# H2O: Secure Interactions in IoT via Behavioral Fingerprinting
## 3 General Model  
In this section, we describe the general model adopted by our approach and the main actors involved in. Table 2 reports the abbreviations used throughout this paper. In the classical definition of the Internet of Things (hereafter, IoT) the network is represented as a graph \(G=\langle N,E\rangle\), where \(N\) is a set of nodes representing objects and \(E\) is a set of edges representing relationships between pairs of objects. An edge is built if two objects got in touch somewhere in the past and exchanged some messages. Usually a directed graph is considered, so that an edge direction identifies the destination of the \begin{table}
\begin{tabular}{l l c c c} \hline \hline
**Approach** & **Approach Type** & **H-O** & **O-O** & **H-H** \\ \hline Our approach & Fingerprint, Biometrics, Consensus & x & x & x \\ [8; 27; 28; 29] & Biometrics & x & - & - \\ [13; 14] & Behaviometrics & x & - & - \\ [30; 31] & Remote Attestation & - & x & - \\ [21; 22; 23; 32; 44] & Device Fingerprint & - & x & - \\ [16; 17; 35; 36; 37] & Cryptographic & - & x & - \\ [38; 39; 40] & Blockchain & - & x & - \\ [43] & Social Network & - & x & - \\ [19] & Social Network and Biometrics & - & - & x \\ [50] & Social Network and Agent & - & - & x \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of our approach with related ones. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Meaning** \\ \hline \(N\) & set of nodes of the network \\ \(E\) & set of edges of the network \\ \(n_{i}\) & \(i\)th node of the network \\ \(\Gamma(n_{i})\) & the neighbors of \(n_{i}\) \\ \(N_{PAN}\) & subset of nodes belonging to a Personal Area Network (\(PAN\)) \\ \(N_{PIU}\) & subset of public nodes of the network \\ \(N_{PPAN}\) & subset of nodes belonging to a \(PAN\) with high computational capabilities \\ \(N_{LPAN}\) & subset of nodes belonging to a \(PAN\) with low computational capabilities \\ \(N_{PPU}\) & subset of public nodes with high computational capabilities \\ \(N_{LPU}\) & subset of public nodes with low computational capabilities \\ \(P_{n_{i},n_{j}}\) & profile of object \(n_{i}\) respect to object \(n_{j}\) \\ \(S\) & set of features \\ \(r\) & redundancy parameter \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation used throughout this paper. communication. We can define the set of neighbors of a node \(n_{i}\) as the set \(\Gamma(n_{i})=\{n_{j}\in G:(n_{i},n_{j})\in E\}\). In our model, \(N\) is partitioned into two subsets: * The set of objects belonging to a person (denoted by \(N_{PAN}\)). All the objects belonging to this group maintain permanent physical contact with the same user during usage. This set is composed of various personal devices, that can form groups with each other when they are equipped with the short-range communication and sensing modules. Some examples are, for instance, mobile phones, PDAs and wearable devices, such as: human activity trackers, ECG readers, smartwatches, and semi-permanent insulin pumps. * The set of nodes of public use in the environment (denoted by \(N_{PU}\)). This kind of objects are not related to humans, but can be accessed by anyone in the environment (e.g., printers or video surveillance cameras, smart multimedia object, and so forth [51]). Moreover, a further classification, based on the processing and memory capabilities of an object, is possible. Therefore, we can divide the network in the following two groups: * The set of nodes with high processing and memory capabilities. If these objects are of public use in the environment, they will be denoted as \(N_{PPU}\), whereas, if they belong to a \(PAN\), they will be denoted as \(N_{PPAN}\). These nodes can process machine learning models and/or train classifiers for various tasks. Also smart devices that can leverage Cloud solutions to handle complex algorithms [52] belong to this category. * The set of nodes with low capabilities.