Byzantine agreement (also known as the Byzantine fault-tolerant algorithm), as the cornerstone of blockchain, is committed to achieving consensus in distributed networks. However, classic Byzantine consensus agreement faces two major challenges. Firstly, it is strictly constrained by the 1/3 fault-tolerance bound, which means that the system needs at least 3f+1 nodes to tolerate f malicious nodes. Secondly, due to the use of classical cryptographic methods, the security is vulnerable when facing the threat of quantum computing.

Detectable quantum Byzantine agreement was proposed for the three-party consensus by the scientists at ETH Zurich and University of Geneva. However, it inevitably introduces additional assumptions, resulting in a certain probability of being aborted. More seriously, it is limited to tripartite consensus and cannot be extended to more participants. In addition, due to the need of highly complex entangled states, it is difficult to apply it in real-world blockchain technology.

Recently, the team led by Prof. Zeng-Bing Chen and Hua-Lei Yin at Nanjing University have identified quantum digital signatures as a beneficial tool for Byzantine agreement. They've successfully designed a novel quantum Byzantine agreement based on quantum digital signatures and recursion structure. The framework involves two key phases: the broadcasting phase, where the commanding general initiates quantum digital signatures and distribute the messages layer by layer, and the gathering phase, where lieutenants recursively deduce valid information lists and ultimately lead to the final output message.

Fig. 1 Experimental demonstration for quantum Byzantine agreement in a five-node quantum networks

In addition, the team constructed a quantum consensus network with five nodes at Nanjing University, as shown in Fig. 1, and conducted experiments of three-party and five-party consensus for a distributed ledger, one of the most important tasks of blockchain. The experiments confirmed the feasibility of quantum blockchain, breaking the 1/3 fault-tolerance limit, and providing information-theoretical security, achieving nearly 1/2 fault tolerance in the network.

Quantum digital signatures can construct asymmetric multi-party relationships among participants, making the linked channels no longer independent of each other. Different from classical digital signatures, quantum digital signatures based on the fundamental principles of quantum mechanics naturally does not require a trusted third party, and the forwarder and verifier are equivalent. The two basic properties of quantum digital signatures, unforgeability and non-repudiation, ensure that messages will not be tampered with or denied during transmission. This effectively limits the malicious activities of malicious participants within the system, preventing them from intentionally transmitting conflicting messages. Therefore, this work can break through the 1/3 fault-tolerance bound and provide information-theoretical security.

This work surpasses the 1/3 fault-tolerance bound, ensuring information-theoretic security and make Byzantine agreement capable of withstanding quantum computing threats. This underscores quantum advantages in consensus problems, offering a crucial and practical pathway for quantum blockchains and quantum consensus networks. Its applications span financial transactions, supply chain management, IoT devices, smart e-governance, healthcare, and distributed storage.

The study was published in Research on 21 Nov 2023 under the title “Beating the Fault-Tolerance Bound and Security Loopholes for Byzantine Agreement with a Quantum Solution”.

Sources: https://spj.science.org/doi/10.34133/research.0272

Tag: Information Science