We present a simple quantum interactive proof (QIP) protocol using the quantum state teleportation (QST) and quantum energy teleportation (QET) protocols. QET is a technique that allows a receiver at a distance to extract the local energy by local operations and classical communication (LOCC), using the energy injected by the supplier as collateral. QET works for any local Hamiltonian with entanglement and, for our study, it is important that getting the ground state of a generic local Hamiltonian is quantum Merlin Arthur (QMA)-hard. The key motivations behind employing QET for these purposes are clarified. Firstly, in cases where a prover possesses the correct state and executes the appropriate operations, the verifier can effectively validate the presence of negative energy with a high probability (Completeness). Failure to select the appropriate operators or an incorrect state renders the verifier incapable of observing negative energy (Soundness). Importantly, the verifier solely observes a single qubit from the prover's transmitted state, while remaining oblivious to the prover's Hamiltonian and state (Zero-knowledge). Furthermore, the analysis is extended to distributed quantum interactive proofs, where we propose multiple solutions for the verification of each player's measurement. The complexity class of our protocol in the most general case belongs to QIP(3)=PSPACE, hence it provides a secure quantum authentication scheme that can be implemented in small quantum communication devices. It is straightforward to extend our protocol to Quantum Multi-Prover Interactive Proof (QMIP) systems, where the complexity is expected to be more powerful (PSPACE$\subset$QMIP=NEXPTIME). In our case, all provers share the ground state entanglement, hence it should belong to a more powerful complexity class QMIP$^*$.
Ang Liu, XiuâBo Chen, Shengwei Xu, Zhuo Wang · 8 authors
Blockchain technology affords data integrity protection and building trust mechanisms in transactions for distributed networks, and, therefore, is seen as a promising revolutionary information technology. At the same time, the ongoing breakthrough in quantum computation technology contributes toward large-scale quantum computers, which might attack classic cryptography, seriously threatening the classic cryptography security currently employed in the blockchain. As a better alternative, a quantum blockchain has high expectations of being immune to quantum computing attacks perpetrated by quantum adversaries. Although several works have been presented, the problems of impracticality and inefficiency in quantum blockchain systems remain prominent and need to be addressed. First, this paper develops a quantum-secure blockchain (QSB) scheme by introducing a consensus mechanism-quantum proof of authority (QPoA) and an identity-based quantum signature (IQS)-wherein QPoA is used for new block generation and IQS is used for transaction signing and verification. Second, QPoA is developed by adopting a quantum voting protocol to achieve secure and efficient decentralization for the blockchain system, and a quantum random number generator (QRNG) is deployed for randomized leader node election to protect the blockchain system from centralized attacks like distributed denial of service (DDoS). Compared to previous work, our scheme is more practical and efficient without sacrificing security, greatly contributing to better addressing the challenges in the quantum era. Extensive security analysis demonstrates that our scheme provides better protection against quantum computing attacks than classic blockchains. Overall, our scheme presents a feasible solution for blockchain systems against quantum computing attacks through a quantum strategy, contributing toward quantum-secured blockchain in the quantum era.
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.
Modern technology has brought novel types of wealth. In contrast to hard cash, digital currency does not have a physical form. It exists in electronic forms only. To date, it has not been clear what impacts its ongoing growth will have, if any, on wealth distribution. Here, we propose to identify all forms of contemporary wealth into two classes: âdistinguishableâ or âidenticalâ. Traditional tangible moneys are all distinguishable. Financial assets and cryptocurrencies, such as bank deposits and Bitcoin, are boson-like, while non-fungible tokens are fermion - like. We derived their ownership-based distributions in a unified manner. Each class follows essentially the Poisson or the geometric distribution. We contrast their distinct features such as Gini coefficients. Furthermore, aggregating different kinds of wealth corresponds to a weighted convolution where the number of banks matters and Bitcoin follows BoseâEinstein distribution. Our proposal opens a new avenue to understand the deepened inequality in modern economy, which is based on the statistical physics property of wealth rather than the individual ability of owners. We call for verifications with real data.
Due to its minimal energy requirement the PoS consensus protocol has become an attractive alternative to PoW in modern cryptocurrencies. In this protocol the chance of being selected as a block proposer in each round is proportional to the current stake of any node. Thus, nodes with higher stakes will achieve more block rewards, resulting in the so-called rich-getting-richer problem. In this paper, we introduce a new block reward mechanism called the FRD (Fair Reward Distribution) mechanism, in which for each block produced, in addition to a major reward given to the block proposer, a small reward is given to all other nodes. We prove that this reward mechanism makes the PoS protocol fairer in terms of concentration of wealth by developing on the Bagchi-Pal urn model.
