, robust privacy mechanisms are essential. This privacy requirement is critical for IoMT as, generally, these devices are very resource-constrained with limited storage, computation, and communication capabilities. Blockchain technology, with its decentralisation, transparency, and immutability, offers a promising solution for improving IoMT data security and privacy. However, the recent emergence of quantum computing necessitates developing measures to maintain the security and integrity of these data against emerging quantum threats. This work addresses the current gap of a comprehensive review and analysis of the research efforts to secure IoMT data using blockchain in the quantum era. We discuss the importance of blockchain for IoMT privacy and analyse the impact of quantum computing on blockchain to justify the need for these works. We also provide a comprehensive review of the existing literature on quantum-resistant techniques for effective blockchain solutions in IoMT applications. From our detailed review, we present challenges and future opportunities for blockchain technology in this domain.
Engin Zeydan, Luis Blanco, Josep ManguesâBafalluy, Abdullah Aydeger · 8 authors
As evolving digital ecosystems become increasingly interconnected and reliant on digital transactions, secure, private and user-centric identity solutions are garnering more spotlight than ever before. In this paper, we propose an innovative architecture that integrates quantum key distribution (QKD) with blockchain-based self-sovereign identity (SSI) systems for secure key distribution and network/user management for mobile networks with advanced 6G network capabilities. The proposed approach leverages the advanced security guarantes of QKD to ensure the confidentiality and integrity of communications and uses the decentralized and immutable nature of blockchain technology to give individuals/organizations control over their digital identities in mobile environments. We then go on to expound on the foundations of architectural components and discuss its implications for various telecom specific services and applications. Finally, we present challenges and future directions to provide quantum communication support against future digital threats and a decentralized framework for identity management with the global pursuit of more privacy-friendly and usercentric digital services, and offer comparisons with traditional approaches.
In recent years, blockchain technology has developed rapidly and has been widely used in medical, financial, energy and other fields. However, in the process of practical application, each blockchain is a small independent ecosystem, with all transactions and operations limited to the chain, resulting in a large number of mutually heterogeneous to independent blockchains. It presents challenges for cross-chain interactions, cross-organization data sharing, and cross-blockchain expansion, and hinders the wider application of blockchain technology. In addition, the traditional digital signature method based on elliptic curve cipher faces the threat of being cracked by quantum computing attacks. To solve the aforementioned problems, this paper proposed a blockchain smart contract technique based on quantum computing attack resistance(BSCTQCAT). The technique first introduces the digital signature of the lattice cipher into the blockchain to resist the quantum search algorithm attack. Then, based on the smart contract authentication scheme, the nodes on multiple heterogeneous chains are organized into an identity agent layer P2P network, through which transactions on the chain will establish a credible identity management and message authentication mechanism between different chains, solving the current problem that each chain is difficult to communicate with each other. In this paper, the performance of the algorithm is evaluated by simulating the Bitcoin transaction scenario and analyzing the experimental data.
Introduction: Blockchain technology has revolutionized data management and transaction recording, extending its application beyond cryptocurrencies to various sectors, including Central Bank Digital Currencies (CBDCs) Methods: This distributed ledger technology offers a transparent, immutable, and secure transaction platform, reducing the risk of data tampering and increasing resistance to attacks. However, challenges such as performance, scalability, and security continue to exist; these challenges are particularly concerning consensus mechanisms like Proof of Work (PoW). Field-Programmable Gate Arrays (FPGAs) present a promising solution to enhance the efficiency and security of blockchain consensus mechanisms. Results: This study explores the implementation of blockchain in embedded systems using FPGAs and discusses the post-quantum cryptographic algorithms to ensure long-term protection. Conclusion: The research highlights the potential of FPGA-based implementations to revolutionize blockchain applications, emphasizing the need for continuous adaptation and vigilance to address evolving security threats, particularly those posed by quantum computing.
