The development of quantum information platforms such as quantum computers and quantum simulators that will rival classical Turing computations are typically viewed as a threat to secure data transmissions and therefore to crypto-systems and financial markets in general. We propose to use such platforms as a proof-of-work protocol for blockchain technology, which underlies cryptocurrencies providing a way to document the transactions in a permanent decentralised public record and to be further securely and transparently monitored. We reconsider the basis of blockchain encryption and suggest to move from currently used proof-of-work schemes to the proof-of-work performed by analog Hamiltonian optimisers. This approach has a potential to significantly increase decentralisation of the existing blockchains and to help achieve faster transaction times, therefore, removing the main obstacles for blockchain implementation. We discuss the proof-of-work protocols for a few most promising optimiser platforms: quantum annealing hardware based on D-wave simulators and a new class of gain-dissipative simulators.
Farid Ablayev, D. A. Bulychkov, D. A. Sapaev, Alexander Vasiliev · 5 authors
Bitcoin and blockchain in general is a hot topic nowadays. In the paper we propose a quantum empowering of this technology and show how to speed-up the mining procedure using the modified Grover's algorithm.
This paper investigates the power of quantum statistical zero knowledge interactive proof systems in the relativized setting. We prove the existence of an oracle relative to which quantum statistical zero-knowledge does not contain UP intersect coUP, and we prove that quantum statistical zero knowledge does not contain UP relative to a random oracle with probability 1. Our proofs of these statements rely on a bound on output state discrimination for relativized quantum circuits based on the quantum adversary method of Ambainis, following a technique similar to one used by Ben-David and Kothari to prove limitations on a query complexity variant of quantum statistical zero-knowledge.
In the past year cryptocurrencies have gained a lot of attention because of the increase in price. This attention has increased the number of people trading and investing in different cryptocurrencies which has lead to an increased number of transactions flowing through the different networks. This has revealed scalability issues in some of them, especially in the most popular cryptocurrency, Bitcoin. Many people are working on solutions to this problem. One proposed solution replaces the blockchain with a DAG structure. In this report the scalability of Bitcoin’s protocol will be compared to the scalability of the protocol used in the newer cryptocurrency, Nano. The comparison is conducted in terms of throughput and latency. To perform this comparison, an experiment was conducted where tests were run with an increasing number of nodes and each test sent different number of transactions per second from every node. Our results show that Nano’s protocol scales better regarding both throughput and latency, and we argue that the reason for this is that the Bitcoin protocol uses a blockchain as a global data-structure unlike Nano that uses a block-lattice structure where each node has their own local blockchain.
Abstract We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> </mml:math> XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in Elgart et al (2018 J. Funct. Anal . (in press)). This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb–Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.
Divesh Aggarwal, Gavin K. Brennen, Troy Lee, Miklós Sántha · 5 authors
The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.
We consider a problem we call StateIsomorphism: given two quantum states of n qubits, can one be obtained from the other by rearranging the qubit subsystems? Our main goal is to study the complexity of this problem, which is a natural quantum generalisation of the problem StringIsomorphism. We show that StateIsomorphism is at least as hard as GraphIsomorphism, and show that these problems have a similar structure by presenting evidence to suggest that StateIsomorphism is an intermediate problem for QCMA. In particular, we show that the complement of the problem, StateNonIsomorphism, has a two message quantum interactive proof system, and that this proof system can be made statistical zero-knowledge. We consider also StabilizerStateIsomorphism (SSI) and MixedStateIsomorphism (MSI), showing that the complement of SSI has a quantum interactive proof system that uses classical communication only, and that MSI is QSZK-hard.
A decentralized online quantum cash system, called qBitcoin, is given. We design the system which has great benefits of quantization in the following sense. Firstly, quantum teleportation technology is used for coin transaction, which prevents from the owner of the coin keeping the original coin data even after sending the coin to another. This was a main problem in a classical circuit and a blockchain was introduced to solve this issue. In qBitcoin, the double-spending problem never happens and its security is guaranteed theoretically by virtue of quantum information theory. Making a block is time consuming and the system of qBitcoin is based on a quantum chain, instead of blocks. Therefore a payment can be completed much faster than Bitcoin. Moreover we employ quantum digital signature so that it naturally inherits properties of peer-to-peer (P2P) cash system as originally proposed in Bitcoin.
