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AIP conference proceedings

Influence of the Correlation by Beam Splitting in YK Protocol QKD System

Masao Osaki

Published Jan 1, 2004• 0 citations
Publisher

Abstract

The quantum key distribution (QKD) system can provide the absolutely secure communication for distant users [C. H. Bennett and G. Brassard, Proc. of the IEEE Int. Conf. on Computers, Systems, and Signal Processing, pp. 175–179, 1984]. But it requires single photon sources, highly sensitive detectors, and newly constructed quantum channel between the legitimate users. On the other hand, classical (or quantum) noise based key distribution system is one of the candidates to realize the key distribution system with today’s technology [U. M. Maurer, IEEE Trans. Inform. Theory, 39, No.3, pp.733–742, 1993, H. P. Yuen and A. M. Kim, Phys. Lett. A, 241, pp.135–138, 1998]. In such a system, the independence of the noise between a legitimate receiver and an eavesdropper is presupposed. For long haul distant communication, however, amplification of the carrier is indispensable. This amplification process generates correlated fluctuations between them.We analyze how much correlation occurs when a coherent state is amplified and split. Then, the influence on the security level is shown in contrast to the non correlated case.

DOI
10.1063/1.1834447

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The quantum key distribution (QKD) system can provide the absolutely secure communication for distant users [C. H. Bennett and G. Brassard, Proc. of the IEEE Int. Conf. on Computers, Systems, and Signal Processing, pp. 175–179, 1984]. But it requires single photon sources, highly sensitive detectors, and newly constructed quantum channel between the legitimate users. On the other hand, classical (or quantum) noise based key distribution system is one of the candidates to realize the key distribution system with today’s technology [U. M. Maurer, IEEE Trans. Inform. Theory, 39, No.3, pp.733–742, 1993, H. P. Yuen and A. M. Kim, Phys. Lett. A, 241, pp.135–138, 1998]. In such a system, the independence of the noise between a legitimate receiver and an eavesdropper is presupposed. For long haul distant communication, however, amplification of the carrier is indispensable. This amplification process generates correlated fluctuations between them.We analyze how much correlation occurs when a coherent state is amplified and split. Then, the influence on the security level is shown in contrast to the non correlated case.
Abstract Ideal quantum key distribution (QKD) protocols require perfect single photon sources, detectors, and lossless channels. However, the present technology cannot ensure all of the requirements. Among the variants of practical QKD schemes, decoy state QKD in its present form approaches nearly the theoretical security. In any decoy state method, a compromise is made between the security of the key distribution and the rate of key generation by optimizing the two major protocol parameters: the number of decoy states and their relative intensities, and the length of the data string as well. Use of more number of decoy states and higher range of intensities though improve security, their optimization becomes too complex. Therefore, from practical consideration, some restrictions are to be imposed on the choice of decoy states and their intensities. In addition, the treatment of correlations among the laser pulses in security analysis is not fully understood. Normally, lack of correlations or randomness among the signal states is considered to gain security, but, in a different approach, described in the proposed protocol, additional correlation is introduced to improve key generation rate without compromising security. To do that, a one-way function is shared among the legitimate users to provide a semi-random choice of bases depending on the outcome of the receiver’s detector. The initial communication is made through a set of bits with predefined bases and intensity distribution. Then, with the help of the positive outcome of the receiver’s detector, the basis set as well as the length of the bit string for subsequent communications are computed. This results in correlation among the bases and the relative intensities of the signal states and provides a self-checking mechanism to identify eavesdropping. The security analysis of the protocol provides a low error rate and a relatively high key generation rate.
In theory, quantum key distribution (QKD) provides unconditionally secure keys due to the laws of quantum mechanics. However, real-world QKD systems often use strongly attenuated lasers which enables the photon number splitting (PNS) attack. Decoy state protocols weaken an eavesdropper’s chance to perform the compromising PNS attack undetected. In small multi-user QKD networks the photons can be distributed to the users via passive beam splitters. This approach lowers the sender-to-receiver QKD channel efficiency (relative to a standard point-to-point QKD system) and reduces the mean photon number in the sender-to-receiver channel. For this contribution, we investigated the performance of decoy state protocols in a passive multi-user system. We compared this point-to-multipoint setup to a standard point-to-point system by checking the photon number dependent yields, hereby showing that with some restrictions such a system would be safe against the PNS attack.
The performance of a practical quantum key distribution (QKD) system is often limited by the multi-photon state emission of its source and the dark counts of its detectors. Here, we present two methods to improve its performance. The first method is decoy state QKD: the sender randomly sends out weak coherent states with various average photon numbers (which are named as signal state and decoy states). In [14,15], we have performed the first experimental implementation of decoy state QKD over 15km and 60km respectively, thus dramatically increasing the distance and secure key generation rate of practical QKD systems. Our work has been followed up by many research groups worldwide [16-18]. The second scheme is QKD with "dual detectors" [19]: the legitimate receiver randomly uses either a fast (but noisy) detector or a quiet (but slow) detector to measure the incoming quantum signals. The measurement results from the quiet detector can be used to upper bound the eavesdropper's information, while the measurement results from the fast detector are used to generate a secure key. We applied this idea to various QKD protocols. Simulation results demonstrated significant improvements in both BB84 protocol with ideal single photon source and Gaussian-modulated coherent states protocol.
