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Zhongguo kexue. Wulixue Lixue Tianwenxue

A quantum secure multi-party summation protocol based on one-direction quantum walks on a circle

Jin-Tao WANG, Xia Li, Tian-Yu Ye

Published Feb 21, 2024• 9 citations
Publisher

Abstract

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.

DOI
10.1360/sspma-2023-0447

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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.
In order to compare the size relationship and the equality of private integers from two users without any risk of leaking their secrets, we put forward a novel two-round two-party quantum private comparison (QPC) protocol with a third party (TP) based on one-direction quantum walks on a circle (ODQWC). Here, TP is allowed to launch all kinds of possible attacks except the collusion attack. This protocol adopts quantum walk (QW) states as the initial quantum resource, which are actually a kind of two-particle product states. This protocol doesn’t need any pre-shared secret key or quantum entanglement swapping operation, and only adopts unitary operations andd-dimensional single particle measurements. Security analysis validates the security of the proposed protocol against both the outside attacks and the participant attacks. Compared with previous QPC protocols based on QW, this protocol is more efficient under certain conditions. Moreover, we construct quantum circuits for this protocol and reveal its correctness and feasibility by IBM Qiskit simulator.
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.
Abstract Quantum walks, as the quantum mechanical counterpart of classical random walks, is an advanced tool for constructing quantum algorithms. Quantum secret sharing protocols based on quantum walks reduce the demand for entangled state preparation and simplify the complexity of quantum operations. However, existing quantum secret sharing protocols based on quantum walks have relatively limited functionality. This paper proposes a hierarchical quantum secret sharing protocol based on two-direction quantum walks on a circle and linear homogeneous recurrence relations. In this protocol, the secret distributor first verifies the participants’ identities simultaneously using a symmetric bivariate polynomial, then uses two-particle product states to carry secrets and encrypts them using evolution operators and global shifting operators. Finally, participants who satisfy the hierarchical access structure can simultaneously reconstruct their private classical sequence and quantum state sequence. Correctness analyses demonstrate that qualified participants can accurately obtain and reconstruct the secret information. In terms of security, the protocol can resist both external and internal attacks simultaneously. Lastly, efficiency analysis and comparisons demonstrate that the protocol outperforms other quantum secret sharing protocols based on quantum walks and holds an efficiency advantage.
In quantum secure multi-party summation protocols, some attackers can impersonate legitimate participants in the summation process, and easily steal the summation results from the participants. This is often overlooked for existing secure multi-party summation protocols, thus rendering them insecure. Based on commutative encryption, a quantum secure multi-party summation protocol with identity authentication is proposed in this paper. In the protocol, each participant encodes a secret integer on photons via unitary operations. At the same time, a one-way hash function technique with a key is utilized to perform identity authentication operations for each participant. Finally, the summation is calculated with the help of a semi-trusted third party. The analysis of the protocol shows that the proposed protocol is correct and resistant to common and impersonation attacks. Compared to related protocols, the use and measurement of single photons makes the protocol easier to implement into existing technology. Furthermore, the simulation experiments on the IBM Q Experience cloud platform demonstrate the effectiveness of the presented protocol.
participants can simultaneously obtain the summation result without revealing their secret inputs. Our protocol uses single photon states as the information carriers. In addition, each participant with secret input only performs simple single-particle operators rather than particle preparation and any complex quantum measurements. These features make our protocol more feasible to implement. We demonstrate the correctness and security of the proposed protocol, which is resistant to participant attack and outside attack. In the end, we compare in detail the performance of the quantum summation protocol in this paper with other schemes in terms of different indicators. By comparison, our protocol is efficient and easy to implement.
Abstract A previous study [Entropy 25.4 (2023): 590] proposed a quantum secure multi-party summation protocol wherein n participants could obtain the modulo-2 summation result using single photons and single-particle operations. Owing to the absence of an entanglement state, this protocol was more practical than other quantum summation protocols that used entanglement properties. Thus, this study investigated the claim that this proposed protocol prevented the participants’ secret inputs from being disclosed. It was found that the previously proposed protocol was vulnerable to a quantum Trojan horse attack owing to the circular qubit transmission mode. Using a security loophole, this study proposed an attack strategy that allowed an outside attacker to steal any participant’s secret input without being detected by a third party and participants. In addition, a simulation experiment was conducted to demonstrate the feasibility of the proposed attack and evaluate the number of quantum Trojan horse probes that the attacker must inject into regular qubit sequences. Finally, a solution was proposed by modifying the protocol to securely prevent quantum Trojan horse attacks.