Mauritz Kop is TTLF Fellow and Visiting Scholar at Stanford Law School, Stanford University; Founder of MusicaJuridica and strategic intellectual property lawyer at AIRecht, a technology consultancy firm based in Amsterdam. His present cross-disciplinary, comparative research focuses on human-centred artificial intelligence (AI), the Ethical, Legal, Socio-Economic, and Policy Implications of Quantum Technology (Quantum-ELSPI), and sustainable disruptive innovation policy pluralism. Mateo Aboy is Principal Research Scholar in Biomedical Innovation, Precision Medicine, AI & Law at the LML, University of Cambridge and Affiliated Professor and Fellow at the Centre for Advanced Studies in Biomedical Innovation Law (CeBIL), University of Copenhagen. Timo Minssen is Professor of Law and the Founding Director of the Center for Advanced Studies in Biomedical Innovation Law (CeBIL), University of Copenhagen. Specializing in IP, tech-transfer, antitrust and the regulation of health and life science innovation, he is also a senior advisor at the Swedish law firm X-officio and a Quantum Law Researcher at Lund University. Abstract One of the central goals of intellectual property rights (IPRs) and related rights is to incentivize and reward creative and innovative efforts that promote scientific and technical progress and stimulate fair competition through the distribution and commercialization of technologies. Yet, an excessive proliferation of exclusive rights can also result in fundamentally anticompetitive environments with potentially negative effects on scientific research, product development, fair distribution and equitable access to the technology. Hence, a reasonable balance must be found between the stimulation of sustainable innovation and competition, the promotion of scientific research and protection through IPRs. To reconcile these factors, each new technology has led to judicial responses and even modifications to the law. We are on the verge of a technological revolution associated with quantum technologies, including quantum computing and quantum/artificial intelligence hybrids. Its complexity and global significance are creating challenges, which could not have been foreseen when the IP system was developed. This article utilizes the insights gained from qualitative and quantitative studies to (a) inquire which IPRs and related rights are currently directed to quantum computing and (b) examine whether the strategic use of overlapping IPRs might lead to innovation distortions such as excessive anticompetitive effects and underuse associated with property fragmentation. Emphasis is laid on the question if, and if so to what degree, IP portfolio approaches could result in inappropriate proliferations of exclusive rights, raise anticommons concerns and denote unwanted concentrations of first mover market power. It concludes by outlining potential proactive responses to mitigate these risks, while addressing the major future open and closed innovation opportunities, implications and challenges posed by quantum technology in general and quantum computing in particular. Current advances in quantum technology highlight the unique characteristics, promises and perils of quantum technologiesâsuch as the unprecedented capabilities of quantum sensors, secured communications and the potential for quantum computing to solve problems beyond the reach of classical processors by implementing quantum algorithms on programmable quantum computers. The spectrum of potential applications is vast and ranges from uses in health and life sciences (eg, modelling chemical processes at the quantum using quantum simulation) to national security (eg, military uses quantum cryptography, communications and computation). In light of these actual and potential capabilities, national governments have invested over $25 billion into quantum computing research by mid-2021,1 and some reports announce that by September 2021, the quantum technology industry has attracted more than $1 billion in venture capital.2 This will have clear implications not only for the future of business, science, government and the global power game but also for society itself.3 While the predicted consequences of quantum technology remain in part speculative, it becomes increasingly evident that the ethico-legal frameworks for incentivizing, protecting, governing and regulating quantum technologies will have to be carefully studied. These frameworks might potentially have to be adaptedâor newly interpretedâconsidering the new realities presented by second-generation (2G) quantum devices. International organizations, such as the World Economic Forum (WEF), have therefore engaged in developing âthe first set of principles for responsible design and adoption of quantum computing technologies in order to incentivize the development of the technology while minimizing the possible risksâ.4 Consequently, scrutinizing the existing framework for IPRs and how they apply to quantum computing, including their governance and regulatory dimensions, as well the interplay of IPRs with new forms of potentially closed or more decentralized and open innovation systems, are becoming ever more relevant. One of the primary goals of IPRs and related rights, such as patents, copyrights, trade secrets and trade marks, is to reward and protect creative and innovative efforts in order to promote scientific and technical progress, as well as stimulating fair competition through the distribution and commercialization of technologies.5 For example, an effective and predictable patent protection regime is generally regarded as necessary to encourage risky and costly research in complex technologies that take a long time to reach the market but are relatively easy to copy such as many pharmaceuticals. Other IPRs, such as trade secrets, could become more relevant regarding highly complex technologies that are not so easy to copy and face less regulatory barriers. However, overprotection through IPRs can also lead to a situation that would create a fundamentally anticompetitive environment.6 For example, a proliferation of patent rights upstream could potentially hinder essential innovations further downstream in the course of scientific research and product development because each upstream patent allows its owner to create another obstacle on the road to product