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arXiv:2112.09437

Detectable Quantum Byzantine Agreement for Any Arbitrary Number of Dishonest Parties

Vicent Cholvi

Published Dec 17, 2021• 0 citations
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Abstract

Reaching agreement in the presence of arbitrary faults is a fundamental problem in distributed computation, which has been shown to be unsolvable if one-third of the processes can fail, unless signed messages are used. In this paper, we propose a solution to a variation of the original BA problem, called Detectable Byzantine Agreement (DBA), that does not need to use signed messages. The proposed algorithm uses what we call $Q$-correlated lists, which are generated by a quantum source device. Once each process has one of these lists, they use them to reach the agreement in a classical manner. Although, in general, the agreement is reached by using $m+1$ rounds (where $m$ is the number of processes that can fail), if less than one-third of the processes fail it only needs one round to reach the agreement.

DOI
10.48550/arxiv.2112.09437

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Reaching agreement in the presence of arbitrary faults is a fundamental problem in distributed computation, which has been shown to be unsolvable if one-third of the processes can fail, unless signed messages are used. In this paper, we propose a solution to a variation of the original BA problem, called Detectable Byzantine Agreement (DBA), that does not need to use signed messages. The proposed algorithm uses what we call QQQ-correlated lists, which are generated by a quantum source device. Once each process has one of these lists, they use them to reach the agreement in a classical manner. Although, in general, the agreement is reached by using m+1m+1m+1 rounds (where mmm is the number of processes that can fail), if less than one-third of the processes fail it only needs one round to reach the agreement.
Abstract Reaching agreement in the presence of arbitrary faults is a fundamental problem in distributed computation, which has been shown to be unsolvable if one-third of the processes can fail, unless signed messages are used. In this paper, we propose a solution to a variation of the original BA problem, called Detectable Byzantine Agreement (DBA), that does not need to use signed messages. The proposed algorithm uses what we call Q-correlated lists, which are generated by a quantum source device. Once each process has one of these lists, they use them to reach the agreement in a classical manner. Although, in general, the agreement is reached by using m+1m+1m+1 m + 1 rounds (where m is the number of processes that can fail), if less than one-third of the processes fail it only needs one round to reach the agreement.
Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to detectable Byzantine agreement (DBA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm that solves the DBA and achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system.
Quantum entanglement can be employed in some distributed communication tasks to reduce computation and communication overheads, yielding speedups over their classical counterparts. However, existing quantum Byzantine protocols often entail excessive communication and entanglement resource consumption. Conversely, classical schemes face insecurity with the impending reality of quantum computers. To address these challenges, we present a novel quantum Detectable Weak Byzantine Agreement (DWBA) protocol with high practicability, security and optimal fault-tolerance bound. For all n players, our protocol can complete the consensus of infinite classical information via fixed n + 1 -entangled qubits and a digest function, which requires infinite entanglement resources in previous schemes. Moreover, our protocol can tolerate arbitrary t ( t < n ) faulty players without necessitating any additional initial setup information (e.g., digital signature, private random coins). In terms of efficiency, our protocol only requires O (1) rounds and O ( ( n − t ) 2 ) communication complexity, constituting an order of magnitude improvement over previous protocols. In addition, the DWBA problem solved by our protocol is inherently stronger than the 3-player Detectable Byzantine Agreement (DBA) problem solved by previous protocols, and in a weaker but sufficiently practical model, our protocol can achieve Weak Byzantine Agreement (WBA).
Byzantine agreement, the underlying core of blockchain, aims to make every node in a decentralized network reach consensus. Classical Byzantine agreements unavoidably face two major problems. One is 1/3 fault-tolerance bound, which means that the system to tolerate f malicious players requires at least 3 f + 1 players. The other is the security loopholes from its classical cryptography methods. Here, we propose a Byzantine agreement framework with unconditional security to break this bound with nearly 1/2 fault tolerance due to multiparty correlation provided by quantum digital signatures. It is intriguing that quantum entanglement is not necessary to break the 1/3 fault-tolerance bound, and we show that weaker correlation, such as asymmetric relationship of quantum digital signature, can also work. Our work strictly obeys two Byzantine conditions and can be extended to any number of players without requirements for multiparticle entanglement. We experimentally demonstrate three-party and five-party consensus for a digital ledger. Our work indicates the quantum advantage in terms of consensus problems and suggests an important avenue for quantum blockchain and quantum consensus networks.
In this paper, we propose a protocol of quantum communication to achieve Byzantine agreement among multiple parties. Our protocol's striking feature compared to the existing protocols is that we do not use entanglement to achieve the agreement. The role played by entangled states in other protocols is replaced in our protocol by a group of semi-honest list distributors. Such a replacement makes the implementation of our protocol more feasible. Moreover, our protocol is efficient in the sense that it achieves agreement in only three rounds which is a significant improvement with respect to the alternative agreement protocol not using entanglement. In the first round, a list of numbers that satisfies some special properties is distributed to every participant by list distributors via quantum secure communication. Then, in the second and third rounds, those participants exchange some information to reach an agreement.
Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to Byzantine agreement (BA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm, based on a quantum solution of the detectable BA, which achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system.