We propose a new, unifying framework that yields an array of cryptographic primitives with certified deletion. These primitives enable a party in possession of a quantum ciphertext to generate a classical certificate that the encrypted plaintext has been information-theoretically deleted, and cannot be recovered even given unbounded computational resources. - For X \in {public-key, attribute-based, fully-homomorphic, witness, timed-release}, our compiler converts any (post-quantum) X encryption to X encryption with certified deletion. In addition, we compile statistically-binding commitments to statistically-binding commitments with certified everlasting hiding. As a corollary, we also obtain statistically-sound zero-knowledge proofs for QMA with certified everlasting zero-knowledge assuming statistically-binding commitments. - We also obtain a strong form of everlasting security for two-party and multi-party computation in the dishonest majority setting. While simultaneously achieving everlasting security against all parties in this setting is known to be impossible, we introduce everlasting security transfer (EST). This enables any one party (or a subset of parties) to dynamically and certifiably information-theoretically delete other participants' data after protocol execution. We construct general-purpose secure computation with EST assuming statistically-binding commitments, which can be based on one-way functions or pseudorandom quantum states. We obtain our results by developing a novel proof technique to argue that a bit b has been information-theoretically deleted from an adversary's view once they output a valid deletion certificate, despite having been previously information-theoretically determined by the ciphertext they held in their view. This technique may be of independent interest.
The examination investigates the joining of quantum-safe cryptographic calculations into blockchain innovation, zeroing in on grid-based cryptography and hash-based marks. Because of the inescapable danger presented by quantum processing, this study proposes a quantum-safe blockchain system intended to upgrade the security and flexibility of circulated records. The cross-section-based cryptography calculation uses the computational intricacy of grid issues, offering protection from quantum goes like Shor's calculation. Simultaneously, hash-based marks give lightweight and quantum-safe choices for advanced marks, supporting the general validity of blockchain exchanges. The examination includes a multi-staged approach, incorporating a complete writing survey, hypothetical system improvement, algorithmic execution, and exhaustive investigation of versatility, execution, and information security. Reproduction results will illuminate ensuing equipment executions, approving the down-to-earth attainability of the proposed quantum-safe blockchain. Besides, the review digs into moral and administrative contemplations, adding to the foundation of capable rules for quantum-safe blockchain innovation. Insights into the performance of lattice-based cryptography and hash-based signatures, as well as the provision of a blueprint for future research in quantum-resistant distributed ledger systems, are among the anticipated contributions. The powerful idea of quantum advancements and blockchain requires continuous investigation, and the exploration makes way for future examinations concerning quantum-safe agreement components, upgraded Quantum Key Dispersion, and interdisciplinary coordinated efforts.
Peter Nimbe, Benjamin Asubam Weyori, Jacob Kofi Mensah, Anokye Acheampong Amponsah · 6 authors
Quantum blockchain is a distributed database that is decentralized, encrypted, and based on quantum information theory and computation. This comes as a result of the recent progress made in quantum computing and the need for quantum equivalents of classical blockchains. Algorithms, frameworks, models, tools, architectures, and databases, of which quantum blockchain is a part, are still being standardized. Recently, the growth of quantum information theory and computation has resulted in a rise in the number of research ongoing in this domain. This chapter presents an insight into quantum blockchain using the PRISMA technique with results registered and analyzed. The literature is analyzed based on some parameters or categorizations accompanied by graphical and tabular representations.
Omega John Unogwu, Ruchi Doshi, Kamal Kant Hiran, Maad M. Mıjwıl
Quantum-resistant blockchains refer to cryptographic processes that are resistant to attacks via quantum computers. Present public-key algorithms depend on the difficulty of deciphering the discrete log and factorization problem of large prime numbers. Shor's algorithm can be used to break the hash signatures by quantum computers. Therefore, it is necessary for the development of a post-quantum secure signature scheme or quantum-resistant blockchain for post-quantum blockchain security. This chapter will discuss the impact quantum computers are predicted to have on public key cryptography based on the following topics: quantum computers, public key cryptography, quantum threat to PKI, Shor's and Grover's algorithms, post-quantum cryptography, and quantum-resistant blockchain.
Blockchain is a new but quickly growing technology in the world, which was developed by a pseudonymous Satoshi Nakamoto in 2009 as the cryptocurrency Bitcoin. Blockchain was un-hackable but now, due to use of quantum computers, it is possible to tamper with blockchain. As a counter to this, the researchers have come up with quantum blockchain using the principles of quantum cryptography. Today we see that the technology has given birth to many new technologies as well. One of its examples is non-fungible tokens (NFTs). These are a new sort of blockchain-based token that is unique and indivisible. They were first created in 2014. These are blockchain-based virtual assets. Since early 2021, the phenomena and its marketplaces have increased dramatically.