development, adding to the cost and slowing the pace of downstream innovation.7 Dealing with this potential dilemma, commonly referred to as the âTragedy of the Anticommonsâ, requires a reasonable balance to be found between the stimulation of innovation competition, the enhancement of scientific research and the careful protection of intellectual property rights.8 To maintain such a reasonable balance, each new technology has involved modifications to the law. This is nothing new. The first patents, during the Industrial Revolution, were mostly directed to mechanical devices and articles of manufacture. When chemical law the existing framework to solve new problems posed by and of based on and by the of and as well as in and have also led to many and a of law and We are currently on the verge of a new technological revolution associated with quantum technologies, including quantum its complexity might create challenges, which could have been foreseen when the system was this this article (a) which IPRs and rights would be to quantum technology and (b) an of whether the strategic use of of IP rights to the of a quantum IP portfolio potentially might lead to anticompetitive of market and competition and In this it would progress in an of quantum quantum will therefore be laid on the question if, and if so to what degree, overlapping IPRs could result in an inappropriate of global exclusive rights for first and in an unwanted of market power. To these this article will first with an of what quantum computing and how it can be will which of IP are at present the of quantum will these the first of on the patent for quantum will use the insights gained from qualitative and quantitative studies to the implications and possible responses to to mitigate and to future based on the of and Quantum computing its from principles of quantum (eg, and the of the Quantum the between and and the of at the beyond classical including such as and the of is the of the the of of such as of and Quantum and general are to be in an that the of at Quantum or are the quantum of can be a or a or a of We this with a a quantum in of possible quantum In to quantum can be while of each This is as quantum quantum to the in which a potential that is in For these are quantum In quantum computing is for some of the problems on which such as and for the of and Quantum are when modelling or of using quantum These at complex However, quantum also have For example, quantum can to complex and such as the but they to these The of artificial intelligence (eg, and quantum and can solve and chemical can problems that are currently not with the of classical computers. AI and quantum computing of based on classical and to artificial AI algorithms using classical with quantum algorithms that principles has the potential to including in the of and computing is to In the between quantum technology and AI the a new on science that quantum quantum and quantum will an in the development of artificial and the of is the between quantum computing and intellectual property Quantum can be by of intellectual and property rights, such as rights patents, copyrights, trade secrets, design rights and trade We which IP rights can be of these be it or We also whether are in protection and whether are IP rights are rights, these as as possible from the of an IP be in and and of protection in the or the Quantum on their in the and on their the of the technology quantum and quantum the of quantum processors such as and quantum the and the the the and quantum the the quantum set quantum quantum quantum the quantum and and quantum computing and the and the actual or of a quantum a quantum a a and a In a is to access the of the quantum in and This is a of through the In are with quantum and AI have to the of the AI system to this of including the that processes the and that are patent so by a can be generally a of and a and technical to technical problems that have been and into of articles of and processes are for patent While and are not might potentially algorithms and to the that is directed to a technical result or and if it is a of an that a technical can be further by the of IP rights, can the of a quantum by rights, design and and creative and algorithms or These can to the potential for the of these algorithms to solve technological problems as and system that technical to a technical The protection for is generally as it is also by the of to the life of the for One of the for this is that the system and the patent system have In quantum computing is more to and than the and It requires more to the than to the a the and devices necessary to become to and as in trade between the and The patent system to incentivize to and market their with the of on It to encourage the of innovative and the of research and development by exclusive rights to the the or its the it to design and and of can be In of and are from The are for patent the technology quantum and quantum the of quantum processors such as and quantum and the and the the the and the the quantum set and quantum The computing can be by as The including its quantum and is also for it the of and Quantum computing algorithms are not they are However, the of quantum algorithms to solve technical problems can potentially be patent These are using and system that to be in an to they the in the and technical in to incentivize and technological progress and of of is to stimulate and of by of to on the of their to the World on and the World creative of and can be by as if they are the of is not its The that is by general principles and are not The are part of the the of an is in a it can be by an can also be by a The are for quantum the quantum and and quantum computing and the and These the of these are of creative and in a of It is possible that for quantum computing will be of or for use with classical computing, it is that and will into the and some for is not by This the question of whether and be by for and of and can be IP whether or patents, in a to trade secrets, which generally on the quantum computing system of It is also possible to from a classical computing into a quantum the In of AI that of the is in the these IP a of potential IP rights potentially in the that to be including a on the the for the of AI and are concerns and of is a of in the existing because they are and not for AI and for to