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International Journal of Quantum Information

A quantum secure multi-party summation protocol with quantum Fourier transform

Hong-Ming Pan

Published Jun 8, 2024• 0 citations
Publisher

Abstract

In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, [Formula: see text] users can calculate the addition modulo [Formula: see text] of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, [Formula: see text] users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from [Formula: see text] users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs [Formula: see text]-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack.

DOI
10.1142/s0219749924500382

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In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, [Formula: see text] users can calculate the addition modulo [Formula: see text] of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, [Formula: see text] users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from [Formula: see text] users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs [Formula: see text]-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack.
We present a secure multi-party quantum summation protocol based on quantum teleportation, in which a malicious, but non-collusive, third party (TP) helps compute the summation. In our protocol, TP is in charge of entanglement distribution and Bell states are shared between participants. Users encode the qubits in their hand according to their private bits and perform Bell-state measurements. After obtaining participants’ measurement results, TP can figure out the summation. The participants do not need to send their encoded states to others, and the protocol is therefore congenitally free from Trojan horse attacks. In addition, our protocol can be made secure against loss errors, because the entanglement distribution occurs only once at the beginning of our protocol. We show that our protocol is secure against attacks by the participants as well as the outsiders.
We present a secure multi-party quantum summation protocol based on quantum teleportation, in which a malicious, but non-collusive, third party (TP) helps compute the summation. In our protocol, TP is in charge of entanglement distribution and Bell states are shared between participants. Users encode the qubits in their hand according to their private bits and perform Bell-state measurements. After obtaining participants' measurement results, TP can figure out the summation. The participants do not need to send their encoded states to others, and the protocol is therefore congenitally free from Trojan horse attacks. In addition, our protocol can be made secure against loss errors, because the entanglement distribution occurs only once at the beginning of our protocol. We show that our protocol is secure against attacks by the participants as well as the outsiders.
Recently, Yang et al. (Quantum Inf Process:17:129, 2018) proposed a secure multi-party quantum summation protocol allowing the involved participants to sum their secrets privately. They claimed that the proposed protocol can prevent each participant's secret from being known by others. However, this study shows that the participant who prepares the initial quantum states can obtain other participants' secrets with an inverse quantum Fourier transform attack. A modification is then proposed here to solve this problem.
A multi-party quantum summation with a single [Formula: see text]-level quantum system is proposed, in which a semi-honest third party (TP) is employed. Only sequential communication of a single quantum [Formula: see text]-level system (for any prime [Formula: see text]) is required in the presented protocol, resulting in advantages in scalability. In addition, it can be realized with state-of-the-art technology. Due to the semi-honest TP, the protocol is not only secure against outside attacks, but also secure against participant attacks.
This paper presents a novel quantum secure multi-party summation protocol based on one-direction quantum walks on a circle (ODQWC), which allows the summation computation of different integer sequences from “n” secret holders. Crucially, it ensures that this process does not infringe on the privacy of these secret holders by delivering quantum walk states in a circular pattern. Our proposed protocol employs two-particle product states rather than quantum entangled states as the initial quantum resource and eliminates the need for different secret holders to perform quantum entanglement swapping operations. Instead, it emphasizes imposing one-direction evolution operators on quantum walk states. Additionally, our protocol requires single-particle measurements. Security analysis validates that our proposed protocol can effectively counter external attacks and those initiated by participants. Under specific conditions, our proposed protocol can be adapted into a quantum secure multi-party bit summation protocol based on ODQWC.
Abstract In this paper, by utilizing d -dimensional single-particle states, three semiquantum cryptography protocols, i.e., the multi-party semiquantum private comparison (MSQPC) protocol, the multi-party semiquantum multiplication (MSQM) protocol and the multi-party semiquantum summation (MSQS) protocol, can be achieved simultaneously under the assistance of two semi-honest quantum third parties (TPs). Here, the proposed MSQPC scheme is the only protocol which is devoted to judging the size relationship of secret integers from more than two semiquantum participants without a pre-shared key. And the proposed MSQM protocol absorbs the innovative concept of semiquantumness into quantum multiplication for the first time, which can calculate the modulo d multiplication of private inputs from more than two semiquantum users. As for the proposed MSQS protocol, it is the only semiquantum summation protocol which aims to accomplish the modulo d addition of more than three semiquantum users’ private integers. Neither quantum entanglement swapping nor unitary operations are necessary in the three proposed protocols. The security analysis verifies in detail that both the external attacks and the internal attacks can be resisted in the three proposed protocols.