Jelle Don, Serge Fehr, Christian Majenz, Christian Schaffner
Commit-and-open Sigma-protocols are a popular class of protocols for constructing non-interactive zero-knowledge arguments and digital-signature schemes via the Fiat-Shamir transformation. Instantiated with hash-based commitments, the resulting non-interactive schemes enjoy tight online-extractability in the random oracle model. Online extractability improves the tightness of security proofs for the resulting digital-signature schemes by avoiding lossy rewinding or forking-lemma based extraction. In this work, we prove tight online extractability in the quantum random oracle model (QROM), showing that the construction supports post-quantum security. First, we consider the default case where committing is done by element-wise hashing. In a second part, we extend our result to Merkle-tree based commitments. Our results yield a significant improvement of the provable post-quantum security of the digital-signature scheme Picnic. Our analysis makes use of a recent framework by Chung et al. [arXiv:2010.11658] for analysing quantum algorithms in the QROM using purely classical reasoning. Therefore, our results can to a large extent be understood and verified without prior knowledge of quantum information science.
Zebo Yang, Tara Salman, Raj Jain, Roberto Di Pietro
Blockchain technology has been prominent recently due to its applications in cryptocurrency. Numerous decentralized blockchain applications have been possible due to blockchains' nature of distributed, secured, and peer-to-peer storage. One of its technical pillars is using public-key cryptography and hash functions, which promise a secure, pseudo-anonymous, distributed storage with non-repudiation. This security is believed to be difficult to break with classical computational powers. However, recent advances in quantum computing have raised the possibility of breaking these algorithms with quantum computers, thus, threatening the blockchains' security. Quantum-resistant blockchains are being proposed as alternatives to resolve this issue. Some propose to replace traditional cryptography with post-quantum cryptography—others base their approaches on quantum computer networks or quantum internets. Nonetheless, a new security infrastructure (e.g., access control/authentication) must be established before any of these could happen. This article provides a theoretical analysis of the quantum blockchain technologies that could be used for decentralized identity authentication. We put together a conceptual design for a quantum blockchain identity framework (QBIF) and give a review of the technical evidence. We investigate its essential components and feasibility, effectiveness, and limitations. Even though it currently has various limitations and challenges, we believe a decentralized perspective of quantum applications is noteworthy and likely.
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.
Zhengying Cai, Shi Liu, Zhangyi Han, Rui Wang · 5 authors
Traditional anti-quantum methods and multi-signature technologies to secure the blockchain against quantum attacks will quickly reduce the efficiency and scalability of the industrial blockchain, where the computational resources will experience a polynomial rise with the increasing number of traders. Here, a quantum blind multi-signature method is proposed for the multi-party transaction to provide anti-quantum security. First, the proposed multi-party transaction frame and quantum key distribution in the industrial blockchain are introduced. It integrates a novel quantum blind multi-signature algorithm that is based on the quantum entanglement mechanism, and it is absolutely secure in theory. Second, the anti-quantum multi-signature algorithm is illustrated, where there are four phases, i.e., initialization, signing, verification, and implementation. Third, the security and complexity of the proposed framework are analyzed and compared with related methods in references, and our proposed method is verified to be able to offer good computational performance and blockchain scalability for multi-party transaction. Last, the paper is summarized and future research directions are proposed.
As a result of the limited resources available in IoT local devices, the large scale cloud consumer's data that are produced by IoT related machines are contracted out to the cloud. Cloud computing is unreliable, using it can compromise user privacy, and data may be leaked. Because cloud-data and grid infrastructure are both growing exponentially, there is an urgent need to explore computational sources and cloud large-data protection. Numerous cloud service categories are assimilated into numerous fields, such as defense systems and pharmaceutical databases, to compute information space and allocation of resources. Attribute Based Encryption (ABE) is a sophisticated approach which can permit employees to specify a higher level of security for data stored in cloud storage facilities. Numerous obsolete ABE techniques are practical when applied to small data sets to generate cryptograms with restricted computational properties; their properties are used to generate the key, encrypt it, and decrypt it. To address the current concerns, a dynamic non-linear polynomial chaotic quantum hash technique on top of secure block chain model can be used for enhancing cloud data security while maintaining user privacy. In the proposed method, customer attributes are guaranteed by using a dynamic non- polynomial chaotic map function for the key initialization, encryption, and decryption. In the proposed model, both organized and unorganized massive clinical data are considered to be inputs for reliable corroboration and encoding. Compared to existing models, the real-time simulation results demonstrate that the stated standard is more precise than 90% in terms of bit change and more precise than 95% in terms of dynamic key generation, encipherment, and decipherment time.