E O Kiktenko, N O Pozhar, M N Anufriev, A S Trushechkin · 8 authors
Abstract Blockchain is a distributed database which is cryptographically protected against malicious modifications. While promising for a wide range of applications, current blockchain platforms rely on digital signatures, which are vulnerable to attacks by means of quantum computers. The same, albeit to a lesser extent, applies to cryptographic hash functions that are used in preparing new blocks, so parties with access to quantum computation would have unfair advantage in procuring mining rewards. Here we propose a possible solution to the quantum era blockchain challenge and report an experimental realization of a quantum-safe blockchain platform that utilizes quantum key distribution across an urban fiber network for information-theoretically secure authentication. These results address important questions about realizability and scalability of quantum-safe blockchains for commercial and governmental applications.
Gorjan Alagic, Yfke Dulek, Christian Schaffner, Florian Speelman
Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.
The concept of a Turing machine has been well defined. It would be sufficient to show that Bitcoin uses a dual stack architecture that acts as a dual counter machine. Such systems have already been demonstrated as being Turing complete. We demonstrate that Bitcoin script is a minimal family of which λ and R are members. Further using the compositional product rule and the iteration rule we demonstrate that Bitcoin scripting is Turing complete with the limitations imposed on any realworld computer. This limitation is that there cannot be an infinite tape. Iterations can be simulated using an “unrolled” loop function with allocation to the “Alt” stack. As the product rule states that if A, B are machines, then A.B is also a machine. The iteration rule shows that if A is a machine then (A) is also a machine. Further the minimum power of A under which the observed square of the final configuration is blank. The consequence of these rules is that for every partial recursive function of in variables we can show that it can be evaluated by machine of the proposed family.
Bitcoin is a digital currency and payment system based on classical cryptographic technologies which works without a central administrator such as in traditional currencies. It has long been questioned what the impact of quantum computing would be on Bitcoin, and cryptocurrencies in general. Here, we analyse three primary directions that quantum computers might have an impact in: mining, security, and forks. We find that in the near-term the impact of quantum computers appear to be rather small for all three directions. The impact of quantum computers would require considerably larger number of qubits and breakthroughs in quantum algorithms to reverse existing hash functions.
The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008. Its distributed nature allows currency transactions without a central authority by using cryptographic methods and a data structure called the blockchain. In this paper we use the no-cloning theorem of quantum mechanics to introduce Quantum Bitcoin, a Bitcoin-like currency that runs on a quantum computer. We show that our construction of quantum shards and two blockchains allows untrusted peers to mint quantum money without risking the integrity of the currency. The Quantum Bitcoin protocol has several advantages over classical Bitcoin, including immediate local verification of transactions. This is a major improvement since we no longer need the computationally intensive and time-consuming method Bitcoin uses to record all transactions in the blockchain. Instead, Quantum Bitcoin only records newly minted currency which drastically reduces the footprint and increases efficiency. We present formal security proofs for counterfeiting resistance and show that a quantum bitcoin can be re-used a large number of times before wearing out - just like ordinary coins and banknotes. Quantum Bitcoin is the first distributed quantum money system and we show that the lack of a paper trail implies full anonymity for the users. In addition, there are no transaction fees and the system can scale to any transaction volume.
Broadbent Anne, Zhengfeng Ji, Song Fang, Watrous John
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every problem in the complexity class QMA has a quantum zero-knowledge proof system. More specifically, assuming the existence of an unconditionally binding and quantum computationally concealing commitment scheme, we prove that every problem in the complexity class QMA has a quantum interactive proof system that is zero-knowledge with respect to efficient quantum computations. Our QMA proof system is sound against arbitrary quantum provers, but only requires an honest prover to perform polynomial-time quantum computations, provided that it holds a quantum witness for a given instance of the QMA problem under consideration. The proof system relies on a new variant of the QMA-complete local Hamiltonian problem in which the local terms are described by Clifford operations and standard basis measurements. We believe that the QMA-completeness of this problem may have other uses in quantum complexity.