be a or even a to for quantum computing that and In quantum computing IP this is for IP It can be or IP rights on the can also be and into the or by upstream or downstream be The and and society from a IP rights can only be by such as or or to rights and and be These in an of and patents, of a quantum can trade in some trade and trade with potentially of law and national security beyond the of the IP a in technological a is the with AI and some technologies, the of quantum computing systems, with the of trade rights, could a trade secrets to protect and quantum computing applications and quantum This might of of technology to the and that a trade not protect This IP can be by that unwanted a quantum and design can be and modelling on the for which protection is by an of IP such as design rights, rights and trade using a of IP rights to and protect the of the IP portfolio of the quantum owner could result in an of global exclusive rights for first of essential in is a that are in IP protection from is a potential of IP protection this new of rights not Other quantum technologiesâsuch as quantum quantum and the quantum for IP protection using the of IP a innovation law future quantum to be and Its and could be by an of IP rights, with each The to quantum sensors, quantum and and devices with the of quantum technology. it is the with technologies, IP framework is not with quantum technology in IP is to be an in time and the that can be for the essential of quantum technologies be to equitable a and sustainable innovation policy it could be that IP rights not be to the of their and It might well be to in a quantum technology It could be to such in an intellectual property have been have further that quantum technology and not to be by IP or beyond the it has been that is âTragedy of the on quantum technology be IP incentivize market and market at the For to encourage fair competition and market IP law to be with antitrust The question is whether the in and IP overprotection could create for market and raise concerns regarding fair competition, of and the of new might hinder innovation and could potentially lead to the âTragedy of the that have been for many in the In this an anticommons which would underuse by rights by a of IP portfolio and patent could progress in an of quantum quantum In trade in property anticommons In protection might have a negative on the and protection to the that are in the of technologies and to remain It is to and carefully these and to take proactive it necessary based on the insights gained from technological approaches must also take into and the for of IP These can have effects if and with the of the IP system and its forms of and forms of governing IP as well as to IP protection must be on the and a of and it is in further that such approaches are by studies that and While this apply to IPRs and rights, the will the of such an that has on the and in quantum We a patent to including the has been the over the for quantum and are the quantum what are to protect these more IP research to these of it is for and to they can to existing and regulatory with reasonable of in this present from a more patent on the of quantum computing with the of from the actual in this technical the use the International by the of The a system to to technical that is are into and The is an of the It is by the and & and the by In this patent use of the system to related to quantum patent the new to the technical of quantum computing to the quantum computing with a of the that have been by the and computing, based on by the of the patent For the of patent are as the of and We a of quantum computing from and that of these have been of the patent protection for quantum computing has in the of the patent that these quantum computing with directed to and for quantum processors or (eg, quantum quantum quantum and quantum (eg, of quantum such as quantum quantum and quantum access and of quantum algorithms (eg, algorithms based on quantum applications of the quantum and and quantum and quantum (eg, quantum computing, for and quantum and quantum of in quantum computing at the and The of that the and are currently over quantum computing of the in quantum computing patent has of that the of in was the as in in the the of quantum computing from to This to a of which is than the for quantum technologies over this in the has been the of for quantum computing The has of the the the has only that have been quantum computing, has been the of for of the quantum technology but in the of quantum computing, it for a to the the patent has the in the of quantum computing in or that not are to result in distortions regarding the of patent for for patent law (eg, for quantum to be of the the patent for and quantum computing as well as the of their that and currently have the patent in quantum These with were in the of quantum computing and some of the with However, to they have their over the patent quantum and of that new can patent portfolio this is not only possible for such as which in and by based on the of but also for an a firm on quantum processors for quantum computing systems, the patent of technology such as and This is an IP is new to the to their to their innovations to For example, the to design and its This has in the of of the quantum a quantum on quantum processors for quantum computing and a for quantum in patent on quantum such as and can their quantum computing from their and but these new have to from based on the of their IP the of the and the of or a on a new on quantum computing, it the potential for technology and disruptive innovation from new on quantum of the patent less than in the classical computing and In to and and that and new are the For billion more quantum computing than market market or billion market In that patent protection will be more for the new and and on quantum (eg, than for the technology currently the classical computing and the of quantum that have and are in the of the patent applications have not been and are also part of the This is highly relevant from a policy to trade secrets, these patent to raise the of for patent they from these and it more to of protection for patent In this to their which in effective patent and for trade secrets to and and quantum computing the of quantum computing that the patent system is in a technical trade secrets be a IP