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.
Marta Irene García Cid, Dileepsai Bodanapu, Alberto Gatto, Paolo Martelli · 6 authors
A new interactive quantum zero-knowledge protocol for identity authentication implementable in currently available quantum cryptographic devices is proposed and demonstrated. The protocol design involves a verifier and a prover knowing a pre-shared secret, and the acceptance or rejection of the proof is determined by the quantum bit error rate. It has been implemented in modified Quantum Key Distribution devices executing two fundamental cases. In the first case, all players are honest, while in the second case, one of the users is a malicious player. We demonstrate an increase of the quantum bit error rate around 25% in the latter case compared to the case of honesty. The protocol has also been validated for distances from a back-to-back setup to more than 60 km between verifier and prover. The security and robustness of the protocol has been analysed, demonstrating its completeness, soundness and zero-knowledge properties.
Cryptocurrency mining processes always lead to a high energy consumption at considerably high production cost, which is nearly one-third of cryptocurrency (e.g. Bitcoin) price itself. As the core of mining process is based on SHA-256 cryptographic hashing function, by using the alternative quantum computers, hybrid quantum computers or more larger quantum computing devices like quantum annealers, it would be possible to reduce the mining energy consumption with a quantum hardware's low-energy-operation characteristics. Within this work we demonstrated the use of optimized quantum mining facilities which would replace the classical SHA-256 and high energy consuming classical hardware in near future.
We show the following unconditional results on quantum commitments in two related yet different models: 1. We revisit the notion of quantum auxiliary-input commitments introduced by Chailloux, Kerenidis, and Rosgen (Comput. Complex. 2016) where both the committer and receiver take the same quantum state, which is determined by the security parameter, as quantum auxiliary inputs. We show that computationally-hiding and statistically-binding quantum auxiliary-input commitments exist unconditionally, i.e., without relying on any unproven assumption, while Chailloux et al. assumed a complexity-theoretic assumption, ${\bf QIP}\not\subseteq{\bf QMA}$. On the other hand, we observe that achieving both statistical hiding and statistical binding at the same time is impossible even in the quantum auxiliary-input setting. To the best of our knowledge, this is the first example of unconditionally proving computational security of any form of (classical or quantum) commitments for which statistical security is impossible. As intermediate steps toward our construction, we introduce and unconditionally construct post-quantum sparse pseudorandom distributions and quantum auxiliary-input EFI pairs which may be of independent interest. 2. We introduce a new model which we call the common reference quantum state (CRQS) model where both the committer and receiver take the same quantum state that is randomly sampled by an efficient setup algorithm. We unconditionally prove that there exist statistically hiding and statistically binding commitments in the CRQS model, circumventing the impossibility in the plain model. We also discuss their applications to zero-knowledge proofs, oblivious transfers, and multi-party computations.
In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities -- i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms proposed by Rosmanis. Namely, for an arbitrary distribution $D$ on Boolean functions, the probability an algorithm equipped with $τ_c$ classical and $τ_q$ quantum queries succeeds in finding a preimage of $1$ for a function sampled from $D$ is at most $ν_D \cdot(2\sqrt{τ_c} + 2τ_q + 1)^2$, where $ν_D$ captures the average (over $D$) fraction of preimages of $1$. As applications of our hardness results, we first revisit and generalize the security of the Bitcoin protocol called the Bitcoin backbone, to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we examine the generic security of hash functions against hybrid adversaries. Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a ``modified Grover'' where the initial state depends on the distribution $D$. We show how to analyze its success probability for arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.
