Quantum Private Comparison Protocol Based on Continuous Variables

Ashwin Saxena, Kishore Thapliyal, Anirban Pathak

A continuous variable (CV) controlled quantum dialogue (QD) scheme is proposed. The scheme is further modified to obtain two other protocols of (CV) secure multiparty computation. The first one of these protocols provides a solution of two-party socialist millionaire problem, while the second protocol provides a solution for a special type of multi-party socialist millionaire problem which can be viewed as a protocol for multiparty quantum private comparison. It is shown that the proposed scheme of (CV) controlled (QD) can be performed using bipartite entanglement and can be reduced to obtain several other two- and three-party cryptographic schemes in the limiting cases. The security of the proposed scheme and its advantage over corresponding discrete variable (DV) counterpart are also discussed. Specifically, the ignorance of an eavesdropper, i.e., information encoded by Alice/Bob, in the proposed scheme is shown to be more than that in the corresponding (DV) scheme, and thus the present scheme is less prone to information leakage inherent with the (DV) (QD) based schemes. It is further established that the proposed scheme can be viewed as a (CV) counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.

Zhiwei Sun, Dongyang Long

Wanqing Wu, Xiaoxue Ma

László Gyöngyösi

We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous-variable quantum key distribution (CVQKD). In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier CVs (continuous-variables). The multicarrier communication formulates Gaussian sub-channels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single-carrier Gaussian CVs. We derive the formulas through the AMQD (adaptive multicarrier quadrature division) scheme, the SVD-assisted (singular value decomposition) AMQD, and the multiuser AMQD-MQA (multiuser quadrature allocation). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison to single-carrier CVQKD. We derive the private classical capacity of a Gaussian sub-channel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one-way and two-way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.

Feng Wang, Ming‐Xing Luo, Hui-Ran Li +2 more

László Gyöngyösi, Sándor Imre

Summary We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution CVQKD. In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier continuous variables (CVs). The multicarrier communication formulates Gaussian subchannels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single‐carrier Gaussian CVs. We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD. We derive the private classical capacity of a Gaussian subchannel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one‐way and two‐way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.