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Volumn 7, Issue 7, 2007, Pages 639-664

Zero-error attacks and detection statistics in the coherent one-way protocol for quantum cryptography

Author keywords

Eavesdropping; Quantum cryptography; Quantum key distribution

Indexed keywords

ERROR STATISTICS;

EID: 34547535907     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (52)

References (39)
  • 9
    • 27144544067 scopus 로고    scopus 로고
    • B. Kraus, N. Gisin and R. Renner, Phys. Rev. Lett. 95, 080501 (2005); R. Renner, N. Gisin, B. Kraus, Phys. Rev. A 72, 012332 (2005)
    • B. Kraus, N. Gisin and R. Renner, Phys. Rev. Lett. 95, 080501 (2005); R. Renner, N. Gisin, B. Kraus, Phys. Rev. A 72, 012332 (2005)
  • 17
    • 85035299752 scopus 로고    scopus 로고
    • Attacks based on unambiguous state discrimination were first invented against BB84 and similar protocols: M. Dušek, M. Jahma, N. Lǔtkenhaus, Phys. Rev. A 62, 022306 (2000).
    • Attacks based on unambiguous state discrimination were first invented against BB84 and similar protocols: M. Dušek, M. Jahma, N. Lǔtkenhaus, Phys. Rev. A 62, 022306 (2000).
  • 18
    • 0142120515 scopus 로고    scopus 로고
    • They were generalized in: P. Raynal, N. Lütkenhaus, S.J. van Enk, Phys. Rev. A 68, 022308 (2003).
    • They were generalized in: P. Raynal, N. Lütkenhaus, S.J. van Enk, Phys. Rev. A 68, 022308 (2003).
  • 20
    • 34547552729 scopus 로고    scopus 로고
    • Usually, when speaking of USD measurements, the goal is to discriminate all the n possible states. Therefore the measurement has n+1 outcomes, which either identify the state unambiguously, or say that the discrimination was inconclusive, Such are in particular the USD attacks as defined in [16].
    • Usually, when speaking of USD measurements, the goal is to discriminate all the n possible states. Therefore the measurement has n+1 outcomes, which either identify the state unambiguously, or say that the discrimination was inconclusive, Such are in particular the USD attacks as defined in [16].
  • 21
    • 34547540439 scopus 로고    scopus 로고
    • The inconclusive result is a projection onto a subspace. If in this subspace there are still pulse sequences that are linearly independent from all the others as is the case in particular for the USD attacks under study in this paper, each of these sequences could then in turn be unambiguously discriminated with some probability
    • The inconclusive result is a projection onto a subspace. If in this subspace there are still pulse sequences that are linearly independent from all the others (as is the case in particular for the USD attacks under study in this paper), each of these sequences could then in turn be unambiguously discriminated with some probability.
  • 22
    • 34547512551 scopus 로고    scopus 로고
    • Note that this attack is not possible on the differential phase shift protocol [3] because there no empty pulses are used. But other USD attacks are possible, as studied in: M. Curty, L.-L. Zhang, H.-K. Lo, N. Lütkenhaus, Quant. Inf. Comput. 7, 665 (2007)
    • Note that this attack is not possible on the differential phase shift protocol [3] because there no empty pulses are used. But other USD attacks are possible, as studied in: M. Curty, L.-L. Zhang, H.-K. Lo, N. Lütkenhaus, Quant. Inf. Comput. 7, 665 (2007)
  • 23
    • 34547529611 scopus 로고    scopus 로고
    • If Bob's detectors have a dead time, the analysis of USD4a is more subtle, because the first non-empty pulse can be detected with the probability we have written in the main text; but the following pulse can be detected only if the first one has not been detected. This may introduce an asymmetry: the logical bit 1 may be detected more often than the logical bit 0. In the extreme case of bright pulses, the first non-empty pulse always triggers the detector, therefore only the logical bit 1 is detected. In the other extreme case, where Eve sends out a single photon, there is no asymmetry, because only one detection can take place.
    • If Bob's detectors have a dead time, the analysis of USD4a is more subtle, because the first non-empty pulse can be detected with the probability we have written in the main text; but the following pulse can be detected only if the first one has not been detected. This may introduce an asymmetry: the logical bit 1 may be detected more often than the logical bit 0. In the extreme case of bright pulses, the first non-empty pulse always triggers the detector, therefore only the logical bit 1 is detected. In the other extreme case, where Eve sends out a single photon, there is no asymmetry, because only one detection can take place.
  • 24
    • 34547552436 scopus 로고    scopus 로고
    • Of course, the fact that Eve forwards always a single photon can be verified by the absence of the expected coincidence counts in two or three of Bob's detectors. But this is not a serious concern: the probability of coincidence is small, and we can easily suppose that Eve sends sometimes a brighter pulse when she has a conclusive result in USD3. If she does so, she can reproduce the coincidence rates. Alice and Bob could still detect this attack by checking if the cases of coincidences are equally distributed among all possible bit and decoy sequences; but it is pointless to make such a detailed analysis here. Finally note that it may be advantageous for Eve to send other states that a single-photon state, for instance vacuum-substracted coherent states
    • Of course, the fact that Eve forwards always a single photon can be verified by the absence of the expected coincidence counts in two or three of Bob's detectors. But this is not a serious concern: the probability of coincidence is small, and we can easily suppose that Eve sends sometimes a brighter pulse when she has a conclusive result in USD3. If she does so, she can reproduce the coincidence rates. Alice and Bob could still detect this attack by checking if the cases of coincidences are equally distributed among all possible bit and decoy sequences; but it is pointless to make such a detailed analysis here. Finally note that it may be advantageous for Eve to send other states that a single-photon state, for instance vacuum-substracted coherent states.
  • 28
    • 34547547546 scopus 로고    scopus 로고
    • In the absence of empty decoy sequences, it never happens that three consecutive pulses are empty; two additional interferometers, checking the coherence across two and three time slots respectively, would then be enough to make USD attacks impossible
    • In the absence of empty decoy sequences, it never happens that three consecutive pulses are empty; two additional interferometers, checking the coherence across two and three time slots respectively, would then be enough to make USD attacks impossible.
  • 30
    • 34547499277 scopus 로고    scopus 로고
    • This is after Alice and Bob applied a random permutation on their qubit pairs and random bit-flip operations, and assuming they apply optimal error correction and privacy amplification. See [9] for details. Note that we don't consider here the possible classical preprocessing A' → A
    • This is after Alice and Bob applied a random permutation on their qubit pairs and random bit-flip operations, and assuming they apply optimal error correction and privacy amplification. See [9] for details. Note that we don't consider here the possible classical "preprocessing" A' → A.
  • 33
    • 26944451694 scopus 로고    scopus 로고
    • For untrusted-device scenario, see Ref. [14]; for the trusted-device scenario: A. Niederberger, V. Scarani, N. Gisin, Phys. Rev. A 71, 042316 (2005)
    • For untrusted-device scenario, see Ref. [14]; for the trusted-device scenario: A. Niederberger, V. Scarani, N. Gisin, Phys. Rev. A 71, 042316 (2005)
  • 36
    • 34547533300 scopus 로고    scopus 로고
    • The Holevo bound is computed here for the task of bitwise distinguishing the states. One can check that the Holevo bound remains the same if Eve tried to get information on longer strings of bits
    • The Holevo bound is computed here for the task of bitwise distinguishing the states. One can check that the Holevo bound remains the same if Eve tried to get information on longer strings of bits.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.