Blockchains have gained substantial attention from academia and industry for their ability to facilitate decentralized trust and communications. However, the rapid progress of quantum computing poses a significant threat to the security of existing blockchain technologies. Notably, the emergence of Shor's and Grover's algorithms raises concerns regarding the compromise of the cryptographic systems underlying blockchains. Consequently, it is essential to develop methods that reinforce blockchain technology against quantum attacks. In response to this challenge, two distinct approaches have been proposed. The first approach involves post-quantum blockchains, which aim to utilize classical cryptographic algorithms resilient to quantum attacks. The second approach explores quantum blockchains, which leverage the power of quantum computers and networks to rebuild the foundations of blockchains. This paper aims to provide a comprehensive overview and comparison of post-quantum and quantum blockchains while exploring open questions and remaining challenges in these domains. It offers an in-depth introduction, examines differences in blockchain structure, security, privacy, and other key factors, and concludes by discussing current research trends.
In the realm of algorithmic economics, voting systems are evaluated and compared by examining the properties or axioms they satisfy. While this pursuit has yielded valuable insights, it has also led to seminal impossibility results such as Arrow's and Gibbard-Satterthwaite's Impossibility Theorems, which pose challenges in designing ideal voting systems. Enter the domain of quantum computing: recent advancements have introduced the concept of quantum voting systems, which have many potential applications including in security and blockchain. Building on recent works that bypass Arrow's Impossibility Theorem using quantum voting systems, our research extends Quantum Condorcet Voting (QCV) to counter the Gibbard-Satterthwaite Impossibility Theorem in a quantum setting. To show this, we introduce a quantum-specific notion of truthfulness, extend ideas like incentive compatibility and the purpose of onto to the quantum domain, and introduce new tools to map social welfare functions to social choice functions in this domain.
Marta Misiaszek-Schreyner, Miriam Kosik, Mirek Sopek
We explore the potential of Time-Bin Conference Key Agreement (TB CKA) protocol as a means to achieve consensus among multiple parties. We provide an explanation of the underlying physical implementation, i.e. TB CKA fundamentals and illustrate how this process can be seen as a natural realization of the global common coin primitive. Next, we present how TB CKA could be embodied in classical consensus algorithms to create hybrid classical-quantum solutions to the Byzantine Agreement problem.
Abstract The rapid advancement of quantum computing has sparked a considerable increase in research attention to quantum technologies. These advances span fundamental theoretical inquiries into quantum information and the exploration of diverse applications arising from this evolving quantum computing paradigm. The scope of the related research is notably diverse. This paper consolidates and presents quantum computing research related to the financial sector. The finance applications considered in this study include portfolio optimization, fraud detection, and Monte Carlo methods for derivative pricing and risk calculation. In addition, we provide a comprehensive analysis of quantum computing’s applications and effects on blockchain technologies, particularly in relation to cryptocurrencies, which are central to financial technology research. As discussed in this study, quantum computing applications in finance are based on fundamental quantum physics principles and key quantum algorithms. This review aims to bridge the research gap between quantum computing and finance. We adopt a two-fold methodology, involving an analysis of quantum algorithms , followed by a discussion of their applications in specific financial contexts. Our study is based on an extensive review of online academic databases, search tools, online journal repositories, and whitepapers from 1952 to 2023, including CiteSeerX, DBLP, ResearchGate, Semantic Scholar, and scientific conference publications. We present state-of-the-art findings at the intersection of finance and quantum technology and highlight open research questions that will be valuable for industry practitioners and academicians as they shape future research agendas.
Blockchain-based cryptocurrencies have become an extremely important, highly-used, technology. A major criticism of cryptocurrencies, however, is their energy consumption. In May 2022 Bitcoin alone was reported to be consuming 150 terawatt-hours of electricity annually; more than many entire countries. Hence, any meaningful efficiency increase in this process would have a tremendous positive impact. Meanwhile, practical applications of quantum information technologies, and in particular of near-term quantum computers (NISQ) continue to be an important research question. Here, we study the efficiency benefits of moving cryptocurrency mining from current ASIC-based miners to quantum, and in particular NISQ, miners. While the time-efficiency benefits of quantum technologies is extremely well-studied, here we focus on energy savings. We show that the transition to quantum-based mining could incur an energy saving, by relatively conservative estimates, of about roughly 126.7TWH, or put differently the total energy consumption of Sweden in 2020.
