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arXiv:1907.02656

Improvement on "Secure multi-party quantum summation based on quantum Fourier transform"

Jun Gu, Tzonelih Hwang

Published Jul 5, 2019• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1907.02656

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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.
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.
Improvements on "Multi-Party Quantum Summation without a Third Party based on ddd-Dimensional Bell States"
In 2021, Wu et al. presented a multi-party quantum summation scheme exploiting the entanglement properties of d-dimensional Bell states (Wu et al. in Quantum Inf Process 20:200, 2021). In particular, the authors proposed a three-party quantum summation protocol and then extended their work to a multi-party case. It is claimed that their protocol is secure against outside and participants' attacks. However, this work points out that Wu's protocol has a loophole, i.e., two or more dishonest participants who meet a specific location relationship can conspire to obtain the private inputs of some honest participants without being detected. Accordingly, improvements are proposed to address these issues.
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.
The secure multiparty quantum summation is an important primitive of quantum cryptography. The existing multiparty quantum summation protocols have (n, n) threshold approach, where n out of total n players need compute the summation protocol. In this brief, we present a generalized secure multiparty quantum summation protocol. In our protocol, the linear secret sharing (LSS) and Quantum Fourier Transform (QFT) are used to take the advantages of both classical and quantum summation. We show that the outside and participant attacks are not possible in our protocol. We simulate it using the real quantum processor released by IBM corporation on “cloud”.
Recently, Yang et al. (Quantum Inf Process 18, 74, 2019) proposed a two-party quantum key agreement protocol over a collective noisy channel. They claimed that their quantum key agreement protocol can ensure both of the participants have equal influence on the final shared key. However, this study shows that the participant who announces the permutation operation can manipulate the final shared key by himself/herself without being detected by the other. To avoid this loophole, an improvement is proposed here.
Tian et al. (EPJ Quantum Technol 11(1):35, 2024 ) proposed three semi-quantum summation protocols that enable resource-limited participants to securely compute the sum of their private inputs with assistance from a semi-honest third party (TP). In these protocols, participants do not need quantum measurement devices to achieve secure computation. Although the protocols have been analyzed against common attacks to demonstrate their robustness, this study identifies two significant issues in Tian et al.’s work: a security loophole and a design flaw. The security loophole permits a malicious participant to steal another participant’s private input without detection, while the design flaw prevents participants from obtaining the correct summation result when the number of participants is odd. To address these issues, this study proposes improved semi-quantum summation protocols under the same assumptions and environment.