to the of the (eg, the quantum can be and secured at the from the and even these can be access through the with the and the that and be in the In it is that the quantum computing that in this will be in the by the time the market a to the by technology market patent rights would incentivize to patent protection it requires in for in of trade secrets that can be as long as the secrets are secured and their of from their market and patent the have these of and are more to patent their in order to the exclusive property rights and venture in a are in the In this a for are also to their through the patent system as to as trade These be into when and and regulatory related to quantum has that it is for IP frameworks to disruptive technologies and their on the IP as it is to the of the IP system on the of such technologies. to encourage fair competition and market IP law to be and with regulatory law and antitrust as well as the by and These approaches in for such as the and the global competition in quantum technology that governments and will have to carefully such and the interplay between IPRs and related rights with quantum For quantum IPRs be as part of the new IP which regulatory such as the AI the the and to the This IP promises an intellectual property system to to technologies advances in and The to set global in The in the protection of the of IP by and the of and of IP a global to the pace of innovation in the Quantum was to IP protection for and and including the of the These could apply to and is when such Yet, the of exclusive with or to encourage and innovation the quantum In this a innovation that possible (eg, access and and (eg, and reward and that is to and decentralized innovation However, it is also evident that many will face and challenges, from potential of the in of the or that âTragedy of the to global competition and with to the protection and of quantum technology. This not that new approaches quantum technology not be might be if problems with the IP system are or Yet, patent on quantum computing the patent system is as to the system be based on and of to the IP system to promote the and the challenges posed by quantum computing must also be based on a of the IP how the forms of protection and to what a and of IP and can mitigate unwanted While for anticommons and the related of the patent to have in the technology patent for the quantum computing is not a and as actual or potential by patent protection or of the IP such as the of the IP system for unwanted overlapping can be from and of the patent can be with and the IP for the patent this would the and of the and of the on the as well as careful to the and into the patent at the patent It is clear that this would also patent the and in the the of the patent or of the to the of by of the are more or less and a more of each of the have a or more on the of protection of patents, the and of what as well as on the of protection for technologies or even IP For the future of quantum technologies and quantum computing, the question is to the and in order to the for the enhancement of innovation and the of upstream patent some the of an with to the in a of These âthe effects of factors, such as for scientific and the of innovation, and that might for technological could also be the framework for research and or possible that can be found the of patent In that some have a more and but of competition or antitrust Other and to such as and The in the of patent or These would the exclusive rights but the into While it how these are in technology these to or in the patent system and potential anticommons by it possible for patent to use forms of or to their rights into property rights not be to solve problems that they were to on the IP rights not be the only not the innovation and could apply innovation policy and IP such as antitrust law and and as well as and to and balance the effects of innovation the innovation and reward and industry and more between when regulatory IP rights might be less in a and and distribution become in the if a fair global distribution of quantum technologies is the it will be to on and technology to and on a This article qualitative on potential IP overprotection of quantum technologies to the IPRs could denote an inappropriate of global exclusive rights for first result in market and for quantum and to anticommons concerns including underuse by quantitative that IP overprotection requires a of existing IP for quantum technologies, to or IP and an unwanted of market power. In to to these the article on patent to quantum computers. found that to be so such patent overprotection problems in the quantum computing to the that their consequences would hinder innovation in this of quantum as more and more quantum patent the an quantum computing However, in by trade secrets or secrets, remain the of as these innovations is not by set and be or to potential innovation by IPRs and antitrust in the quantum computing must maintain a and with and In this quantum is the In law policy a regime that a between and overprotection of regime that for an innovation while and to first and their The that this is not a is by IP which a that between of and In have to regarding for open or closed innovation systems, into to access and In it is to these and and to take proactive it necessary based on the insights gained from research, and technological approaches take into and the for of IP protection and their interplay with antitrust in quantum computing, quantum and quantum the time is for research and the to new and intellectual property that encourage competition and incentivize sustainable These must the balance between rights technology national security policy and the of a global quantum while rights and and quantum and law further the of IP portfolio trade and secrets, patent and new of property industry and quantum and research These are for further scientific
It has been proposed in the literature that the volume of Einstein-Rosen bridge is equal to complexity of state preparation ("Complexity=Volume" conjecture). Taking this statement outside the horizon, one might be tempted to propose "Complexity=Time" correspondence. In this Essay we argue that in a blockchain protocol, which is the foundation of all modern cryptocurrencies, time is emergent and it is defined according to a version of "Complexity=Time".