Since its advent in 2011, boson sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson sampling using input states that depend on the current block information and commit their samples to the network. Afterwards, CGBS strategies are determined which can be used to both validate samples and reward successful miners. By combining rewards for miners committing honest samples together with penalties for miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. We provide numerical evidence that these validation tests are hard to spoof classically without knowing the binning scheme ahead of time and show the robustness of our protocol to small partial distinguishability of photons. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware.
Most currently used cryptographic tools for protecting data are based on certain computational assumptions, which makes them vulnerable with respect to technological and algorithmic developments, such as quantum computing. One existing option to counter this potential threat is quantum key distribution, whose security is based on the laws of quantum physics. Quantum key distribution is secure against unforeseen technological developments. A second approach is post-quantum cryptography, which is a set of cryptographic primitives that are believed to be secure even against attacks with both classical and quantum computing technologies. From this perspective, this study reviews recent progress in the deployment of the quantum-secured infrastructure based on quantum key distribution, post-quantum cryptography, and their combinations. Various directions in the further development of the full-stack quantum-secured infrastructure are also indicated. Distributed applications, such as blockchains and distributed ledgers, are also discussed.
Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single measurement. We show how to delegate polynomial-time quantum computations in the OTS model. This also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This provides the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for n EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.
Current solutions to quantum vulnerabilities of widely used cryptographic schemes involve migrating users to post-quantum schemes before quantum attacks become feasible. This work deals with protecting quantum procrastinators: users that failed to migrate to post-quantum cryptography in time. To address this problem in the context of digital signatures, we introduce a technique called signature lifting, that allows us to lift a deployed pre-quantum signature scheme satisfying a certain property to a post-quantum signature scheme that uses the same keys. Informally, the said property is that a post-quantum one-way function is used "somewhere along the way" to derive the public-key from the secret-key. Our constructions of signature lifting relies heavily on the post-quantum digital signature scheme Picnic (Chase et al., CCS'17). Our main case-study is cryptocurrencies, where this property holds in two scenarios: when the public-key is generated via a key-derivation function or when the public-key hash is posted instead of the public-key itself. We propose a modification, based on signature lifting, that can be applied in many cryptocurrencies for securely spending pre-quantum coins in presence of quantum adversaries. Our construction improves upon existing constructions in two major ways: it is not limited to pre-quantum coins whose ECDSA public-key has been kept secret (and in particular, it handles all coins that are stored in addresses generated by HD wallets), and it does not require access to post-quantum coins or using side payments to pay for posting the transaction.
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based on random circuit sampling, that Google and USTC have successfully carried out starting in 2019. We show that, whenever the outputs of these experiments pass the now-standard Linear Cross-Entropy Benchmark (LXEB), under plausible hardness assumptions they necessarily contain $Ω(n)$ min-entropy, where $n$ is the number of qubits. To achieve a net gain in randomness, we use a small random seed to produce pseudorandom challenge circuits. In response to the challenge circuits, the quantum computer generates output strings that, after verification, can then be fed into a randomness extractor to produce certified nearly-uniform bits -- thereby "bootstrapping" from pseudorandomness to genuine randomness. We prove our protocol sound in two senses: (i) under a hardness assumption called Long List Quantum Supremacy Verification, which we justify in the random oracle model, and (ii) unconditionally in the random oracle model against an eavesdropper who could share arbitrary entanglement with the device. (Note that our protocol's output is unpredictable even to a computationally unbounded adversary who can see the random oracle.) Currently, the central drawback of our protocol is the exponential cost of verification, which in practice will limit its implementation to at most $n\sim 60$ qubits, a regime where attacks are expensive but not impossible. Modulo that drawback, our protocol appears to be the only practical application of quantum computing that both requires a QC and is physically realizable today.