This project focuses on Zero-Knowledge Proofs (ZKPs), a groundbreaking cryptographic technique reshaping data authentication while preserving maximum confidentiality.ZKPs enable the verification of truthfulness in statements without disclosing associated data, ensuring the utmost protection of sensitive information.With applications spanning various domains, including secure authentication protocols, privacy-preserving transactions in decentralized systems like blockchain, and confidential data verification across digital interactions, ZKPs offer versatile solutions for secure communications.The project aims to safeguard sensitive business information during outsourcing service processes.The implementation of ZKPs intends to establish a secure communication framework that fosters trust among stakeholders without compromising sensitive details, ensuring enhanced confidentiality in outsourced operations.At its core, ZKPs empower a prover to convince a verifier of a statement's validity without revealing underlying data, establishing an unmatched level of security and privacy.This concept shields against unauthorized access and data breaches, fostering trust between entities without the exchange of sensitive details.The versatility of ZKPs extends beyond authentication, influencing secure voting systems, safeguarding digital identities, and facilitating confidential transactions while upholding user privacy.
The exponential advancement of quantum computing poses unprecedented threats to conventional cryptographic systems employed in banking infrastructure. This paper presents a comprehensive quantum-enhanced cryptographic framework that integrates post-quantum algorithms with distributed ledger technologies to establish resilient financial security systems. Through systematic analysis of lattice-based cryptography, hash-based signatures, and multivariate cryptographic schemes, this research demonstrates significant improvements in computational security while maintaining operational efficiency. The proposed framework achieves 99.7% security resilience against quantum attacks while reducing transaction processing overhead by 23% compared to traditional RSA-based systems. Experimental validation across simulated banking environments reveals enhanced performance metrics in key generation, digital signatures, and secure communication protocols. The integration of quantum-resistant algorithms with blockchain-based consensus mechanisms provides a robust foundation for future-proof banking security architectures.
Abstract Popular Secp256k1 and Schnorr algorithms offer strong security in current Blockchains. However, they are vulnerable to quantum attacks. To solve this problem, several quantum-resistant algorithms have been proposed. However, the performance evaluations and tangible analyses of these algorithms on current Blockchains have not been studied yet. In this context, a performance analysis of quantum-resistant algorithms on a Blockchain can provide valuable insight into the efficiency of quantum-resistant algorithms in real-world scenarios. To address this need, we prototyped and analyzed a quantum-resistant Blockchain using the Falcon algorithm. Falcon is selected because it provides smaller signature and key size compared to Crystals-Dilithium and Sphincs+. We then measured in real-time the key size, transaction signature size, and transaction verification time. The paper also discusses the potential scalability limitations of the proposed quantum-resistant Blockchain and suggests an approach to select quantum-resistant algorithms based on different Blockchain use cases. Our approach and benchmark results have implications for the future development and adoption of quantum-resistant Blockchains.
This thesis is the culmination of research conducted between 2019 and 2023. It is divided into three parts. Inthe first part, we explore algorithms related to the Covid-19 pandemic, such as Pool Testing, a well-establishedtechnique where samples from multiple patients are pooled for collective testing, allowing for cost reduction and time savings. We propose algorithms taking into account the a priori probabilities that individual tests are positive, which can be evaluated during a prior clinical examination of the patient. We also examine Pool Testingin emergency situations, where certain samples need to be analyzed according to some prescribed priority order. In both cases, we propose new algorithms and analyze them in detail. This section also deals with DNA privacy preservation in Covid-19 tests. In the second part, we present our results in experimental mathematics, where we have discovered several new conjectures on continued fractions through automated exploration. All those conjectures have been numerically tested to assess their plausibility. Finally, the third part of this thesis is devoted to various results in the field of computer security, such as a previously unknown attack on the Mathematica software, a new protection mechanism against counterfeit medication, and new observations on zero-knowledge proofs.
It is well-known that digital signatures can be constructed from one-way functions in a black-box way. While one-way functions are essentially the minimal assumption in classical cryptography, this is not the case in the quantum setting. A variety of qualitatively weaker and inherently quantum assumptions (e.g. EFI pairs, one-way state generators, and pseudorandom states) are known to be sufficient for non-trivial quantum cryptography. While it is known that commitments, zero-knowledge proofs, and even multiparty computation can be constructed from these assumptions, it has remained an open question whether the same is true for quantum digital signatures schemes (QDS). In this work, we show that there $\textit{does not}$ exist a black-box construction of a QDS scheme with classical signatures from pseudorandom states with linear, or greater, output length. Our result complements that of Morimae and Yamakawa (2022), who described a $\textit{one-time}$ secure QDS scheme with classical signatures, but left open the question of constructing a standard $\textit{multi-time}$ secure one.