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Laser Physics Letters

On the secrecy of a simple and effective implementation of BB84 quantum cryptography protocol

S. N. Molotkov

Published May 31, 2019• 11 citations
Publisher

Abstract

Abstract A simple and effective fiber implementation of the BB84 protocol is proposed, which does not use phase modulators at the receiving side and do not require adjustment of the polarization state at the output of the communication channel. The implementation of the protocol permits to prove of the secrecy of keys based on the fundamental entropic uncertainty relations. The secret key length is expressed only in terms of the values observed on the reception side, with various detector parameters, such as quantum efficiency and the probability of dark counts, are taken into account automatically for the secret key length, but implicitly in terms of the observed parameters.

DOI
10.1088/1612-202x/ab189b

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Abstract A simple and effective fiber implementation of the BB84 protocol is proposed, which does not use phase modulators at the receiving side and do not require adjustment of the polarization state at the output of the communication channel. The implementation of the protocol permits to prove of the secrecy of keys based on the fundamental entropic uncertainty relations. The secret key length is expressed only in terms of the values observed on the reception side, with various detector parameters, such as quantum efficiency and the probability of dark counts, are taken into account automatically for the secret key length, but implicitly in terms of the observed parameters.
Quantum cryptography has attracted much recent attention due to its potential for providing secret communications that cannot be decrypted by any amount of computational effort. This is the first analysis of the secrecy of a practical implementation of the BB84 protocol that simultaneously takes into account and presents the full set of analytical expressions for effects due to the presence of pulses containing multiple photons in the attenuated output of the laser, the finite length of individual blocks of key material, losses due to error correction, privacy amplification, and authentication, errors in polarization detection, the efficiency of the detectors, and attenuation processes in the transmission medium. The analysis addresses eavesdropping attacks on individual photons rather than collective attacks in general. Of particular importance is the first derivation of the necessary and sufficient amount of privacy amplification compression to ensure secrecy against the loss of key material which occurs when an eavesdropper makes optimized individual attacks on pulses containing multiple photons. It is shown that only a fraction of the information in the multiple photon pulses is actually lost to the eavesdropper.
Abstract A novel quantum key distribution (QKD) protocol is proposed, which uses six states of three states in two bases. The protocol provides a greater range of key distribution compared to known QKD protocols. The protocol has an accurate proof of secrecy based on fundamental entropy uncertainty relations, the use of which is possible with the entanglement version of the protocol. The implementation of the protocol does not require adjustment of the polarization state at the output of the communication line, since the receiving side does not use active polarization-sensitive elements—phase modulators, which virtually excludes active probing of the active elements of the system.
In real fiber-optic quantum cryptography systems, the avalanche photodiodes are not perfect, the source of quantum states is not a single-photon one, and the communication channel is lossy. For these reasons, key distribution is impossible under certain conditions for the system parameters. A simple analysis is performed to find relations between the parameters of real cryptography systems and the length of the quantum channel that guarantee secure quantum key distribution when the eavesdropper’s capabilities are limited only by fundamental laws of quantum mechanics while the devices employed by the legitimate users are based on current technologies. Critical values are determined for the rate of secure real-time key generation that can be reached under the current technology level. Calculations show that the upper bound on channel length can be as high as 300 km for imperfect photodetectors (avalanche photodiodes) with present-day quantum efficiency (η ≈ 20%) and dark count probability (p dark ∼ 10−7).
Abstract A proof of the secrecy of the quantum key distribution through an untrusted node is given. The use of entropy uncertainty relations allows us to obtain an exact solution for the length of the secret key in the single-photon case. Comparison with the exact solution for the BB84 protocol is made and the principal difference in the logical structure of the key secrecy proofs in these protocols is clearly shown, which, in our opinion, is important for the development of quantum cryptography systems.
Quantum cryptography, the principles of which are based on classical mechanics laws, solves exceptionally the issue of key distribution in classical cryptography. BB84, the first quantum key distribution created by Charles Bennett and Gilles Brassard in 1984 offers unconditional security and allows the transmission of a key with the length equal to the length of the message. According to Vernom, using the key with the above feature once together with an encryption algorithm leads to the formation of a most secure cryptographic system. The paper presents a method for improving the BB84 quantum protocol, using ten states of polarization, quantum memory and direct communication in both directions. The implementation of both the proposed method and the BB84 protocol was done through a C# application.