Anna G. Hughes, Jack S. Baker, Santosh Kumar Radha
Advancements in quantum computing are fuelling emerging applications across disciplines, including finance, where quantum and quantum-inspired algorithms can now make market predictions, detect fraud, and optimize portfolios. Expanding this toolbox, we propose the selector algorithm: a method for selecting the most representative subset of data from a larger dataset. The selected subset includes data points that simultaneously meet the two requirements of being maximally close to neighboring data points and maximally far from more distant data points where the precise notion of distance is given by any kernel or generalized similarity function. The cost function encoding the above requirements naturally presents itself as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is well-suited for quantum optimization algorithms - including quantum annealing. While the selector algorithm has applications in multiple areas, it is particularly useful in finance, where it can be used to build a diversified portfolio from a more extensive selection of assets. After experimenting with synthetic datasets, we show two use cases for the selector algorithm with real data: (1) approximately reconstructing the NASDAQ 100 index using a subset of stocks, and (2) diversifying a portfolio of cryptocurrencies. In our analysis of use case (2), we compare the performance of two quantum annealers provided by D-Wave Systems.
We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions...) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT. At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way, without public-key primitives, and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.
This paper presents a new method for quantum identity authentication (QIA) protocols. The logic of classical zero-knowledge proofs (ZKPs) due to Schnorr is applied in quantum circuits and algorithms. This novel approach gives an exact way with which a prover $P$ can prove they know some secret by encapsulating it in a quantum state before sending to a verifier $V$ by means of a quantum channel - allowing for a ZKP wherein an eavesdropper or manipulation can be detected with a fail-safe design. This is achieved by moving away from the hardness of the Discrete Logarithm Problem towards the hardness of estimating quantum states. This paper presents a method with which this can be achieved and some bounds for the security of the protocol provided. With the anticipated advent of a `quantum internet', such protocols and ideas may soon have utility and execution in the real world.
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Physical Unclonable Functions (PUFs) and Hardware Security
Anupama Ray, Sai Sakunthala Guddanti, Vishnu Ajith, Dhinakaran Vinayagamurthy
Ethereum is one of the most valuable blockchain networks in terms of the total monetary value locked in it, and arguably been the most active network where new blockchain innovations in research and applications are demonstrated. But, this also leads to Ethereum network being susceptible to a wide variety of threats and attacks in an attempt to gain unreasonable advantage or to undermine the value of the users. Even with the state-of-art classical ML algorithms, detecting such attacks is still hard. This motivated us to build a hybrid system of quantum-classical algorithms that improves phishing detection in financial transaction networks. This paper presents a classical ensemble pipeline of classical and quantum algorithms and a detailed study benchmarking existing Quantum Machine Learning algorithms such as Quantum Support Vector Machine and Variational Quantum Classifier. With the current generation of quantum hardware available, smaller datasets are more suited to the QML models and most research restricts to hundreds of samples. However, we experimented on different data sizes and report results with a test data of 12K transaction nodes, which is to the best of the authors knowledge the largest QML experiment run so far on any real quantum hardware. The classical ensembles of quantum-classical models improved the macro F-score and phishing F-score. One key observation is QSVM constantly gives lower false positives, thereby higher precision compared with any other classical or quantum network, which is always preferred for any anomaly detection problem. This is true for QSVMs when used individually or via bagging of same models or in combination with other classical/quantum models making it the most advantageous quantum algorithm so far. The proposed ensemble framework is generic and can be applied for any classification task
Jack S. Baker, Haim Horowitz, Santosh Kumar Radha, Stenio Fernandes · 9 authors
Electron dynamics, financial markets and nuclear fission reactors, though seemingly unrelated, all produce observable characteristics evolving with time. Within this broad scope, departures from normal temporal behavior range from academically interesting to potentially catastrophic. New algorithms for time series anomaly detection (TAD) are therefore certainly in demand. With the advent of newly accessible quantum processing units (QPUs), exploring a quantum approach to TAD is now relevant and is the topic of this work. Our approach - Quantum Variational Rewinding, or, QVR - trains a family of parameterized unitary time-devolution operators to cluster normal time series instances encoded within quantum states. Unseen time series are assigned an anomaly score based upon their distance from the cluster center, which, beyond a given threshold, classifies anomalous behavior. After a first demonstration with a simple and didactic case, QVR is used to study the real problem of identifying anomalous behavior in cryptocurrency market data. Finally, multivariate time series from the cryptocurrency use case are studied using IBM's Falcon r5.11H family of superconducting transmon QPUs, where anomaly score errors resulting from hardware noise are shown to be reducible by as much as 20% using advanced error mitigation techniques.