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.
Our aim is to determine conditions for quantum computing technology to give rise to security risks associated with quantum Bitcoin mining. Specifically, we determine the speed and energy efficiency a quantum computer needs to offer an advantage over classical mining. We analyze the setting in which the Bitcoin network is entirely classical except for a single quantum miner who has small hash rate compared to that of the network. We develop a closed-form approximation for the probability that the quantum miner successfully mines a block, with this probability dependent on the number of Grover iterations the quantum miner applies before making a measurement. Next, we show that, for a quantum miner that is "peaceful", this success probability is maximized if the quantum miner applies Grover iterations for 16 minutes before measuring, which is surprising as the network mines blocks every 10 minutes on average. Using this optimal mining procedure, we show that the quantum miner outperforms a classical computer in efficiency (cost per block) if the condition $Q < Crb$ is satisfied, where $Q$ is the cost of a Grover iteration, $C$ is the cost of a classical hash, $r$ is the quantum miner's speed in Grover iterations per second, and $b$ is a factor that attains its maximum if the quantum miner uses our optimal mining procedure. This condition lays the foundation for determining when quantum mining, and the known security risks associated with it, will arise.
Quantum computing is no longer a thing of the future. Shor’s 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.
Deployment of optical network infrastructure and network services is growing exponentially for beyond 5G networks. Since the uptake of e-commerce and e-services has seen unprecedented serge in recent months due to the global COVID-19 pandemic era, the security of such transactions in optical communication has gained much importance. Optical fiber communication networks are vulnerable to several types of security threats, such as single point failure, wormhole attacks, and sybil attacks. Therefore, blockchain is a promising solution to protect confidential information against attacks and helps in achieving trusted network architecture by creating a distributed ledger platform. Recently, blockchain has received much attention because of its decentralized and distributed ledger technology. Hence, blockchain has also been employed to protect network against such attacks. However, blockchain technology's security relies on the platform of computational complexity, and because of the evolution of quantum computers, it will become insecure in the near future. Therefore, for enhancing blockchain security, research focus on combining quantum key distribution (QKD) with blockchain. This new technology is known as quantum-secured blockchain. The article describes the attacks in optical networks and provides a solution to protect network against security attacks by employing quantum-secured blockchain in optical networks. It provides a brief overview of blockchain technology with its security loopholes and focuses on QKD, which makes blockchain technology more robust against quantum-attacks. Next, the article provides a broad view of quantum-secured blockchain and presents the network architecture for future research and development of secure and trusted optical communication networks using quantum-secured blockchain.
Dan A. Bard, Joseph J. Kearney, Carlos A. Pérez-Delgado
Proof-of-Work (PoW) is a fundamental underlying technology behind most major blockchain cryptocurrencies. It has been previously pointed out that quantum devices provide a computational advantage in performing PoW in the context of Bitcoin. Here we make the case that this quantum advantage extends not only to all existing PoW mechanisms, but to any possible PoW as well. This has strong consequences regarding both quantum-based attacks on the integrity of the entirety of the blockchain, as well as more legitimate uses of quantum computation for the purpose of mining Bitcoin and other cryptocurrencies. For the first case, we estimate when these quantum attacks will become feasible, for various cryptocurrencies, and discuss the impact of such attacks. For the latter, we derive a precise formula to calculate the economic incentive for switching to quantum-based cryptocurrency miners. Using this formula, we analyze several test scenarios, and conclude that investing in quantum hardware for cryptocurrency mining has the potential to pay off immensely.