Blockchain-based platforms utilise cryptographic protocols to enforce the correct behaviour of users, as well as to guarantee a sufficient level of protection against malicious adversaries. Cryptography is, however, an ever-evolving discipline, and any breakthrough would have immediate consequences on the security of blockchain-based applications. A possible threat currently under investigation is given by the development of quantum computers, since several wide-adopted cryptographic protocols have been proved to be unsafe against quantum-capable adversaries. In this work, we propose a novel approach for the management of cryptographic primitives in smart-contract-based ledgers, discussing how it fits in both a (partially) permissioned and a fully permissionless setting. The cryptographic protocols are managed in a flexible manner via a set of smart-contracts defined on the ledger itself, in this way the choice of algorithms and parameters can change quickly. Among the advantages of this approach, we remark how it allows designing an adaptive post-quantum-based blockchain that keeps up with ongoing technological advances. In general, the introduction of new features and the application of fixes to a blockchain cause forks in the chain, which may cause major disruptions. The use of smart contracts in blockchain management allows to avoid this problem, dynamically introducing new protocols or deprecating old ones without compromising previous data. The Cryptographic Kernel approach has been adopted by Quadrans, an open-source, public, decentralised smart-contract-based blockchain with a specific focus on the needs of industry, complex supply chains, and IOT devices.
As emerging next-generation information technologies, blockchains have unique advantages in information transparency and transaction security. They have attracted great attentions in social and financial fields. However, the rapid development of quantum computation and the impending realization of quantum supremacy have had significant impacts on the advantages of traditional blockchain based on traditional cryptography. Here, we propose a blockchain algorithm based on asymmetric quantum encryption and a stake vote consensus algorithm. The algorithm combines a consensus algorithm based on the delegated proof of stake with node behaviour and Borda count (DPoSB) and quantum digital signature technology based on quantum state computational distinguishability with a fully flipped permutation ([Formula: see text]) problem. DPoSB is used to generate blocks by voting, while the quantum signature applies quantum one-way functions to guarantee the security of transactions. The analysis shows that this combination offers better protection than other existing quantum-resistant blockchains. The combination can effectively resist the threat of quantum computation on blockchain technology and provide a new platform to ensure the security of blockchain.
Saeed Banaeian Far, Azadeh Imani Rad, Maryam Rajabzadeh Asaar
Quantum computing is the primary concern against security and privacy issues; And it is known that no digital assets have provable ownership in the post-quantum age. As a digital asset or investing method, cryptocurrencies are not far from this fact. This study presents a practical and comprehensive framework to secure current cryptocurrencies against quantum computers by offering a hard fork. The currently-using cryptocurrencies can apply the mentioned hard fork for providing security in the post-quantum age. To keep the currencies’ previous values in their post-quantum forks, the mentioned hard fork is designed based on a 1-to-1 proof of burn (PoB) consensus: a hash function and hash-based signature as two quantum-secure tools, are applied to prepare the migration to the quantum-secure fork. For example, and to show that the hard fork works, the quantum-secure fork of Bitcoin (QBTC) will be presented and analyzed in the heuristic form.
Smart contracts are cryptographic protocols that are enforced without a judiciary. Smart contracts are used occasionally in Bitcoin and are prevalent in Ethereum. Public quantum money improves upon cash we use today, yet the current constructions do not enable smart contracts. In this work, we define and introduce quantum payment schemes, and show how to implement prudent contracts -- a non-trivial subset of the functionality that a network such as Ethereum provides. Examples discussed include: multi-signature wallets in which funds can be spent by any 2-out-of-3 owners; restricted accounts that can send funds only to designated destinations; and "colored coins" that can represent stocks that can be freely traded, and their owner would receive dividends. Our approach is not as universal as the one used in Ethereum since we do not reach a consensus regarding the state of a ledger. We call our proposal prudent contracts to reflect this. The main building block is either quantum tokens for digital signatures (Ben-David and Sattath QCrypt'17, Coladangelo et al. Crypto'21), semi-quantum tokens for digital signatures (Shmueli'22) or one-shot signatures (Amos et al. STOC'20). The solution has all the benefits of public quantum money: no mining is necessary, and the security model is standard (e.g., it is not susceptible to 51\% attacks, as in Bitcoin). Our one-shot signature construction can be used to upgrade the Bitcoin network to a quantum payment scheme. Notable advantages of this approach are: transactions are locally verifiable and without latency, the throughput is unbounded, and most importantly, it would remove the need for Bitcoin mining. Our approach requires a universal large-scale quantum computer and long-term quantum memory; hence we do not expect it to be implementable in the next few years.
