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arXiv:1408.1540 · Physical Review A

Quantum Byzantine agreement via Hardy correlations and entanglement swapping

Ramij Rahaman, Marcin Wieśniak, Marek Żukowski

Published Oct 1, 2015• 19 citations
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Abstract

We present a device-independent quantum scheme for the Byzantine generals problem. The protocol is for three parties. Party $C$ is to send two identical one-bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one-bit messages informing the other party on the message received from $C$. A bit-flipping error in one of the transmissions does not allow the receiving parties to establish what was the message of $C$. Our quantum protocol is based on Hardy's argument, which uses a set of conditions impossible for classical systems, but satisfied by predictions for a unique two-qubit state. The scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the receivers), then any error by $C$ (cheating by one of the commanding generals) is impossible. $A$ and $B$ do not have to exchange protocol messages to be sure of this.

DOI
10.1103/physreva.92.042302

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We present a device-independent quantum scheme for the Byzantine generals problem. The protocol is for three parties. Party CCC is to send two identical one-bit messages to parties AAA and BBB. The receivers AAA and BBB may exchange two one-bit messages informing the other party on the message received from CCC. A bit-flipping error in one of the transmissions does not allow the receiving parties to establish what was the message of CCC. Our quantum protocol is based on Hardy's argument, which uses a set of conditions impossible for classical systems, but satisfied by predictions for a unique two-qubit state. The scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the receivers), then any error by CCC (cheating by one of the commanding generals) is impossible. AAA and BBB do not have to exchange protocol messages to be sure of this.
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.
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.
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.
We exhibit that, when given a classical Byzantine agreement protocol designed in the private-channel model, it is feasible to construct a quantum agreement protocol that can effectively handle a full-information adversary. Notably, both protocols have equivalent levels of resilience, round complexity, and communication complexity. In the classical private-channel scenario, participating players are limited to exchanging classical bits, with the adversary lacking knowledge of the exchanged messages. In contrast, in the quantum full-information setting, participating players can exchange qubits, while the adversary possesses comprehensive and accurate visibility into the system's state and messages. By showcasing the reduction from quantum to classical frameworks, this paper demonstrates the strength and flexibility of quantum protocols in addressing security challenges posed by adversaries with increased visibility. It underscores the potential of leveraging quantum principles to improve security measures without compromising on efficiency or resilience. By applying our reduction, we demonstrate quantum advantages in the round complexity of asynchronous Byzantine agreement protocols in the full-information model. It is well known that in the full-information model, any classical protocol requires Ω(n)Ω(n)Ω(n) rounds to solve Byzantine agreement with probability one even against Fail-stop adversary when resilience t=Θ(n)t=Θ(n)t=Θ(n). We show that quantum protocols can achieve O(1)O(1)O(1) rounds (i) with resilience t0t0t0, therefore surpassing the classical lower bound.
Bit commitment is an essential primitive in quantum cryptography. It is the basic building block of many cryptographic protocols in which it provides security over distrustful parties. This paper proposes a secured quantum two-bit commitment protocol for any two classical bits. The protocol contains two parties - a committer and a receiver - who share both quantum and classical communication channels. The main phases of this protocol are commitment and revealing phases where the concealing and binding conditions are proved in order to accept the commitment message. The proposed framework utilizes different security layers to hide specific quantum states in a superposition alongside trivial one qubit operations. The secured unitary transformations are applied by the two parties to meet the concealing and binding conditions. To verify the success of the proposed protocol, the measured output of the two parties are compared. The protocol operates under the assumption that the two parties might cheat and the possible existence of an eavesdropper.