Internal losses in systems of quantum cryptography can be used at attacks by an eavesdropper. As a result, the security of keys cannot be ensured for a number of protocols. This problem can be solved by using geometrically uniform coherent states with a larger number of bases. The security of keys at the number of bases N b /2 = 4 and the number of states N b = 8 can be guaranteed even without the control of the intensity of input states.
Internal losses in systems of quantum cryptography can be used at attacks by an eavesdropper. As a result, the security of keys cannot be ensured for a number of protocols. This problem can be solved by using geometrically uniform coherent states with a larger number of bases. The security of keys at the number of bases N b /2 = 4 and the number of states N b = 8 can be guaranteed even without the control of the intensity of input states.
It has been shown that the coherent quantum cryptography protocol (Coherent One Way) and, correspondingly, fiber optic systems involving this protocol for quantum key distribution, are vulnerable to an attack with repeated measurements and do not guarantee the security of distributed keys in a communication channel with losses. The coherent quantum cryptography system is used in Switzerland as one of the key distribution channels in the framework of the network project SECOQC (SEcure COmmunications based on Quantum Cryptography). A critical attack with repeated measurements was missed when the cryptographic strength of this protocol was analyzed. The critical length of the communication channel has been determined; this is a value above which secure key distribution is certainly impossible. Beginning with the critical length, an eavesdropper knows the entire distributed key, does not introduce errors at the receiver end, and remains undetected. For typical parameters in a real system (the average photon number μ = 0.5 and the quantum efficiency of avalanche detectors η = 0.1, see N. Gisin, G. Ribordy, H. Zbinden, et al., arXiv:quant-ph/0411022 and D. Stucki, C. Barreiro, S. Fasel, et al., arXiv:quant-ph/08095264), the security of keys cannot be guaranteed even for a communication channel whose length is as small as wished.
Since a source of quantum states is not strictly single-photon and losses exist in a communication channel, an attack with unambiguous measurements is possible, leading to loss of security. The problem of the stability of quantum key distribution protocols in a channel with large losses is still unsolved. A radical solution of this problem has been proposed by completely excluding unambiguous measurements by an eavesdropper. The problem is solved by means of counting of classical reference pulses. The conservation of the number of classical sync pulses results in the impossibility of unambiguous measurements. In this case, losses in the communication channel are considered as a priori unknown and can vary during a series of messages.
Abstract The quantum key distribution protocol utilizing 8 geometrically uniform coherent states is considered. We analyze its security against a generalized photon-number-splitting attack. This protocol allows for several basis configurations, and we demonstrate that one of these configurations is more vulnerable. We also use the previously described methods for attack improvement, namely, modification of observable’s coefficients and using extra photon as assistance for increasing success probability.
It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of S.N. Molotkov [ JETP Lett. , 101 (8), 579 (2015) ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.
Since a strictly single-photon source is not yet available, in quantum cryptography systems, one uses, as information quantum states, coherent radiation of a laser with an average number of photons of μ ≈ 0.1–0.5 in a pulse, attenuated to the quasi-single-photon level. The linear independence of a set of coherent quasi-single-photon information states leads to the possibility of unambiguous measurements that, in the presence of losses in the line, restrict the transmission range of secret keys. Starting from a certain value of critical loss (the length of the line), the eavesdropper knows the entire key, does not make errors, and is not detected—the distribution of secret keys becomes impossible. This problem is solved by introducing an additional reference state with an average number of photons of μcl ≈ 103–106, depending on the length of the communication line. It is shown that the use of a reference state does not allow the eavesdropper to carry out measurements with conclusive outcome while remaining undetected. A reference state guarantees detecting an eavesdropper in a channel with high losses. In this case, information states may contain a mesoscopic average number of photons in the range of μ q ≈ 0.5–102. The protocol proposed is easy to implement technically, admits flexible adjustment of parameters to the length of the communication line, and is simple and transparent for proving the secrecy of keys.
Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.