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Laser Physics

A simple coherent attack and practical security of differential phase shift quantum cryptography

Dmitry Anatolevich Kronberg

Published Jan 17, 2014• 10 citations
Publisher

Abstract

The differential phase shift quantum key distribution protocol reveals good security against such powerful attacks as unambiguous state discrimination and beam splitting attacks. Its complete security analysis is complex due to high dimensions of the supposed spaces and density operators. In this paper, we consider a particular and conceptually simple coherent attack, available in practical implementations. The main condition for this attack is the length of used coherent state tuples of order 8–12. We show that under this condition, no high level of practical distance between legitimate users can be achieved.

DOI
10.1088/1054-660x/24/2/025202

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The differential phase shift quantum key distribution protocol reveals good security against such powerful attacks as unambiguous state discrimination and beam splitting attacks. Its complete security analysis is complex due to high dimensions of the supposed spaces and density operators. In this paper, we consider a particular and conceptually simple coherent attack, available in practical implementations. The main condition for this attack is the length of used coherent state tuples of order 8–12. We show that under this condition, no high level of practical distance between legitimate users can be achieved.
The analysis is based on the error rate and the secure communication rate as functions of distance for three quantum-key-distribution (QKD) protocols: the Bennett–Brassard 1984, the Bennett–Brassard–Mermin 1992, and the coherent differential-phase-shift keying (DPSK) protocols. We consider the secure communication rate of the DPSK protocol against an arbitrary individual attack, including the most commonly considered intercept-resend and photon-number splitting attacks, and concluded that the simple and efficient differential-phase-shift-keying protocol allows for more than 200 km of secure communication distance with high communication rates.
In the well-established framework of quantum key distribution (QKD), differential phase shift (DPS) protocols have known information-theoretic security bounds defining tolerable error rates under optimal adversaries. In this work, we revisit the security of 3- and nnn -pulse DPS QKD by explicitly analyzing two specific, physically implementable individual attacks: minimum error discrimination (MED) and quantum cloning. Using semidefinite programming, we characterize these attacks in detail and quantify their induced quantum bit error rates (QBER) and resulting secure key rates under realistic system assumptions. The critical QBER thresholds for these attacks are approximately 20%, significantly higher than the theoretical lower bounds of 6% for individual and 4% for coherent attacks, indicating these are suboptimal adversarial strategies. This study primarily serves as a practical exercise to benchmark known attacks, providing explicit measures that aid experimental validation, protocol calibration, and risk assessment within current technological capabilities. Additionally, we explore finite-size effects and the effectiveness of phase randomization in weak coherent source-based protocols as protection against unambiguous state discrimination attacks.
The performance of a two-way quantum-key-distribution (QKD) system are analyzed using the differential-phase-shift keying (DPSK) protocol. The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984, the Bennett-Brassard-Mermin 1992, and the coherent differential-phase-shift keying protocols. We discussed the security of DPSK protocol against any type of individual photon splitting attack and concluded that the simple and efficient DPSK protocol allows for more than 200km of secure communication distance with high communication rates.
We investigate limitations imposed by sequential attacks on the performance of differential-phase-shift quantum key distribution protocols that use pulsed coherent light. In particular, we analyze two sequential attacks based on unambiguous state discrimination and minimum error discrimination, respectively, of the signal states emitted by the source. Sequential attacks represent;I special type of intercept-resend attacks and, therefore, they provide ultimate upper bounds on the maximal distance achievable by quantum key distribution schemes.