We investigate the security against the intercept/resend and translucent attacks on the quantum key distribution protocol based on the pre- and post-selection effect. In 2001, Bub proposed the quantum cryptography scheme, which was an application of the so-called mean king’s problem. We evaluate a probability that legitimate users cannot detect eavesdropper’s malicious acts for Bub’s protocol. We also estimate a probability that the eavesdropper guesses right at the random secret key one of the legitimate users tries to share with the other one. From rigorous mathematical and numerical analyses, we conclude that Bub’s protocol is weaker than the Bennett–Brassard protocol of 1984 (BB84) against both the intercept/resend and translucent attacks. Because Bub’s protocol uses a two-way quantum channel, the analyses of its security are tough to accomplish. We refer to their technical points accurately in the current paper. For example, we impose some constraints upon the eavesdropper’s strategies in order to let their degrees of freedom be small.

中文翻译：

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基于前后选择效应的量子密钥分发协议的拦截/重发和半透明攻击

我们研究了基于预选和后选效应对量子密钥分发协议的拦截/重发和半透明攻击的安全性。2001 年，Bub 提出了量子密码方案，这是对所谓的均值王问题的应用。我们评估了合法用户无法检测到窃听者对 Bub 协议的恶意行为的概率。我们还估计窃听者正确猜测合法用户之一试图与另一个用户共享的随机密钥的概率。通过严格的数学和数值分析，我们得出结论，Bub 的协议在拦截/重发和半透明攻击方面都比 1984 年的 Bennett-Brassard 协议 (BB84) 弱。因为 Bub 的协议使用双向量子通道，对其安全性的分析很难完成。我们在当前论文中准确地引用了他们的技术要点。例如，我们对窃听者的策略施加一些限制，以使他们的自由度很小。