We consider authentication of messages sent from transmitters to a receiver over a multiple access channel, where each transmitter shares a secret key with the legitimate receiver. Additionally, there exists a computationally unbounded opponent who has access to noisy observations of the messages transmitted and can initiate impersonation or substitution attacks. We require that the legitimate receiver must be able to authenticate the messages he receives with respect to predetermined groups of transmitters, but at the same time must be kept ignorant of the transmitter’s identity of a given message in a given group. We propose an information-theoretic formulation of these anonymity constraints as well as an authentication coding scheme for which the asymptotic probability of successful attack is shown to optimally scale with the length of the secret keys shared between each transmitter and the legitimate receiver. Our results quantify the positive impact of the multiple access setting compared to the single-user setting on the probability of successful attack.

中文翻译：

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具有匿名约束的高度安全的多用户通信和身份验证

我们考虑对通过多路访问信道从发送器发送到接收器的消息进行身份验证，其中每个发送器与合法接收器共享一个密钥。此外，存在一个计算上无界的对手，他可以访问对传输的消息的嘈杂观察，并可以发起模仿或替代攻击。我们要求合法接收者必须能够验证他接收到的关于预定发送器组的消息，但同时必须不知道发送器在给定组中的给定消息的身份。我们提出了这些匿名约束的信息理论公式，以及一种认证编码方案，其中成功攻击的渐近概率显示为与每个发射器和合法接收器之间共享的密钥长度进行最佳缩放。我们的结果量化了多路访问设置与单用户设置相比对成功攻击概率的积极影响。