论文标题
从删除渠道中的信息理论难题到量子密码学的可否认性
From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography
论文作者
论文摘要
从无内存的删除通道产生的输出，其均匀随机输入已知长度$ n $，一个人在通道输入上获得后分布。该分布的香农熵与统一先前的熵之间的差异衡量了由长度$ m $输出传达的通道输入的信息。我们首先是根据实验数据的猜想，即后端的熵通过恒定字符串$ \ texttt {000} \ ldots $，$ \ texttt {111} \ ldots $最小化，并通过交替的字符串$ \ texttt {0101}} {0101} \ ldots $ $ \ $ \ \ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \;我们介绍了涉及二进制（子/超级）序列的相关组合定理，并证明了使用聚类技术的单个和双重删除的最小熵构。然后，我们使用隐藏单词统计的结果来证明在渐近极限中的最小化猜想，通过显示Flajolet，Szpankowski和Vallée的分析 - 组合方法如何依赖于生成功能，可以应用于固定输出长度和$ n \ rightarrow \ rightarrow \ rightarrow \ iffty $。 接下来，我们重新审视量子密钥交换（QKE）中可否认性的概念。我们介绍并形式化了胁迫者必需的QKE的概念。然后，我们建立了秘密通信与否定性之间的联系，以提出DC-QKE，DC-QKE是一种简单且可证明的可胁迫人必需QKE的构造。我们将否定性与量子信息理论中的基本概念联系起来，并提出了一种基于纠缠蒸馏以实现信息理论可否认性的通用方法，然后分析其他紧密相关的结果，例如无条件安全的量子位承诺和否认性的不可能之间的关系。最后，我们基于完全同态加密提出了有效的抗胁迫和量子安全投票方案。
From the output produced by a memoryless deletion channel with a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that of the uniform prior measures the amount of information about the channel input which is conveyed by the output of length $m$. We first conjecture on the basis of experimental data that the entropy of the posterior is minimized by the constant strings $\texttt{000}\ldots$, $\texttt{111}\ldots$ and maximized by the alternating strings $\texttt{0101}\ldots$, $\texttt{1010}\ldots$. We present related combinatorial theorems involving binary (sub/super)-sequences and prove the minimal entropy conjecture for single and double deletions using clustering techniques. We then prove the minimization conjecture in the asymptotic limit using results from hidden word statistics by showing how the analytic-combinatorial methods of Flajolet, Szpankowski and Vallée, relying on generating functions, can be applied to resolve the case of fixed output length and $n\rightarrow\infty$. Next, we revisit the notion of deniability in quantum key exchange (QKE). We introduce and formalize the notion of coercer-deniable QKE. We then establish a connection between covert communication and deniability to propose DC-QKE, a simple and provably secure construction for coercer-deniable QKE. We relate deniability to fundamental concepts in quantum information theory and suggest a generic approach based on entanglement distillation for achieving information-theoretic deniability, followed by an analysis of other closely related results such as the relation between the impossibility of unconditionally secure quantum bit commitment and deniability. Finally, we present an efficient coercion-resistant and quantum-secure voting scheme, based on fully homomorphic encryption.