V Vignesh, S. Harihara Gopalan, M.S. Kiran Mohan, R S Ramya · 5 authors
Abstract Protection measures are essential to present day blockchain innovation ever, since they can exist short of empowered outsider, which implies that there may not be a disclosed trustworthy individual or group responsible for frameworks. Security of the present frameworks depends on estimating the firmness assumptions and large numbers of the benchmark cryptographic functions proven to be powerless for crucial monetary and a variety of applications against the approach of undeniable quantum machines. Upgrading blockchain innovation with the future of quantum states in a shared manner will enhance the degree of protection and security by-laws of physical science, which is never feasible from non-quantum data hypothetical perspectives. In this article, we propose a quantum-built way to deal with harness of security for a democratic application with the execution, utilizing Hyperledger Sawtooth.
We propose the first generalization of the famous Non-Interactive Zero-Knowledge (NIZK) proofs to quantum languages (NIZKoQS) and we provide a protocol to prove advanced properties on a received quantum state non-destructively and non-interactively (a single message being sent from the prover to the verifier). In our second orthogonal contribution, we improve the costly Remote State Preparation protocols [Cojocaru et al. 2019 ; Gheorghiu and Vidick 2019 ] that can classically fake a quantum channel (this is at the heart of our NIZKoQS protocol) by showing how to create a multi-qubit state from a single superposition. Finally, we generalize these results to a multi-party setting and prove that multiple parties can anonymously distribute a GHZ state in such a way that only participants knowing a secret credential can share this state, which could have applications to quantum anonymous transmission, quantum secret sharing, quantum onion routing and more.
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
Michele Ciampi, Alexandru Cojocaru, Elham Kashefi, Atul Mantri
Secure two-party computation considers the problem of two parties computing a\njoint function of their private inputs without revealing anything beyond the\noutput. In this work, we consider the setting where the two parties (a\nclassical Alice and a quantum Bob) can communicate only via a classical\nchannel. Our first result shows that it is in general impossible to realize a\ntwo-party quantum functionality with black-box simulation in the case of\nmalicious quantum adversaries. In particular, we show that the existence of a\nsecure quantum computing protocol that relies only on classical channels would\ncontradict the quantum no-cloning argument.\n We circumvent this impossibility following three different approaches. The\nfirst is by considering a weaker security notion called one-sided simulation\nsecurity. This notion protects the input of one party (the quantum Bob) in the\nstandard simulation-based sense and protects the privacy of the other party's\ninput (the classical Alice). We show how to realize a protocol that satisfies\nthis notion relying on the learning with errors assumption. The second way to\ncircumvent the impossibility result, while at the same time providing standard\nsimulation-based security also against a malicious Bob, is by assuming that the\nquantum input has an efficient classical representation.\n Finally, we focus our attention on the class of zero-knowledge\nfunctionalities and provide a compiler that takes as input a classical proof of\nquantum knowledge (PoQK) protocol for a QMA relation R and outputs a\nzero-knowledge PoQK for R that can be verified by classical parties. The direct\nimplication of our result is that Mahadev's protocol for classical verification\nof quantum computations (FOCS'18) can be turned into a zero-knowledge proof of\nquantum knowledge with classical verifiers. To the best of our knowledge, we\nare the first to instantiate such a primitive.\n
This article considered deficiencies of the flourishing blockchain technology manifested by the development of quantum computation. We show that the future blockchain technology would under constant threats from the following aspects: 1) Speed up the generation of nonces; 2) Faster searching for hash collisions; 3) Break the security of the classical encryption. We also demonstrate that incorporating some quantum properties into blockchain makes it more robust and more efficient. For example people can establish a quantum-security blockchain system that utilizes quantum key distribution (QKD), and quantum synchronization and detectable Byzantine agreement (DBA) can help the blockchain systems achieve faster consensus even if there exist a number of malicious nodes.
The posthoc verification protocol [J. F. Fitzsimons, M. Hajdu{\v s}ek, and T. Morimae, Physical Review Letters {\bf120}, 040501 (2018)] enables an information-theoretically-sound non-interactive verification of quantum computing, but the message from the prover to the verifier is quantum and the verifier has to do single-qubit measurements. The Mahadev protocol removes these quantum parts, but the soundness becomes the computational one. In this paper, we construct an information-theoretically-sound non-interactive classical verification protocol for quantum computing with a trusted center. The trusted center sends random BB84 states to the prover, and the classical descriptions of these BB84 states to the verifier. The messages from the center to the prover and the verifier are independent of the instance. By slightly modifying our protocol, we also construct a non-interactive statistical zero-knowledge proof system for QMA with the trusted center.
