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arXiv:2102.10228

$\mathcal{PT}$-Symmetric Quantum State Discrimination for Attack on BB84 Quantum Key Distribution

Yaroslav Balytskyi, Manohar Raavi, Anatoliy O. Pinchuk, Sang‐Yoon Chang

Published Feb 20, 2021• 0 citations
arXivHTMLPDF

Abstract

Quantum Key Distribution or QKD provides symmetric key distribution using the quantum mechanics/channels with new security properties. The security of QKD relies on the difficulty of the quantum state discrimination problem. We discover that the recent developments in $\mathcal{PT}$ symmetry can be used to expedite the quantum state discrimination problem and therefore to attack the BB84 QKD scheme. We analyze the security of the BB84 scheme and show that the attack significantly increases the eavesdropping success rate over the previous Hermitian quantum state discrimination approach. We design and analyze the approaches to attack BB84 QKD protocol exploiting an extra degree of freedom provided by the $\mathcal{PT}$-symmetric quantum mechanics.

DOI
10.48550/arxiv.2102.10228

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Quantum Key Distribution or QKD provides symmetric key distribution using the quantum mechanics/channels with new security properties. The security of QKD relies on the difficulty of the quantum state discrimination problem. We discover that the recent developments in PT\mathcal{PT}PT symmetry can be used to expedite the quantum state discrimination problem and therefore to attack the BB84 QKD scheme. We analyze the security of the BB84 scheme and show that the attack significantly increases the eavesdropping success rate over the previous Hermitian quantum state discrimination approach. We design and analyze the approaches to attack BB84 QKD protocol exploiting an extra degree of freedom provided by the PT\mathcal{PT}PT-symmetric quantum mechanics.
Classical cryptographic systems are increasingly challenged by advances in computing power and new algorithmic techniques, particularly with the rise of quantum computing, which threatens the security of current encryption methods. This has spurred interest in quantum-resistant cryptography, aimed at creating algorithms that can withstand attacks from quantum computers. Traditionally, secure key transport over alternate channels has been a significant challenge, but quantum mechanics offers a solution. Quantum Key Distribution (QKD) is a revolutionary method for secure communication that leverages quantum principles. Unlike traditional methods, QKD provides unconditional security, with key security ensured by the laws of physics rather than computational difficulty. The BB84 protocol, introduced in 1984 by Bennett and Brassard, is a leading QKD scheme known for its simplicity and effectiveness in generating eavesdropping-resistant cryptographic keys. It facilitates secure key transport over alternate channels. This documentation aims to advance QKD security by practically implementing and analyzing the BB84 protocol. Through detailed theoretical analysis, simulation studies, and experimental validation, the practical impacts, and limitations of BB84-based QKD systems are examined. Additionally, a practical implementation of quantum key distribution using a sudoku key demonstrates the process's simplicity and effectiveness. These findings are expected to pave new paths in the field of cryptanalysis in the emerging Quantum Age.
Quantum Key Distribution (QKD) provides an innovative approach for secure communication by utilizing the principles of quantum mechanics. Among various QKD protocols, the BB84 protocol remains the most widely studied and implemented due to its simplicity and theoretical security guarantees. However, practical implementations of BB84 are vulnerable to several eavesdropping attacks and channel imperfections. This paper presents a comprehensive study on the detection and analysis of eavesdropping attacks in the BB84 protocol. The work focuses on common attacks such as intercept-resend attack, photon-number splitting attack, Trojan horse attack, and phase-covariant cloning attack. The effect of these attacks on Quantum Bit Error Rate (QBER) is analyzed in detail. Simulation-based observations are discussed to demonstrate how QBER increases under malicious interference. The study further explores statistical methods for detecting eavesdropping and examines practical countermeasures including decoy states, privacy amplification, and error correction techniques. The paper concludes that BB84 remains robust against eavesdropping when proper detection and mitigation mechanisms are employed.
Abstract Quantum key distribution (QKD) has a promise of unconditionally secure communication between the remote sides. The real-world QKD implementations, however, have numerous loopholes, both of engeneering and physical origin, and compromise the security promise. In this work, we investigate two attack strategies on the passive side channel of the light source along with the optimal cloning attack on the BB84 protocol with decoy-states. We calculate an upper bound of a secret key rate for these situations and show that the joint measurement attack on the signal and side channel degree of freedom is more effective to the adversary.
Standard security proofs of quantum-key-distribution (QKD) protocols often rely on symmetry arguments. In this paper, we prove the security of a three-state protocol that does not possess rotational symmetry. The three-state QKD protocol we consider involves three qubit states, where the first two states $\ensuremath{\mid}{0}_{z}⟩$ and $\ensuremath{\mid}{1}_{z}⟩$ can contribute to key generation, and the third state $\ensuremath{\mid}+⟩=(\ensuremath{\mid}{0}_{z}⟩+\ensuremath{\mid}{1}_{z}⟩)∕\sqrt{2}$ is for channel estimation. This protocol has been proposed and implemented experimentally in some frequency-based QKD systems where the three states can be prepared easily. Thus, by founding on the security of this three-state protocol, we prove that these QKD schemes are, in fact, unconditionally secure against any attacks allowed by quantum mechanics. The main task in our proof is to upper bound the phase error rate of the qubits given the bit error rates observed. Unconditional security can then be proved not only for the ideal case of a single-photon source and perfect detectors, but also for the realistic case of a phase-randomized weak coherent light source and imperfect threshold detectors. Our result in the phase error rate upper bound is independent of the loss in the channel. Also, we compare the three-state protocol with the Bennett-Brassard 1984 (BB84) protocol. For the single-photon source case, our result proves that the BB84 protocol strictly tolerates a higher quantum bit error rate than the three-state protocol, while for the coherent-source case, the BB84 protocol achieves a higher key generation rate and secure distance than the three-state protocol when a decoy-state method is used.
As quantum computing threatens classical cryptography like RSA via Shor's algorithm, Quantum Key Distribution (QKD)—especially BB84—offers physics-based security. BB84 leverages quantum principles: Heisenberg Uncertainty, No-Cloning Theorem, and superposition, shifting from math complexity to unbreakable physical laws using polarized photons for key exchange. The protocol detects eavesdropping through Quantum Bit Error Rate (QBER), showing 25% errors in Intercept-Resend attacks. Key challenges like Photon Number Splitting (PNS) attacks are addressed via decoy states. Compared to B92 and E91, BB84 balances feasibility and security best. Despite issues like signal loss, BB84 provides provably secure communication, restoring trust in a post-quantum world.
Abstract Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users.