Muhammad Asad Ullah, Jason William Setiawan, Junaid ur Rehman, Hyundong Shin
Blockchain has revolutionized many fields, such as distributed sensor networks, finance, and cryptocurrency. Consensus between distributed network nodes is at the core of such blockchain technologies. The three primary performance measures for any consensus algorithm are scalability, security, and decentralization. This paper evaluates the usefulness and practicality of quantum consensus algorithms for blockchain-enhanced sensor, and computing networks and evaluates them against the aforementioned performance measures. In particular, we investigate their noise robustness against quantum decoherence in quantum processors and over fiber-optic channels. We observe that the quantum noise generally increases the error rate in the list distribution. However, the effect is variable on different quantum consensus schemes. For example, the entanglement-free scheme is more affected than entanglement-based schemes for the local noise cases, while in the case of noisy optical fiber links, the effect is prominent on all quantum consensus schemes. We infer that the current quantum protocols with noisy intermediate-scale quantum devices and noisy quantum communication can only be employed for modular units in intraenterprise-level blockchain, such as Zilliqa, for sensor, and computing networks.
Blockchain systems based on the proof-of-work (PoW) consensus introduce entropy to the system in a natural way due to the randomness of mining. However, for non-PoW consensus (e.g., proof-of-stake and delegated proof-of-stake consensus) blockchain systems, a different approach to introducing entropy, such as the distributed random number generation (dRNG) algorithm, must be established. The dRNG algorithm is one of the key challenges in developing the consensus mechanism, as well as one of the relevant parameters for determining the merit of the consensus mechanism. In this paper, we first derive a publicly verifiable quantum random numbers generation protocol based on the certifiable randomness scheme from any untrusted quantum device, which offers features, such as fairness, no trusted third party, and publicly verifiable. Then, based on verifiable quantum random numbers, we propose a new consensus algorithm. The algorithm selects block proposer and block verification committees for each round using verifiable quantum random numbers, resulting in better randomness, fairness, and efficiency of the entire consensus process. In addition, the new consensus algorithm is not only resistant to adaptive adversary models as well as to collusion attacks, but also requires negligible computation for each user to avoid unnecessary consumption of power resources. Finally, we analyze the verifiable randomness, fairness, liveness, and communication complexity of the consensus algorithm.
Quantum entanglement has shown distinguished features beyond any classical state. Many methods have been presented to verify unknown entanglement with the complete information about the density matrices by quantum state tomography. In this work, we aim to identify unknown entanglement with only partial information of the state space. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear entanglement witness expressed by density matrix elements. First, we verify unknown bipartite entanglement and study the robustness of entanglement witnesses against the white noise. Second, we generalize such verification to partially unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type and W-type states. Third, we give a quantum-information application related to the quantum zero-knowledge proof. It further provides a useful method in blindly verifying universal quantum computation resources. These results may be interesting in entanglement theories, quantum communication, and quantum networks.
The methods of data verification are discussed, which are intended for the distant control of autonomous mobile robotic agents via networks, combining optical data links. The problem of trust servers is considered for position verification and position-based cryptography tasks. In order to obtain flexible quantum and classical verification procedures, one should use the collective interaction of agents and network nodes, including some elements of the blockchain. Multiple-valued logic functions defined within discrete k-valued AllenâGivone algebra are proposed for the logically linked list of entries and the distributed ledger, which can be used for distant data verification and breakdown restoration in mobile agents with the help of partner network nodes. A distributed ledger scheme involves the assigning by distant partners of random hash values, which further can be used as keys for access to a set of distributed data storages, containing verification and restoration data. Multiple-valued logic procedures are simple and clear enough for high-dimensional logic modelling and for the design of combined quantum and classical protocols.
