This paper investigates the secret-key-authenticated-capacity region, where information-theoretic authentication is defined by the ability of the decoder to accept and decode messages originating from a valid encoder while rejecting messages from other invalid sources. The model considered here consists of a valid encoder-decoder pairing that can communicate through a channel controlled by an adversary who is also able to eavesdrop on the encoder’s transmissions. Over multiple rounds of communication, the adversary first decides whether or not to replace the decoder’s observation with an arbitrary one of the adversary’s choosing, with the goal of the adversary being to have the decoder accept and decode their observation as a valid message (different from that of the encoder). To combat the adversary, the encoder and decoder share a secret key. The secret-key-authenticated-capacity region here is then defined as the region of jointly achievable message rate, authentication rate (a to be defined per symbol measure that will generally represent the likelihood that an adversary can fool the decoder), and the key-consumption rate (how many bits of secret key are needed per symbol sent). This is the first of a two-part study, with the parts differing in their measure of the authentication rate. In this first study, the authentication rate is the exponent of blocklength-normalized exponent of the expected probability of false authentication. For this metric, we provide an inner bound which improves on those existing in the literature. This is achieved by adopting and merging different classical techniques in novel ways. Within these classical secret-key-based authentication techniques, one technique derives authentication capability from secure channel coding to send the secret key with the message, and the other technique derives its authentication capability directly from obscuring the source.

中文翻译：

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启用密钥的认证容量区域，第 I 部分：平均认证


本文研究了密钥认证能力区域，其中信息论认证是由解码器接受和解码来自有效编码器的消息同时拒绝来自其他无效源的消息的能力来定义的。这里考虑的模型由有效的编码器-解码器对组成，可以通过对手控制的通道进行通信，对手也能够窃听编码器的传输。在多轮通信中，对手首先决定是否用对手选择的任意一个来替换解码器的观察，对手的目标是让解码器接受并解码他们的观察作为有效消息（不同于编码器的那个）。为了对抗对手，编码器和解码器共享一个密钥。然后，此处的秘密密钥验证容量区域被定义为联合可实现的消息速率、验证速率（按符号度量定义的一个区域，该度量通常代表对手欺骗解码器的可能性）和密钥-消耗率（每个发送的符号需要多少位密钥）。这是由两部分组成的研究中的第一部分，各部分的认证率衡量标准有所不同。在第一项研究中，认证率是预期错误认证概率的块长度归一化指数。对于这个指标，我们提供了一个内部界限，它改进了文献中现有的界限。这是通过以新颖的方式采用和融合不同的经典技术来实现的。 在这些经典的基于密钥的身份验证技术中，一种技术从安全通道编码中获取身份验证功能以随消息一起发送密钥，而另一种技术则直接从隐藏源中获取其身份验证功能。