In this paper, we propose a formal security model and a construction methodology of interactive aggregate message authentication codes with detecting functionality (IAMDs). The IAMD is an interactive aggregate MAC protocol which can identify invalid messages with a small amount of tag-size. Several aggregate MAC schemes that can detect invalid messages have been proposed so far by using non-adaptive group testing in the prior work. In this paper, we utilize adaptive group testing to construct IAMD scheme, and we show that the resulting IAMD scheme can identify invalid messages with a small amount of tag-size compared to the previous schemes. To this end, we give the formalization of adaptive group testing and IAMD, and propose a generic construction starting from any aggregate MAC and any adaptive group testing method. In addition, we compare instantiations of our generic constructions, in terms of total tag-size and several properties. Furthermore, we show advantages of IAMD by implementing constructions of (non-)adaptive aggregate message authentication with detecting functionality and comparing these ones in terms of the data-size and running time of verification algorithms.

在本文中，我们提出了一种形式化的安全模型和一种具有检测功能的交互式聚合消息认证码（IAMD）的构造方法。 IAMD 是一种交互式聚合 MAC 协议，可以识别具有少量标签大小的无效消息。迄今为止，在先前的工作中已经通过使用非自适应组测试提出了几种可以检测无效消息的聚合MAC方案。在本文中，我们利用自适应组测试来构建 IAMD 方案，并且我们表明，与之前的方案相比，所得的 IAMD 方案可以用少量标签大小识别无效消息。为此，我们给出了自适应组测试和 IAMD 的形式化，并提出了从任何聚合 MAC 和任何自适应组测试方法开始的通用构造。此外，我们还根据总标签大小和几个属性来比较通用结构的实例。此外，我们通过实现具有检测功能的（非）自适应聚合消息认证的结构，并在验证算法的数据大小和运行时间方面对这些认证进行比较，展示了 IAMD 的优势。