Practical quantum digital signature

Hua-Lei Yin, Yao Fu, and Zeng-Bing Chen

Phys. Rev. A 93, 032316 – Published 11 March 2016

Abstract

Guaranteeing nonrepudiation, unforgeability as well as transferability of a signature is one of the most vital safeguards in today's e-commerce era. Based on fundamental laws of quantum physics, quantum digital signature (QDS) aims to provide information-theoretic security for this cryptographic task. However, up to date, the previously proposed QDS protocols are impractical due to various challenging problems and most importantly, the requirement of authenticated (secure) quantum channels between participants. Here, we present the first quantum digital signature protocol that removes the assumption of authenticated quantum channels while remaining secure against the collective attacks. Besides, our QDS protocol can be practically implemented over more than 100 km under current mature technology as used in quantum key distribution.

Received 8 June 2015
Revised 16 September 2015

DOI:https://doi.org/10.1103/PhysRevA.93.032316

Physics Subject Headings (PhySH)

Quantum algorithms Quantum communication Quantum cryptography

Quantum Information, Science & Technology

Authors & Affiliations

Hua-Lei Yin^*, Yao Fu^†, and Zeng-Bing Chen^‡

Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and The CAS Center for Excellence in QIQP and the Synergetic Innovation Center for QIQP, University of Science and Technology of China, Hefei, Anhui 230026, China

^*hlyin@mail.ustc.edu.cn
^†yaofu@mail.ustc.edu.cn
^‡zbchen@ustc.edu.cn

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Vol. 93, Iss. 3 — March 2016

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Images

Figure 1
Practical implementation of the three-participant QDS protocols. Alice's setups for Scheme I (II) are shown, respectively, on the upper (lower) panel on the left. For the parts of Bob and Charlie, the setups are located on the right, which are shared by both schemes. AM, amplitude modulator used to prepare the decoy state; PM, polarization modulator used to prepare polarization states or active basis selection; BS, 50:50 beam splitter used to prepare two copies of the quantum states; PBS, polarization beam splitter; D1-D4, single-photon detectors.
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Figure 2
Signature rates versus total secure transmission distance. For simulation purposes, we employ the following experimental parameters: the intrinsic loss coefficient of the ultralow-loss telecom fiber channel is 0.160 $dB {km}^{- 1}$ [22]. For superconducting nanowire single-photon detectors, the detection efficiency is 93% and the dark count rate is $1.0 \times 10^{- 7}$ [28]. The quantum bit error rate between Alice's and Bob's (Charlie's) system is $E ≃ 1.0 %$ . The ratio of random sampling is $β = M_{t} / M = 30 %$ . The security (robustness) bound is $ɛ_{sec} < 1.0 \times 10^{- 5}$ ( $ɛ_{rob} < 1.0 \times 10^{- 6}$ ). The verification and authentication thresholds ${T_{v}, T_{a}}$ of two-photon six-state (four-state) QDS is ${6.45 %, 1.50 %}$ ( ${4.05 %, 1.20 %}$ ); ${T_{v}, T_{a}}$ of six-state and four-state QDS in Schemes I (II) are ${4.07 %, 1.17 %}$ ( ${4.275 %, 1.20 %}$ ) and ${3.46 %, 1.12 %}$ ( ${3.44 %, 1.12 %}$ ), respectively. The intensities of six-state QDS for Scheme I are $μ = 0.34$ , $ν = 0.16$ , $ω = 0.01$ , and 0. The probabilities of six-state QDS for Scheme I are $P_{μ} = 55 %$ , $P_{ν} = 25 %$ , $P_{ω} = 18 %$ , and $P_{0} = 2 %$ . The intensities of four-state QDS for Scheme I are $μ = 0.12$ , $ν = 0.08$ , $ω = 0.008$ , and 0. The probabilities of four-state QDS for Scheme I are $P_{μ} = 52 %$ , $P_{ν} = 23 %$ , $P_{ω} = 23 %$ , and $P_{0} = 2 %$ . The intensities of six-state QDS for Scheme II are $μ_{1} = 0.17$ , $ν_{1} = 0.08$ , and 0. The probabilities of six-state QDS for Scheme II are $P_{μ_{1} μ_{1}} = 57 %$ , $P_{0, μ_{1}} = 1 %$ , $P_{μ_{1}, 0} = 1 %$ , $P_{ν_{1}, ν_{1}} = 30 %$ , $P_{0, ν_{1}} = 5 %$ , $P_{ν_{1}, 0} = 5 %$ , and $P_{00} = 1 %$ . The intensities of four-state QDS for Scheme II are $μ_{1} = 0.075$ , $ν_{1} = 0.04$ , and 0. The probabilities of four-state QDS for Scheme II are $P_{μ_{1} μ_{1}} = 60 %$ , $P_{0, μ_{1}} = 1 %$ , $P_{μ_{1}, 0} = 1 %$ , $P_{ν_{1}, ν_{1}} = 27 %$ , $P_{0, ν_{1}} = 5 %$ , $P_{ν_{1}, 0} = 5 %$ , and $P_{00} = 1 %$ .
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Figure 3
Schematic representation of different bit strings. The left black frame (right yellow frame) rectangle represents the string of test (untested) bits. The horizontal red shadow (vertical blue shadow) represents the bit string of Bob's (Charlie's) conclusive results.
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