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Physical Review A

Comment on “Secure multiparty computation with a dishonest majority via quantum means”

Yanbing Li, Qiaoyan Wen, Su‐Juan Qin

Published Jul 27, 2011• 13 citations
Publisher

Abstract

In a recent paper [K. Loukopoulos and D. E. Browne, Phys. Rev. A 81, 062336 (2010)], five schemes for secure multiparty computation utilizing the Greenberger-Horne-Zeilinger (GHZ) quantum correlation were presented, which were claimed to be secure in some kinds of security models. However, this study points out that schemes C and D2 could be attacked by corrupted parties replacing photon and exchanging classical information.

DOI
10.1103/physreva.84.016301

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In a recent paper [K. Loukopoulos and D. E. Browne, Phys. Rev. A 81, 062336 (2010)], five schemes for secure multiparty computation utilizing the Greenberger-Horne-Zeilinger (GHZ) quantum correlation were presented, which were claimed to be secure in some kinds of security models. However, this study points out that schemes C and D2 could be attacked by corrupted parties replacing photon and exchanging classical information.
We introduce a scheme for secure multiparty computation utilizing the quantum correlations of entangled states. First we present a scheme for two-party computation, exploiting the correlations of a Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a near-private computation scheme. We then present a variation of this scheme which is passively secure with threshold t=2t=2t=2, in other words, remaining secure when pairs of players conspire together provided they faithfully follow the protocol. Furthermore, we show that the passively secure variant can be modified to be secure when cheating parties are allowed to deviate from the protocol. We show that this can be generalized to computations of nnn-party polynomials of degree 2 with a threshold of $n\ensuremath{-}1$. The threshold achieved is significantly higher than the best known classical threshold, which satisfies the bound t<n/2t<n/2t<n/2. Our schemes, each complying with a different definition of security, shed light on which physical assumptions are necessary in order to achieve quantum secure multiparty computation.
Secure multi-party extremum, as a significant offshoot of secure multi-party computation, has extensive applications in various domains, including healthcare, financial transactions, market analysis, sports events, etc. Nevertheless, most existing secure multi-party extremum protocols rely on computational hard problems and are thus vulnerable to quantum algorithms. This paper presents a quantum secure multi-party extremum protocol that is built upon the correlations of Greenberger–Horne–Zeilinger (GHZ) states. Within this protocol, multiple participants, with the aid of a semi-honest third party, can obtain the maximum and minimum values of their secret inputs. GHZ states act as the information carriers and are transmitted among the participants and the third party. Their unique correlations ensure the secure transmission of quantum particles. The analysis demonstrates that the proposed protocol is capable of not only warding off common external attacks but also resisting internal attacks launched by dishonest participants and the semi-honest third party. Moreover, the protocol boasts correctness and high scalability.
Recently, Chen et al. (DOI 10.1109/SMC.2015. 281) proposed a multiparty quantum key agreement protocol based on Greenberger-Horne-Zeilinger (GHZ) state. They claimed that their protocol can achieve both the security property and the fairness property. However, this study points out that Chen et al.'s protocol cannot achieve the fairness property by an Internal Attack. That is, one of the involved participant (Alice) can determine the final key alone without being detected by other participants.