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.
Robert Benkoczi, Daya Ram Gaur, Naya Nagy, Marius Nagy · 5 authors
This paper studies the effect of quantum computers on Bitcoin mining. The shift in computational paradigm towards quantum computation allows the entire search space of the golden nonce to be queried at once by exploiting quantum superpositions and entanglement. Using Grover’s algorithm, a solution can be extracted in time O(2256/t), where t is the target value for the nonce. This is better using a square root over the classical search algorithm that requires O(2256/t) tries. If sufficiently large quantum computers are available for the public, mining activity in the classical sense becomes obsolete, as quantum computers always win. Without considering quantum noise, the size of the quantum computer needs to be ≈104 qubits.
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.
Scott E. Smart, Jan-Niklas Boyn, David A. Mazziotti
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers [presented in Smart and Mazziotti, Phys. Rev. Lett. 126, 070504 (2021)] in which a contraction of the Schr\"odinger equation is solved for the two-electron reduced density matrix (2-RDM) to resolve the energy splittings of the ortho-, meta-, and para-isomers of benzyne ${\text{C}}_{6}{\text{H}}_{4}$. In contrast to the traditional variational quantum eigensolver, the contracted quantum eigensolver can solve an integration (or contraction) of the many-electron Schr\"odinger equation onto the two-electron space. The quantum solution of the anti-Hermitian part of the contracted Schr\"odinger equation provides a scalable approach with few variational parameters that has its foundations in 2-RDM theory. Experimentally, a variety of error-mitigation strategies enable the calculation, including a linear shift in the 2-RDM targeting the iterative nature of the algorithm as well as a projection of the 2-RDM onto the convex set of approximately $N$-representable 2-RDMs defined by the 2-positive $N$-representability conditions. The relative energies exhibit single-digit millihartree errors, capturing a large part of the electron correlation energy, and the computed natural orbital occupations reflect the significant differences in the electron correlation of the isomers.
Sikha Pentyala, Davis Railsback, Ricardo Maia, Rafael Dowsley · 7 authors
In the classical setting of differential privacy, a privacy-preserving query is performed on a private database, after which the query result is released to the analyst; a differentially private query ensures that the presence of a single database entry is protected from the analyst’s view. In this work, we contribute the first definitional framework for differential privacy in the trusted curator setting (Fig. 1); clients submit private inputs to the trusted curator, which then computes individual outputs privately returned to each client. The adversary is more powerful than the standard setting; it can corrupt up to n-1 clients and subsequently decide inputs and learn outputs of corrupted parties. In this setting, the adversary also obtains leakage from the honest output that is correlated with a corrupted output. Standard differentially private mechanisms protect client inputs but do not mitigate output correlation leaking arbitrary client information, which can forfeit client privacy completely. We initiate the investigation of a novel notion of correlated-output differential privacy to bound the leakage from output correlation in the trusted curator setting. We define the satisfaction of both standard and correlated-output differential privacy as round differential privacy and highlight the relevance of this novel privacy notion to all application domains in the trusted curator model. \nWe explore round differential privacy in traditional "dark pool" market venues, which promise privacy-preserving trade execution to mitigate front-running; privately submitted trade orders and trade execution are kept private by the trusted venue operator. We observe that dark pools satisfy neither classic nor correlated-output differential privacy; in markets with low trade activity, the adversary may trivially observe recurring, honest trading patterns, and anticipate and front-run future trades. In response, we present the first round differentially private market mechanisms that formally mitigate information leakage from all trading activity of a user. This is achieved with fuzzy order matching, inspired by the standard randomized response mechanism; however, this also introduces a liquidity mismatch as buy and sell orders are not guaranteed to execute pairwise, thereby weakening output correlation; this mismatch is compensated for by a round differentially private liquidity provider mechanism, which freezes a noisy amount of assets from the liquidity provider for the duration of a privacy epoch, but leaves trader balances unaffected. We propose oblivious algorithms for realizing our proposed market mechanisms with secure multi-party computation (MPC) and implement these in the Scale-Mamba Framework using Shamir Secret Sharing based MPC. We demonstrate practical, round differentially private trading with comparable throughput as prior work implementing (traditional) dark pool algorithms in MPC; our experiments demonstrate practicality for both traditional finance and decentralized finance settings.
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 Allen–Givone 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.
