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SinkrOn

Finite-Key Analysis of BB84 and B92 QKD with Discrete Phase Randomization and Koashi Bound

Brenendra Putra Oktaviansyah, Totok Sutojo, Muhamad Akrom

Published Apr 2, 2026• 0 citations
Publisher

Abstract

Quantum Key Distribution (QKD) enables theoretically secure key exchange based on fundamental quantum principles such as the no-cloning theorem and Heisenberg’s uncertainty principle. However, practical implementations remain vulnerable to side-channel attacks caused by device imperfections, while many existing studies primarily analyze asymptotic security or isolated attack scenarios rather than realistic finite-key conditions. Unlike prior studies that focus on asymptotic or single-attack analyses, this work presents a comprehensive finite-key security evaluation of BB84 and B92 protocols under hybrid side-channel attacks using Discrete Phase Randomization (DPR) as a lightweight mitigation strategy and the Koashi bound for improved phase-error estimation in B92. Numerical simulations are performed using realistic system parameters with a finite-key size of 100 billion pulses across ten representative attack scenarios. The results show that applying DPR (M = 32) significantly suppresses phase-sensitive attack-induced errors, reducing the quantum bit error rate (QBER) from 11–50% to approximately 1.5–3.02%, thereby restoring practical secure key generation. B92 with the Koashi bound achieves secure transmission distance improvements from 181.6 km to 190.8 km without attacks and reaches 187.0 km under hybrid attacks with DPR, slightly exceeding BB84 in certain conditions. Peak secret key rates reach 0.1363 bit/pulse for BB84 and 0.0741 bit/pulse for B92. These findings demonstrate that non-orthogonal protocols can remain competitive under realistic finite-key constraints using practical mitigation techniques, although literature based induced QBER assumptions remain a limitation.