Subhash Shankar Pandey, Tadasha Dash, Prasanta K. Panigrahi, Ahmed Farouk
Blockchain is a decentralized system that allows transaction transmission and storage according to the roles of the Consensus algorithm and Smart contracts. Non-fungible tokens (NFTs) consolidate the best characteristics of blockchain technology to deliver unique and bona fide tokens, each with distinctive attributes with non-fungible resources. Unfortunately, current classical NFTs are suffering from high costs regarding the consumed power of mining and lack of security. Therefore, this paper presents a new protocol for preparing quantum non-fungible tokens where a quantum state representing NFT is mounted on a blockchain instead of physically giving it to the owner. The proposed scheme is simulated and analyzed against various attacks and proves its ability to secure against them. Furthermore, the presented protocol provides reliable and cheaper NFTs than the classical one.
We propose a new, unifying framework that yields an array of cryptographic primitives with certified deletion. These primitives enable a party in possession of a quantum ciphertext to generate a classical certificate that the encrypted plaintext has been information-theoretically deleted, and cannot be recovered even given unbounded computational resources. - For X \in {public-key, attribute-based, fully-homomorphic, witness, timed-release}, our compiler converts any (post-quantum) X encryption to X encryption with certified deletion. In addition, we compile statistically-binding commitments to statistically-binding commitments with certified everlasting hiding. As a corollary, we also obtain statistically-sound zero-knowledge proofs for QMA with certified everlasting zero-knowledge assuming statistically-binding commitments. - We also obtain a strong form of everlasting security for two-party and multi-party computation in the dishonest majority setting. While simultaneously achieving everlasting security against all parties in this setting is known to be impossible, we introduce everlasting security transfer (EST). This enables any one party (or a subset of parties) to dynamically and certifiably information-theoretically delete other participants' data after protocol execution. We construct general-purpose secure computation with EST assuming statistically-binding commitments, which can be based on one-way functions or pseudorandom quantum states. We obtain our results by developing a novel proof technique to argue that a bit b has been information-theoretically deleted from an adversary's view once they output a valid deletion certificate, despite having been previously information-theoretically determined by the ciphertext they held in their view. This technique may be of independent interest.
Byzantine agreement, the underlying core of blockchain, aims to make every node in a decentralized network reach consensus. Classical Byzantine agreements unavoidably face two major problems. One is $1/3$ fault-tolerance bound, which means that the system to tolerate $f$ malicious players requires at least $3f+1$ players. The other is the security loopholes from its classical cryptography methods. Here, we propose a Byzantine agreement framework with unconditional security to break this bound with nearly $1/2$ fault tolerance due to multiparty correlation provided by quantum digital signatures. \textcolor{black}{It is intriguing that quantum entanglement is not necessary to break the $1/3$ fault-tolerance bound, and we show that weaker correlation, such as asymmetric relationship of quantum digital signature, can also work.} Our work strictly obeys two Byzantine conditions and can be extended to any number of players without requirements for multiparticle entanglement. We experimentally demonstrate three-party and five-party consensus for a digital ledger. Our work indicates the quantum advantage in terms of consensus problems and suggests an important avenue for quantum blockchain and quantum consensus networks.
Leader election is a crucial process in many areas such as cloud computing, distributed systems, task orchestration, and blockchain. Oftentimes, in a distributed system, the network needs to choose a leader, which would be responsible for synchronization between different processors, data storage, information distribution, and more.