Shreya Banerjee, Arghya Mukherjee, Prasanta K. Panigrahi
This paper proposes a protocol to prepare a blockchain using quantum tools which maintains the distributive nature of the blockchain and provides security against a quantum attacker. The authors provide an example of a two blockchain prepared in IBM 5 qubit quantum computer, as a proof of concept with fidelity close to 0.9548.
James Bartusek, Andrea Coladangelo, Dakshita Khurana, Fermi Ma
We investigate the round complexity of maliciously-secure two-party quantum computation (2PQC) with setup, and obtain the following results:
- A three-message protocol (two-message if only one party receives output) in the common random string (CRS) model assuming classical two-message oblivious transfer (OT) with post-quantum malicious security. This round complexity is optimal for the sequential communication setting. Under the additional assumption of reusable malicious designated-verifier non-interactive zero-knowledge (MDV-NIZK) arguments for NP, our techniques give an MDV-NIZK for QMA. Each of the assumptions mentioned above is known from the quantum hardness of learning with errors (QLWE).
- A protocol with two simultaneous rounds of communication, in a quantum preprocessing model, assuming sub-exponential QLWE. In fact, we construct a three-round protocol in the CRS model with only two rounds of online communication, which implies the above result. Along the way, we develop a new delayed technique that we call simulation via teleportation, which may be useful in other settings.
In addition, we perform a preliminary investigation into barriers and possible approaches for two-round 2PQC in the CRS model, including an impossibility result for a natural class of simulators, and a proof-of-concept construction from a strong form of quantum virtual black-box (VBB) obfuscation.
Prior to our work, maliciously-secure 2PQC required round complexity linear in the size of the quantum circuit.
We model the hardware and software architecture for generalized Internet of Things (IoT) by quantum cloud-computing and blockchain. To reduce the measurement error and increase the efficiency of quantum entanglement (i.e. the capability of fault tolerance) in the current quantum computers and communications, we design a quantum-computing chip by modelling it as a multi-input multi-output (MIMO) quantum channel and obtain its channel capacity via our recently derived mutual information formula. To capture the internal qubit data flow dynamics of the channel, we model it via a deep convolutional neural network (DCNN) with generalized stochastic pooling in terms of resource-competition among different quantum eigenmodes or users. The pooling is corresponding to a resource allocation policy with two levels of competitions as in cognitive radio: the first one is on users’ selection in a ‘win–lose’ manner; the second one is on resourcesharing among selected users in a ‘win–win’ manner. To wit, our scheduling policy is the one by mixing a saddle point to a zero-sum game problem and a Pareto optimal Nash equilibrium point to a nonzero- sum game problem. The effectiveness of our policy is proved by diffusion modelling with theory and numerical examples.
In this work we consider the interplay between multiprover interactive proofs, quantum entanglement, and zero knowledge proofs - notions that are central pillars of complexity theory, quantum information and cryptography. In particular, we study the relationship between the complexity class MIP*, the set of languages decidable by multiprover interactive proofs with quantumly entangled provers, and the class PZK-MIP*, which is the set of languages decidable by MIP* protocols that furthermore possess the perfect zero knowledge property. Our main result is that the two classes are equal, i.e., MIP* = PZK-MIP*. This result provides a quantum analogue of the celebrated result of Ben-Or, Goldwasser, Kilian, and Wigderson (STOC 1988) who show that MIP = PZK-MIP (in other words, all classical multiprover interactive protocols can be made zero knowledge). We prove our result by showing that every MIP* protocol can be efficiently transformed into an equivalent zero knowledge MIP* protocol in a manner that preserves the completeness-soundness gap. Combining our transformation with previous results, we obtain the corollaries that i) all languages that can be solved in non-deterministic double exponential time have zero knowledge MIP* protocols and ii) all co-recursively enumerable languages (which include undecidable problems as well as all decidable problems) have zero knowledge MIP* protocols with vanishing promise gap.