Cryptographic world has faced multiple challenges that are included in encoding and decoding transmitting information into a secure communication channel. Quantum cryptography may be another generation of the cryptography world, which is based on the law of physics. After decades of using the classical cryptography, there is an essential need to move a step forward through the most trusted systems, especially enormous amount of data flows through billions of communicating channels (e.g. The internet), and keeping this transmitting information away from eavesdropping is obligatory. Moreover, quantum cryptography has proved its standing against many weaknesses in the classical cryptography. One of these weaknesses is the ability to copy any type of information using a passive attack without an interruption, which is impossible in the quantum system. Theoretically, several quantum observables are utilized to diagnose an action of one particle. These observables are included in measuring mass, movement, speed, etc. The polarization of one photon occurs normally and randomly in the space. Any interruption that happens during sending of a light will cause a deconstruction of the light polarization. Therefore, particles’ movement in a three-dimensional space is supported by Non-Cloning theory that makes eavesdroppers unable to interrupt a communication system. In case an eavesdropper tried to interrupt a photon, the photon will be destroyed after passing the photon into a quantum detector or any measurement device. In the last decades, many Quantum Key Distribution (QKD) protocols have been created to initiate a secret key during encoding and decoding transmitted data operations. Some of these protocols were proven un-secure based on the quantum attacks that were released early. Even though the power of physics is still active and the Non-Cloning theory is unbroken, some QKD protocols failed during the security measurements. The main reason of the failure is based on the inability to provide the authentication between the end users during the quantum and classical channels. The proposed QKD protocol was designed to utilize some advantages of quantum physics as well as solid functions that are used in the classical cryptography. The authentication is a requirement during different communication channels, where both legitimate parties must confirm their identities before starting to submit data (plain-text). Moreover, the protocol uses most needed scenarios to finish the communication without leaking important data. These scenarios have been approved in existing QKD protocols either by classical or quantum systems. The matrix techniques also are used as a part of the preparation of the authentication key, where the end users communicate by an EPR (related to Einstein, Podolsky, and Rosen theory in 1935) channel. The EPR channel will be supported by an entanglement of particles. If the EPR communication succeeded, transferring the converted plain-text is required. Finally, both end users will have an authenticated secret key, and the submission will be done without any interruption.
Cryptography has begun its journey into the field of quantum information theory. Classical cryptography has shown weaknesses, which may be exploited in the future, either by development in mathematics, or by quantum computers. Quantum key distribution (QKD) is a promising path for cryptography to enable secure communication in the future. Although the theory of QKD promises absolute security, the reality is that current quantum crypto systems have flaws in them, as perfect devices have proven impossible to build. However, this can be taken into account in security proofs to ensure security, even with flaws. Security loopholes in QKD systems are being discovered as development progresses. Nevertheless, the system being built at NTNU is intended to address them all, creating a totally secure system. During this thesis, work was continued assembling the interferometer which is the basis for encoding qubits. It was fully connected on an optical table, and interference was obtained. Concerning theoretical work, calculations for a photon source specific parameter was carried out. It consisted of expanding previous framework and applying the results in both an established security proof, and a recent generalization of this proof. Two source effects were in focus, the lasers random phase and its fluctuating pulse intensity. Where analytical derivation was no longer possible, Matlab was used for numerical calculations. Under the conditions of the framework and proofs this thesis lies on, randomized phase turned out to have a negligible improvement over the case of non-random phase. Fluctuating amplitude showed a larger effect, reducing system performance. The input parameters were extreme, thus in a realistic situation it should not affect system performance significantly. However, these fluctuations must be taken into account when proving system security.
We consider the security of the BB84 (Bennett and Brassard 1984 Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing pp 175–9), six-state (Bruß 1998 Phys. Rev. Lett. 81 3018 ) and SARG04 (Scarani et al 2004 Phys. Rev. Lett. 92 057901 ) quantum key distribution protocols when the eavesdropper does not have access to a quantum memory. In this case, Eve’s most general strategy is to measure her ancilla with an appropriate positive operator-valued measure designed to take advantage of the post-measurement information that will be released during the sifting phase of the protocol. After an optimization on all the parameters accessible to Eve, our method provides us with new bounds for the security of six-state and SARG04 against a memoryless adversary. In particular, for the six-state protocol we show that the maximum quantum bit error ratio for which a secure key can be extracted is increased from 12.6% (for collective attacks) to 20.4% with the memoryless assumption.