DOI
10.33395/sinkron.v10i2.15882

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Quantum Key Distribution (QKD) enables theoretically secure key exchange based on fundamental quantum principles such as the no-cloning theorem and Heisenberg’s uncertainty principle. However, practical implementations remain vulnerable to side-channel attacks caused by device imperfections, while many existing studies primarily analyze asymptotic security or isolated attack scenarios rather than realistic finite-key conditions. Unlike prior studies that focus on asymptotic or single-attack analyses, this work presents a comprehensive finite-key security evaluation of BB84 and B92 protocols under hybrid side-channel attacks using Discrete Phase Randomization (DPR) as a lightweight mitigation strategy and the Koashi bound for improved phase-error estimation in B92. Numerical simulations are performed using realistic system parameters with a finite-key size of 100 billion pulses across ten representative attack scenarios. The results show that applying DPR (M = 32) significantly suppresses phase-sensitive attack-induced errors, reducing the quantum bit error rate (QBER) from 11–50% to approximately 1.5–3.02%, thereby restoring practical secure key generation. B92 with the Koashi bound achieves secure transmission distance improvements from 181.6 km to 190.8 km without attacks and reaches 187.0 km under hybrid attacks with DPR, slightly exceeding BB84 in certain conditions. Peak secret key rates reach 0.1363 bit/pulse for BB84 and 0.0741 bit/pulse for B92. These findings demonstrate that non-orthogonal protocols can remain competitive under realistic finite-key constraints using practical mitigation techniques, although literature based induced QBER assumptions remain a limitation.
Quantum Key Distribution (QKD) is increasingly recognized as a robust solution to the vulnerabilities posed by quantum computing to classical encryption systems. This paper presents a comprehensive investigation of the BB84 protocol, the foundational QKD scheme, through simulated quantum communication using IBM’s Qiskit framework. The study models quantum key exchange under both ideal and adversarial conditions, including channel noise and intercept-resend attacks. The Quantum Bit Error Rate (QBER) was measured as a function of noise intensity and eavesdropping, confirming that QBER increases predictably in compromised channels. A threshold of 11% QBER was used to determine the viability of secure key generation. Final key retention rates were analyzed across multiple channel scenarios, revealing BB84’s sensitivity to both photon loss and adversarial interference.\n\nSecurity vulnerabilities such as photon-number-splitting and detector blinding were assessed, and countermeasures including decoy-state protocols and authenticated classical channels were proposed. Four key performance graphs were generated to visualize system behavior under realistic operational conditions. The results support BB84’s theoretical advantage in ensuring information-theoretic security while acknowledging real-world limitations in transmission range and hardware reliability. The paper concludes by addressing future improvements in QKD systems, including satellite-based distribution, quantum repeaters, and device-independent implementations. Through simulation-driven analysis, this study validates BB84 as a practical defense against quantum-enabled attacks and underscores the need for continued development and standardization in post-quantum cryptographic infrastructure.
We analyze the performance of quantum key distribution (QKD) protocols that rely on discrete phase randomization (DPR). For many QKD protocols that rely on weak coherent pulses (WCPs), continuous phase randomization is assumed, which simplifies the security proofs for such protocols. However, it is challenging to achieve such a perfect phase randomization in practice. As an alternative, we can select a discrete set of global phase values for WCPs, but we need to redo the security analysis for such a source. While security proofs incorporating DPR have been established for several QKD protocols, they often rely on computationally intensive numerical optimizations. To address this issue, in this study, we derive analytical bounds on the secret key generation rate of BB84 and measurement-device-independent QKD protocols in the DPR setting. Our analytical bounds closely match the results obtained from more cumbersome numerical methods in the regions of interest.
In the well-established framework of quantum key distribution (QKD), differential phase shift (DPS) protocols have known information-theoretic security bounds defining tolerable error rates under optimal adversaries. In this work, we revisit the security of 3- and nnn -pulse DPS QKD by explicitly analyzing two specific, physically implementable individual attacks: minimum error discrimination (MED) and quantum cloning. Using semidefinite programming, we characterize these attacks in detail and quantify their induced quantum bit error rates (QBER) and resulting secure key rates under realistic system assumptions. The critical QBER thresholds for these attacks are approximately 20%, significantly higher than the theoretical lower bounds of 6% for individual and 4% for coherent attacks, indicating these are suboptimal adversarial strategies. This study primarily serves as a practical exercise to benchmark known attacks, providing explicit measures that aid experimental validation, protocol calibration, and risk assessment within current technological capabilities. Additionally, we explore finite-size effects and the effectiveness of phase randomization in weak coherent source-based protocols as protection against unambiguous state discrimination attacks.
Secure communication has become essential due to the rapid increase in cyber-attacks and data security threats in modern networks. Traditional communication systems mainly rely on classical security methods, which may become vulnerable to advanced attacks. Quantum Key Distribution (QKD) improves secure communication by generating cryptographic keys using quantum principles, making key interception extremely difficult. In this work, a Quantum Random Number Generator (QRNG) is integrated with classical communication to develop a hybrid quantum-classical communication framework. The QRNG generates highly random bits that improve authentication, randomness, and key security. The proposed system compares three QKD protocols: BB84, B92, and E91 using different bit sizes of 8000, 10000, and 13000 bits. The protocols are evaluated using important metrics such as QBER, key rate, entropy, erasure rate, throughput, and correlation. Experimental results show that all protocols achieved entropy values close to 1 and correlation values near zero, indicating strong randomness and secure key generation. Among the evaluated protocols, E91 achieved lower QBER values and higher key rates, while BB84 showed stable and reliable performance. B92 produced comparatively higher error rates under similar conditions. The throughput remained nearly 278–281 bits/sec across all experiments. A ranking-based analysis confirmed that E91 provides the best balance between security, efficiency, and communication performance, making it suitable for future quantum-secure communication systems.
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.
Mode-pairing quantum key distribution (MP-QKD) protocol achieves performance beyond the repeaterless rate-transmittance bound and exhibits excellent practicality by avoiding the requirement for difficult global phase locking. However, the source side of MP-QKD still relies on the assumption of continuous phase randomization, an experimentally infeasible requirement in practice. Therefore, the practical security of the protocol cannot be fully guaranteed. In this work, we propose a discrete-phase-randomized mode-pairing quantum key distribution (DPR-MP-QKD) protocol and analyze the basis-dependence of the source side. Then, we introduce a concrete discrete version of the decoy state method that ensures the security of the DPR-MP-QKD protocol. Finally, simulation results indicate that as the number of discrete phases increases, the key rate performance of DPR-MP-QKD progressively approaches that of the continuous case, with convergence achieved at approximately 14 discrete phases. Moreover, our approach drastically lowers the demand for randomness. While conventional continuous phase randomization demands an unlimited supply of random bits, we show that merely a few bits (e.g., 4) are adequate.