可逆提取器和窃听协议
Invertible Extractors and Wiretap Protocols
摘要：
窃听协议是一对随机化的编码和解码函数，使得对消息的编码的有界部分的知识基本上不揭示关于消息的信息，而对整个编码的知识使用解码器来揭示消息。在本文中，我们研究的概念，有效的可逆提取器，并表明，窃听协议可以构建这样的提取器。然后，我们将为符号固定，仿射和一般来源构建可逆提取器，并将其应用于创建窃听协议，并在其速率（消息长度与其编码的比率）和弹性（观察到的编码位置与编码长度的比率）之间进行渐近最佳权衡。然后，我们将应用我们的研究结果创建窃听协议具有挑战性的通信问题，如主动入侵者谁改变部分的编码，网络编码，入侵者观察任意布尔函数的编码。作为一个副产品，我们的建设，我们获得新的明确提取器的一个有限的家庭仿射源在大领域（特别是概括的概念，符号固定源），这是独立的利益。这些提取器能够零误差地提取整个源熵。关键词：窃听信道，提取器，网络编码，主动入侵，抗暴露密码学。
英文摘要：
A wiretap protocol is a pair of randomized encoding and decoding functions such that knowledge of a bounded fraction of the encoding of a message reveals essentially no information about the message, while knowledge of the entire encoding reveals the message using the decoder. In this paper we study the notion of efficiently invertible extractors and show that a wiretap protocol can be constructed from such an extractor. We will then construct invertible extractors for symbol-fixing, affine, and general sources and apply them to create wiretap protocols with asymptotically optimal trade-offs between their rate (ratio of the length of the message versus its encoding) and resilience (ratio of the observed positions of the encoding and the length of the encoding). We will then apply our results to create wiretap protocols for challenging communication problems, such as active intruders who change portions of the encoding, network coding, and intruders observing arbitrary boolean functions of the encoding. As a by-product of our constructions we obtain new explicit extractors for a restricted family of affine sources over large fields (that in particular generalizes the notion of symbol-fixing sources) which is of independent interest. These extractors are able to extract the entire source entropy with zero error. Keywords: Wiretap Channel, Extractors, Network Coding, Active Intrusion, Exposure Resilient Cryptography.
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