Kriptovalute su digitalni novac utemeljen na kriptografiji i decentraliziranom sustavu. Postoje samo u elektroničkom obliku kao jedinstveni digitalni novčići ("tokeni"). Iza njih ne stoji autoritet države niti ih je moguće svojevoljno proizvesti. Rad se fokusira na značajkama, postavkama, razvoju i svim međuodnosima važnih ekonomskih faktora koji utječu na kriptovalute. U prvom poglavlju navedena su obilježja kriptovaluta. Drugo poglavlje daje primjere i govori o primjeni kriptovaluta u svakodnevnom životu. U trećem poglavlju je raspravljano o trenutnim i budućim regulacijama najmoćnijih zemalja svijeta (G20) , kao i njihovoj zajedničkoj suradnji u želji za jedinstvenim i standardiziranim pravilima, a sve u svrhu što kvalitetnijeg nadzora nad kriptovalutama kako bi se spriječile malverzacije i zaštitili potrošači. Četvrto poglavlje govori o inicijalnoj ponudi kovanica, a peto poglavlje je namijenjeno sigurnosti kriptovaluta. Cilj istraživanja je utvrditi koliko je studentska populacija upoznata i usmjerena prema novim oblicima digitalnog novca, koje značajke kriptovaluta smatraju pozitivnima, a koje negativnima i u kojoj su mjeri investirali ili su spremni investirati dio svojih ulaganja u kriptovalute i sl. Metode istraživanja korištene u radu su kompilacija na temelju proučavanja postojeće literature o temi rada, prikupljanje i analiza podataka vezanih uz kriptovalute, ponajprije podataka vezanih uz cijene i tržišnu kapitalizaciju, anketiranje studenata Ekonomskog fakulteta u Rijeci i metoda dedukcije putem koje su pokazane sve važne karakteristike i obilježja kriptovaluta. Na temelju provedene ankete u kojoj je sudjelovalo 90 studenata Ekonomskog fakulteta u Rijeci zaključak toga dijela istraživanja je da je mlada populacija dobro upoznata s kriptovalutama i njenim glavnim značajkama, ali i određenim nedostatkom informiranosti o tehnologiji (trećina studenata nije čula za pojam "blockchain") i nedovoljnoj odlučnosti oko investiranja i trgovanja u kriptovalute. Povrh toga, dokazan je i negativan utjecaj hakerskih napada i određenih kriminalnih radnji, kao i nestabilnost tržišne cijene na povjerenje studenata, ali i ukupne populacije vezane uz globalni financijski sustav u kriptovalute. Ishod istraživanja omogućio je da zaključimo kako su kriptovalute trenutno u ranoj fazi razvoja i nisu se dovoljno implementirale za široku primjenu u trgovini roba i usluga ili općenito kao sredstvo razmjene. Faktor koji je uključen u istraživanje kako bi opisao veličinu, odnosno obujam neke kriptovalute je tržišna kapitalizacija u dolarima. Temeljna ideja ovog rada je informirati čitatelja o pozitivnim i negativnim značajkama koje se se vežu uz kriptovalute. Na taj način čitatelji će biti bolje informirani i educirani o potencijalnom riziku ulaganja u kriptovalute, kao i većoj razini zaštite prilikom posjedovanja neke digitalne valute.
Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009) and Unruh (Eurocrypt 2012), yet in general the problem remains elusive. We show that this is not only due to a lack of proof techniques: relative to an oracle, we show that classically secure proofs and proofs of knowledge are insecure in the quantum setting. More specifically, sigma-protocols, the Fiat-Shamir construction, and Fischlin's proof system are quantum insecure under assumptions that are sufficient for classical security. Additionally, we show that for similar reasons, computationally binding commitments provide almost no security guarantees in a quantum setting. To show these results, we develop the "pick-one trick", a general technique that allows an adversary to find one value satisfying a given predicate, but not two.
In the paper, we present a kind of quantum voting protocol, which is based on controlled quantum teleportation of local unitary operations in non-symmetric quantum channel. In this protocol, the umpire CA with zero knowledge proof quantum identity authentication ensures voter’s anonymous identity authentication. The counting institution Bob generates a high-dimensional Greenberger-Horne-Zeilinger entangled state to establish a high-dimensional quantum communication channel. Performing the local unitary operation on their low-dimensional quantum ballot, voter’s quantum vote is teleportated by asymmetric matrix measurement and scrutineer Charlie auxiliary measuring. With the scrutineer Charlie’s help, Bob achieves the voting result by the output of unitary operation. Compared with other general quantum operation teleportation quantum voting protocol, the protocol utilizes the quantum information and transmission of quantum channel, which have different dimensions, so single particle information cannot be stolen, and can prevent forgery. The electoral process is fair and undeniable, owing to Charlie’s supervision. Since the success probability of quantum teleportation of local unitary operations is 1, the quantum voting is reliable.