We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the proof-of-stake protocol. The main idea, inspired by the Penrose square-root law and the more recent quadratic voting rule, is to differentiate a voterâs voting power and the voterâs share (fraction of the total in the system). We show that, whereas voter shares form a martingale process that converges to a Dirichlet distribution, their voting powers follow a supermartingale process that decays to zero over time. This prevents any voter from controlling the voting process and, thus, enhances security. For both limiting results, we also provide explicit rates of convergence. When the initial total volume of votes (or stakes) is large, we show a phase transition in share stability (or the lack thereof), corresponding to the voterâs initial share relative to the total. We also study the scenario in which trading (of votes/stakes) among the voters is allowed and quantify the level of risk sensitivity (or risk aversion) in three categories, corresponding to the voterâs utility being a supermartingale, a submartingale, and a martingale. For each category, we identify the voterâs best strategy in terms of participation and trading. Funding: W. Tang gratefully acknowledges financial support through the National Science Foundation [Grants DMS-2113779 and DMS-2206038] and through a start-up grant at Columbia University. D. D. Yaoâs work is part of a ColumbiaâCity University/Hong Kong collaborative project that is supported by InnoHK Initiative, the Government of Hong Kong Special Administrative Region, and the Laboratory for AI-Powered Financial Technologies.
Arman Rasoodl Faridi, Faraz Masood, Ali Haider Shamsan, Mohammad Luqman · 5 authors
Blockchain is one of the most discussed and highly accepted technologies, primarily due to its application in almost every field where third parties are needed for trust. Blockchain technology relies on distributed consensus for trust, which is accomplished using hash functions and public-key cryptography. Most of the cryptographic algorithms in use today are vulnerable to quantum attacks. In this work, a systematic literature review is done so that it can be repeated, starting with identifying the research questions. Focusing on these research questions, literature is analysed to find the answers to these questions. The survey is completed by answering the research questions and identification of the research gaps. It is found in the literature that 30% of the research solutions are applicable for the data layer, 24% for the application and presentation layer, 23% for the network layer, 16% for the consensus layer and only 1% for hardware and infrastructure layer. We also found that 6% of the solutions are not blockchain-based but present different distributed ledger technology.
Quantum entangled states have shown distinguished features beyond any classical state. Many methods like quantum state tomography have been presented to verify entanglement. In this work, we aim to identify unknown entanglements with partial information of the state space by developing a nonlinear entanglement witness. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear inequality expressed by density matrix elements. First, we verify unknown bipartite entanglements and study the robustness of entanglement witnesses against the white noise. Second, we generalize such a verification to unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type states and the cluster states under local channel operations. Third, we give a quantum-information application related to the quantum zero-knowledge proof. Our results provide a useful method in verifying universal quantum computation resources with robustness against white noises. Our work is applicable to detect unknown entanglement without the state tomography.
The advancement of quantum computers undermines the security of classical blockchain, necessitating either a post-quantum upgrade of the existing architecture or creation of an inherently quantum blockchain. Here we propose a practically realizable model of a fully quantum blockchain based on a generalized Gram-Schmidt procedure utilizing dimensional lifting. In this model, information of transactions stored in a multi-qubit state are subsequently encoded using the generalized Gram-Schmidt process. The chain is generated as a result of the reliance of orthogonalized state on the sequence of states preceding it. Various forking scenarios and their countermeasures are considered for the proposed model. It is shown to be secure even against quantum computing attacks using the no-cloning theorem and non-democratic nature of Generalized Gram-Schmidt orthogonalization. Finally, we outline a framework for a quantum token built on the same architecture as our blockchain.
Quantum computing is no longer a thing of the future. Shorâs algorithm proved that a quantum computer couldtraverse key of factoring problems in polynomial time. Because the time-complexity of the exhaustive keysearch for quantum computing has not reliably exceeded the reasonable expiry of crypto key validity, it is believedthat current cryptography systems built on top of computational security are not quantum-safe. Quantumkey distribution fundamentally solves the problem of eavesdropping; nevertheless, it requires quantumpreparatory work and quantum-network infrastructure, and these remain unrealistic with classical computers.In transitioning to a mature quantum world, developing a quantum-resistant mechanism becomes a stringentproblem. In this research, we innovatively tackled this challenge using a non-computational difficulty schemewith zero-knowledge proof in order to achieve repellency against quantum computing cryptanalysis attacks foruniversal classical clients.
