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Laser Physics Letters

Tight finite-key analysis for two-parametric quantum key distribution

S. N. Molotkov

Published Feb 7, 2019• 8 citations
Publisher

Abstract

Abstract The analysis of a new two-parametric quantum cryptography protocol is presented. A fundamentally new feature of the protocol is that the detection of the eavesdropper occurs not only by the number of errors on the receiving side, but also by the number of photocounts in the control time slots. The second feature of this protocol is the fact that the protocol allows fiber implementation (Klimov et al 2018 Laser Phys. Lett . 15 075207), which does not use active optical elements (phase modulators and polarization controllers) on the receiving side.

DOI
10.1088/1612-202x/aafcaf

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Abstract The analysis of a new two-parametric quantum cryptography protocol is presented. A fundamentally new feature of the protocol is that the detection of the eavesdropper occurs not only by the number of errors on the receiving side, but also by the number of photocounts in the control time slots. The second feature of this protocol is the fact that the protocol allows fiber implementation (Klimov et al 2018 Laser Phys. Lett . 15 075207), which does not use active optical elements (phase modulators and polarization controllers) on the receiving side.
A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability.
A new family of two-parameter quantum key distribution protocols is discussed where eavesdropping is detected by using two parameters: bit error rate Q and photon count rate q in control time slots. When a single-photon source is used and mutually orthogonal states are prepared in each basis, the protocol’s maximum tolerable error rate for secure key distribution is the highest, reaching a theoretical upper limit of 50%. When the signal states emitted by the source of attenuated laser light include multiphoton coherent states, the protocol also guarantees secure key distribution over the longest distance as compared to other quantum cryptography systems, up to the channel length for which the channel losses are sufficiently high that all five-photon pulses can be blocked by an eavesdropper.
A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. It is shown that the maximum tolerable error rate for this protocol depends on the counting rate in the control time slot. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability.
This paper proposes a novel design and analyzes security performance of quantum key distribution (QKD) protocol over free-space optics (FSO). Unlike conventional QKD protocols based on physical characteristics of quantum mechanics, the proposed QKD protocol can be implemented on standard FSO systems using subcarrier intensity modulation binary phase shift keying and direct detection with a dual-threshold receiver. Under security constraints, the design criteria for FSO transmitter and receiver, in particular, the modulation depth and the selection of dual-threshold detection, respectively, is analytically investigated. For the security analysis, quantum bit error rate, ergodic secret-key rate, and final key-creation rate are concisely derived in novel closed-form expressions in terms of finite power series, taking into account the channel loss, atmospheric turbulence-induced fading, and receiver noises. Furthermore, Monte-Carlo simulations are performed to verify analytical results and the feasibility of the proposed QKD protocol.
This paper proposes a novel two-way free-space quantum key distribution (QKD) protocol, which can be implemented using standard free-space optical (FSO) systems with subcarrier intensity-modulation (SIM) binary phase-shift-keying (BPSK) and direct-detection (DD) receiver. Different eavesdropping threats, including unauthorized receiver, beam-splitting, and intercept-resend attacks, are considered in the security analysis of the proposed protocol. Under the constraints on security requirements, we analytically investigate the design criteria for transmitter and receiver, in particular, the intensity modulation depth at the transmitter and the dual-threshold setting of the receiver in two-way free-space QKD systems. Quantum bit error rate (QBER), the ergodic secret-key rate, and the probability of detecting eavesdropper of the proposed system are analytically derived in closed-form expressions, considering the atmospheric loss, turbulence, and receiver noises.