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Quantum Electronics

Role of intensity fluctuations in quantum cryptography with coherent states

Dmitry Anatolevich Kronberg, Yury Kurochkin

Published Sep 30, 2018• 15 citations
Publisher

Abstract

A new type of attack in quantum cryptography with coherent states is considered. This attack calls for only a possibility of changing (within some limits) the intensity of the states reaching a receiver. The critical quantum bit error rate (QBER) of the B92 protocol with a strong reference state is calculated for different limitations on intensity.

DOI
10.1070/qel16739

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A new type of attack in quantum cryptography with coherent states is considered. This attack calls for only a possibility of changing (within some limits) the intensity of the states reaching a receiver. The critical quantum bit error rate (QBER) of the B92 protocol with a strong reference state is calculated for different limitations on intensity.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
An attempt to eavesdrop a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, both in the two-state B92 and the four-state BB84 quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently form other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are included. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi information, and with respect only to bits received error-free by Bob. This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
The quantum cryptography has changed the landscape of the conventional cryptography theory and the field of security itself. The Quantum cryptography differs from the classical cryptography in the sense that data and the information are kept secret by the properties of quantum mechanics without importing any extra formulation. In case of classical cryptography the security is based on the conjecture difficulty of factoring and computing a special mathematical function. The first Quantum Key Distribution (QKD) protocol was proposed by C H Bennet and Brassard in 1984[1](BB84). In course of time many variants of QKD protocols have been proposed, all are basically based more or less in the same principle. In this paper role and the beauty of the Quantum Mechanics behind the QKD protocol have been unfolded and explained. The pros-and cons of the protocol have been analyzed in details. The quality of the QKD protocol is measured through a factor called QBER (Quantum Bit Error Rate). The bit error rate is an essential phenomena during the transmission of quantum bit along the quantum channel. Both quantum mechanical and mathematical analysis of QBER have been discussed in the paper. An empirical formula for QBER has been proposed too
In the last ten years, quantum computing has made substantial progress, presenting a strong challenge to traditional encryption methods that depend on solving discrete algorithmic problems. With the advent of the quantum era, conventional encryption methods are becoming more susceptible to attacks. This paper investigates possible attacks that exploit vulnerabilities in quantum cryptography, specifically investigating weaknesses in quantum key distribution (QKD) systems. The text thoroughly explores advanced attack strategies of photon number splitting highlight the existing vulnerabilities. The goal is to highlight the need for strong safeguards to protect against these threats, which requires continuous research and development to improve the robustness of quantum cryptography algorithms. The experimental investigation includes analyzing crucial parameters, including quantum channel length, loss, QKD protocol, quantum bit error rate (QBER), signal-to-noise ratio (SNR), as well as attack parameters such as probability of photon number splitting (PNS), eavesdropper distance, and detection efficiency. The evaluation includes performance indicators such as secure key rate, quantum bit error rate (QBER) vs distance, vulnerability to photon number splitting (PNS) attacks, and the influence on the pace of key generation.
The present thesis aimed to evaluate the efficiency and resilience of quantum cryptographic systems against malicious attacks, with emphasis on Quantum Key Distribution (QKD).Initially, fundamental concepts of quantum computing and quantum inform ation were examined, such as qubits, superposition, entanglement, decoherence and quantum gates, in order to establish the necessary theoretical background for the reader.Subsequently, key QKD protocols, such as BB84, E91, B92, BBM92 and Decoy-State techniques, were analyzed and compared in terms of security, practical applicability, and sensitivity to different categories of attacks.The methodology of the thesis was based on bibliographic and comparative analysis, using evaluation metrics such as Quantum Bit Error Rate (QBER), secret key generation rate, throughput, transmission distance, and channel losses.The analysis showed that simple theoretical attacks, such as intercept-resend, are usually more easily detectable due to an increase in QBER, whereas practical implementation attacks, such as detector blinding, time-shift, trojan-horse and photon-number-splitting attacks, can be more dangerous because they exploit device imperfections and do not always cause an obvious increase in errors.In conclusion, the theoretical security of QKD protocols is strong; however, their actual efficiency depends on the quality of implementation, technological limitations and the balance between protection and the final rate of secure key generation.