The advent of quantum computing threatens blockchain protocols and networks because they utilize non-quantum resistant cryptographic algorithms. When quantum computers become robust enough to run Shor's algorithm on a large scale, the most used asymmetric algorithms, utilized for digital signatures and message encryption, such as RSA, (EC)DSA, and (EC)DH, will be no longer secure. Quantum computers will be able to break them within a short period of time. Similarly, Grover's algorithm concedes a quadratic advantage for mining blocks in certain consensus protocols such as proof of work. Today, there are hundreds of billions of dollars denominated in cryptocurrencies and other digital assets that rely on blockchain ledgers as well as thousands of blockchain-based applications storing value in blockchain networks. Cryptocurrencies and blockchain-based applications require solutions that guarantee quantum resistance in order to preserve the integrity of data and assets in these public and immutable ledgers. The quantum threat and some potential solutions are well understood and presented in the literature. However, most proposals are theoretical, require large QKD networks, or propose new quantum-resistant blockchain networks to be built from scratch. Our work, which is presented in this paper, is pioneer in proposing an end-to-end framework for post-quantum blockchain networks that can be applied to existing blockchain to achieve quantum-resistance. We have developed an open-source implementation in an Ethereum-based (i.e., EVM compatible) network that can be extended to other existing blockchains. For the implementation we have (i) used quantum entropy to generate post-quantum key pairs, (ii) established post-quantum TLS connections and X.509 certificates to secure the exchange of information between blockchain nodes over the internet without needing a large QKD network, (iii) introduced a post-quantum second signature in transactions using Falcon-512 post-quantum keys, and (iv) developed the first on-chain verification of post-quantum signatures using three different mechanisms that are compared and analyzed: Solidity smart-contracts run by the validators for each transaction, modified EVM Opcode, and precompiled smart contracts.
Blockchain technology represented by Bitcoin and Ethereum has been deeply developed and widely used due to its broad application prospects such as digital currency and IoT. However, the security of the existing blockchain technologies built on the classical cryptography depends on the computational complexity problem. With the enhancement of the attackersâ computing power, especially the upcoming quantum computers, this kind of security is seriously threatened. Based on quantum hash, quantum SWAP test and quantum teleportation, a quantum blockchain system is proposed with quantum secure communication. In classical cryptographic theory sense, the security of this system is unconditional since it has nothing to do with the attackersâ computing power and computing resources.
We propose the first generalization of the famous Non-Interactive\nZero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a\nprotocol to prove advanced properties on a received quantum state\nnon-destructively and non-interactively (a single message being sent from the\nprover to the verifier).\n In our second orthogonal contribution, we improve the costly Remote State\nPreparation protocols [CCKW18,CCKW19,GV19] that can classically fake a quantum\nchannel (this is at the heart of our NIZKoQS protocol) by showing how to create\na multi-qubits state from a single superposition.\n Finally, we generalize these results to a multi-party setting and prove that\nmultiple parties can anonymously distribute a GHZ state in such a way that only\nparticipants knowing a secret credential can share this state, which could have\napplications to quantum anonymous transmission, quantum secret sharing, quantum\nonion routing and more.\n
Distributed ledger technology, and specifically blockchain protocols, have been leveraged to define decentralized lotteries to circumvent challenges in traditional lottery systems. Unfortunately, lottery consensus in proof-of-resource (such as proof-of-work, proof-of-stake) blockchains is provably biased towards lottery users that command a majority of the resource determining consensus in their respective cryptocurrency networks, resulting in partial-decentralization. Further, classical consensus protocols are inherently slow in achieving consensus, and thus cannot be considered for designing fast decentralized lotteries.We present a fast, fully-decentralized computational lottery TensorFlip, where the betting users and the lottery house are peers in the same cryptocurrency network, and the bet and winning per player is a consensus based on a rudimentary quantum and classical distributed computation. We employ a two-party verifiable random function construction for computing the lottery winnings. Our lottery operates in the presence of both fail-stop and Byzantine adversaries, under the synchronous network model. Although slower classical consensus based and partially-decentralized blockchain consensus based lotteries may exist, we believe we are the first to propose a quantum and classical computation based deterministic fully-decentralized lottery, with an expected constant round complexity protocol.