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Communications in Theoretical Physics

A New Solution to Detectable Byzantine Agreement Problem

Qin Su-Juan, Wen Qiao-yan, Luoming Meng, Fu-Chen Zhu

Published Dec 1, 2009• 0 citations
Publisher

Abstract

We present a new quantum protocol for solving detectable Byzantine agreement problem between three parties by employing one quantum key distribution protocol. The protocol is suggested by a special four-qubit entangled state instead of singlet states, which shows that singlet states are not necessary to achieve detectable Byzantine agreement.

DOI
10.1088/0253-6102/52/6/07

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We present a new quantum protocol for solving detectable Byzantine agreement problem between three parties by employing one quantum key distribution protocol. The protocol is suggested by a special four-qubit entangled state instead of singlet states, which shows that singlet states are not necessary to achieve detectable Byzantine agreement.
Quantum mechanics provides several methods to generate and securely distribute private lists of numbers suitably correlated to solve the Three Byzantine Generals Problem. So far, these methods are based on three-qutrit singlet states, four-qubit entangled states, and three or two pairwise quantum key distribution channels. Here we show that the problem can be solved using a single qutrit. This scheme presents some advantages over previous schemes, and emphasizes the specific role of qutrits in basic quantum information processing.
In distributed computing,Byzantine agreement is a practical method to solve its fault-tolerance problem.There is a variation of the Byzantine agreement which is called detectable Byzantine agreement.This kind of protocol is unsolvable by classical means,but can be solved using quantum resources——quantum entangled states.A typical quantum detectable Byzantine agreement is the GBKCW protocol.The part with the generation and distribution of the lists in the GBKCW protocol was dealed with.In order to keep the GBKCW protocol from the intercept-and-resend strategy,the property of the determination of entangled states were employed to test the sharing state between the parties.
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.
In distributed computing systems such as blockchain, Byzantine protocol is a practical method to solve its fault-tolerance problem. The Byzantine question has a variant called the “detectable Byzantine protocol.” This type of protocol is unsolvable in the classical field, but it can be solved using quantum physics properties in quantum systems. Based on the wonderful characteristics of quantum entanglement, a method of quantum channel detection, generation and safe distribution of digital lists is designed by using two quantum entangled states of three photons as quantum channels, so as to solve the tripartite Byzantine problem of detection more simply. Finally, the correctness and security of the scheme are analyzed.