Cryptocurrencies have proliferated in recent years, and all of them have more or less optimized the shortcomings of bitcoin. This paper selected four representative cryptocurrencies including LiteCoin, ETH, Zcash, and Ripple, and made a comprehensive comparison of their advantages and disadvantages, attacks and defenses and other aspects, based on reading a significant volume of relevant papers. The comprehensive comparison can more easily highlight the advantages of cryptocurrencies on the market so far, and more importantly, more vulnerabilities will be discovered and more defense methods will be interpreted, which must have certain guiding significance for the future vulnerability repair and defense against attacks of cryptocurrencies to a large extent. This will greatly improve the security of future cryptocurrencies. By analyzing their generation mode, their working mechanism, their security capabilities and their algorithms, the strengths and weaknesses of the four popular cryptocurrencies mentioned above can be summed up very clearly. On the basis of these pros and cons, it will be very easy to delineate where each cryptocurrency is suitable. In addition, potential vulnerabilities could be found by studying the consensus algorithm of each cryptocurrency. What we did was looking for possible attacks based on those vulnerabilities, and trying to find the appropriate defense methods. We have done a very thorough study of the work mentioned above, and have finally achieved a very detailed comparison of the differences between several cryptocurrencies. Finally, we came to the conclusion that each cryptocurrency has different styles in terms of advantages and features, and is relatively easy to spot in terms of weaknesses, making it vulnerable to some large-scale attacks. By comparing these cryptocurrencies in all aspects, a more secure and more powerful cryptocurrency may be created soon.
Abstract Purpose of work is the development of a new method for estimating the quantum resilience of modern blockchain platforms based on the effective solution of cryptanalysis problems for asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS), based on computationally difficult problems of factorization and discrete logarithm. Research method is the use of quantum algorithms providing exponential gain (eg Shor’s algorithm) and quadratic gain (eg Grover’s algorithm). Due to the fact that the class of problems solved by quantum algorithms in polynomial time cannot yet be significantly expanded, more attention is paid to cryptanalysis based on the quantum Shor algorithm and other polynomial algorithms. Results of the study include a classification of well-known algorithms and software packages for cryptanalysis of asymmetric encryption schemes (RSA, El-Gamal) and digital signature (DSA, ECDSA or RSA-PSS) based on computationally difficult problems of factorization and discrete logarithm has been built. A promising method for solving problems of cryptanalysis of asymmetric encryption schemes (RSA, ElGamal) and digital signature (DSA, ECDSA or RSA-PSS) of known blockchain platforms in polynomial time in a quantum computing model is proposed. Algorithms for solving problems of quantum cryptanalysis of two-key cryptography schemes of known blockchain platforms in polynomial time are developed, taking into account the security of the discrete algorithm (DLP) and the discrete elliptic curve algorithm (ECDLP). A structural and functional diagram of the software package for quantum cryptanalysis of modern blockchain platforms “Kvant-K”, adapted to work in a hybrid computing environment of the IBM Q quantum computer (20 and 100 qubits) and the IBM BladeCenter (2022) supercomputer, has been designed. A methodology has been developed for using the “Kvant-K” software package to assess the quantum stability of blockchain platforms: InnoChain (Innopolis University), Waves Enterprise (Waves, Vostok), Hyperledger Fabric (Linux, IBM), Corda Enterprise, Bitfury Exonum, Blockchain Industrial Alliance, Exonum (Bitfury CIS), NodesPlus (b41), Masterchain (Sberbank), Microsoft Azure Blockchain, Enterprise Ethereum Alliance, etc. Practical relevance: The developed new solution for computationally difficult problems of factorization and discrete logarithm, given over finite commutative (and non-commutative) associative algebras, in a quantum model of computing in polynomial time. It is essential that the obtained scientific results formed the basis for the development of the corresponding software and hardware complex “Kvant-K”, which was tested in a hybrid computing environment (quantum computer IBM Q (20 and 100 qubits) and/or 5th generation supercomputer: IBM BladeCenter (2022), RCS based on FPGA Virtex UltraScale (2020), RFNC-VNIIEF (2022) and SKIF P-0.5 (2021). An appropriate method for estimating the quantum stability of these blockchain platforms based on the author’s models, methods and algorithms of quantum cryptanalysis has been developed and tested. Keywords: blockchain and distributed ledger technologies (DLT), SMART contracts, blockchain security threat model, quantum security threat, cryptographic attacks, quantum cryptanalysis, quantum and post-quantum cryptography, quantum algorithms Shor, Grover and Simon algorithms, quantum Fourier transform, factorization and discrete logarithm problem, post-quantum cryptography, quantum resilience of blockchain platforms.