Xiao Qiang Guo, Li Hong Li, Cui Ling Luo, Yi Shuo Shi
The Bit Commitment (BC) is an important basic agreement in cryptography . The concept was first proposed by the winner of the Turing Award in 1995 ManuelBlum. Bit commitment scheme can be used to build up zero knowledge proof, verified secret sharing, throwing coins etc agreement.Simultaneously and Oblivious Transfer together constitute the basis of secure multi-party computations. Both of them are hotspots in the field of information security. We investigated unconditional secure Quantum Bit Commitment (QBC) existence. And we constructed a new bit commitment model – double prover bit commitment. The Quantum Bit Commitment Protocol can be resistant to errors caused by noise.
We propose a coin-flip protocol which yields a string of strong, random coins and is fully simulatable against poly-sized quantum adversaries on both sides. It can be implemented with quantum-computational security without any set-up assumptions, since our construction only assumes mixed commitment schemes which we show how to construct in the given setting. We then show that the interactive generation of random coins at the beginning or during outer protocols allows for quantum-secure realizations of classical schemes, again without any set-up assumptions. As example applications we discuss quantum zero-knowledge proofs of knowledge and quantum-secure two-party function evaluation. Both applications assume only fully simulatable coin-flipping and mixed commitments. Since our framework allows to construct fully simulatable coin-flipping from mixed commitments, this in particular shows that mixed commitments are complete for quantum-secure two-party function evaluation. This seems to be the first completeness result for quantum-secure two-party function evaluation from a generic assumption.
Ivan Damgård, Jakob Funder, Jesper Buus Nielsen, Louis Salvail
Attacks on classical cryptographic protocols are usually modeled by allowing an adversary to ask queries from an oracle. Security is then defined by requiring that as long as the queries satisfy some constraint, there is some problem the adversary cannot solve, such as compute a certain piece of information. In this paper, we introduce a fundamentally new model of quantum attacks on classical cryptographic protocols, where the adversary is allowed to ask several classical queries in quantum superposition. This is a strictly stronger attack than the standard one, and we consider the security of several primitives in this model. We show that a secret-sharing scheme that is secure with threshold $t$ in the standard model is secure against superposition attacks if and only if the threshold is lowered to $t/2$. We use this result to give zero-knowledge proofs for all of NP in the common reference string model. While our protocol is classical, it is sound against a cheating unbounded quantum prover and computational zero-knowledge even if the verifier is allowed a superposition attack. Finally, we consider multiparty computation and show that for the most general type of attack, simulation based security is not possible. However, putting a natural constraint on the adversary, we show a non-trivial example of a protocol that can indeed be simulated.
In this paper, we prove classical coin-flipping secure in the presence of quantum adversaries. The proof uses a recent result of Watrous [Wat09] that allows quantum rewinding for protocols of a certain form. We then discuss two applications. First, the combination of coin-flipping with any non-interactive zero-knowledge protocol leads to an easy transformation from non-interactive zero-knowledge to interactive quantum zero-knowledge. Second, we discuss how our protocol can be applied to a recently proposed method for improving the security of quantum protocols [DFL+09], resulting in an implementation without set-up assumptions. Finally, we sketch how to achieve efficient simulation for an extended construction in the common-reference-string model.
In this paper, we prove classical coin-flipping secure in the presence of quantum adversaries. The proof uses a recent result of Watrous [Wat09] that allows quantum rewinding for protocols of a certain form. We then discuss two applications. First, the combination of coin-flipping with any non-interactive zero-knowledge protocol leads to an easy transformation from non-interactive zero-knowledge to interactive quantum zero-knowledge. Second, we discuss how our protocol can be applied to a recently proposed method for improving the security of quantum protocols [DFL+09], resulting in an implementation without set-up assumptions. Finally, we sketch how to achieve efficient simulation for an extended construction in the common-reference-string model.
Wang Yu-wu, You-Bang Zhan, (1)淮阴师范学院计算机科学系,淮安 223300; (2)淮阴师范学院物理系,淮安 223300
A theoretical scheme for zero-knowledge proof quantum identity authentication is proposed by the absolutely impartial third party CA， which has been realized based on remote state preparation and assisted cloning controlled means. In the process of identification， only CA knows the information of quantum identity card and the first party Alice and the second party Bob can accomplish the quantum identity authentication without knowing it. We discuss the probability of accomplishing this job. The security of this scheme is unconditional and it is guaranteed by quantum mechanism.