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

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.

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