# Secure D2D Group Authentication Employing Smartphone Sensor Behavior Analysis
## 3 Preliminaries and Model Definitions
### System Model  
In the assumption, the whole D2D infrastructure is composed of service network (SN) and multiple user entities (UEs). The utilized structure of the proposed D2D authentication architecture is introduced in Figure 1, which is considered as the specific D2D communication scenario devoted to public safety and emergency rescue in the wild. Potential occasions include most of the isolated nature landscapes such as the mountainous regions, desert areas, tropical rainforests or vast oceans [28], which account for comparatively large proportions of the Earth's surface in total. Most of the regions are depopulated zones. On the other hand, due to the complex and hostile environmental characteristics, it is technically difficult for the involving countries to construct even the basic infrastructure for cellular network coverage in these areas, which requires huge amounts of financial grants. In these regions, few cellular network facilities such as base stations are available, most of the areas are not in the cellular coverage. In this assumption, D2D communication between user entities (UEs) are necessary so as to substitute the cellular connection from the base station. For example, a group of tourists are intended to go hiking in the mountains, where cellular coverage is not available in most of the spots. In this case, interactions between the tourists highly depend on the self-constructed D2D communicating network. It is worth nothing that some UEs are within the effective range of base station. Hence, cellular connections can be achieved for all the participating UEs over the D2D network, even though the UEs are not within the cellular coverage. The corresponding description of service network and the user entities are respectively illustrated below. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Description** \\ \hline SN, UE & Service network, user entity \\ \(\mathbb{G}\),\(\mathbb{G}_{S}\) & Cyclic multiplicative group \\ \(g\), \(w\) & Generator of \(\mathbb{G}\) \\ \(ID_{i}\) & Unique identity of UE \(i\) \\ \(mk\) & System master key \\ \(X_{i}\) & HC and \(\mathbb{PC}_{i}\) partial private key generated by SN \\ \(\dot{\theta}_{i}\) & Partial private key generated by UE itself \\ \(\{a_{0},a_{1},\ldots,a_{t-1}\}\) & Coefficients of function \(f(x)\) \\ \(PK\) & SN public key \\ \(H_{1}\), \(H_{2}\), \(H_{3}\), \(H_{4}\) & Secure hash functions \\ \(\gamma\) & Group key generated by SN \\ \(TS\) & Current time stamps \\ \(m\) & Message to be transmitted \\ \(t\) & Number of participating UEs \\ \hline \end{tabular}
\end{table} 
Table 1: Notations. Figure 1: System Model. The service network (SN) is assumed to be the powerful controlling center for the whole D2D system. SN takes the responsibility of conducting main operations including system initialization, initial registration, key generation and management, identity verification. In the proposed design, SN is designed to be resistant to all kinds of attacks and remains authentic anytime. In the proposed scheme, as the role of SN are taken by the commercial organizations, it cannot be fully trusted. We consider the SN to be an honest-but-curious authority, where the essential key generation and identification processes are all conducted accordingly. Note that the partial private key is only generated for the registered UEs, while the individual UE is designed to generate the remaining partial secret key itself. The key escrow issue is avoided accordingly. Particularly, SN also offers direct cellular connection for the validated devices within its effective range, while the devices beyond its coverage can acquire cellular access indirectly. In our design, SN can be considered as the combination of cellular base station and validated verifier at the same time. The user entities (UEs) are designed to be the terminal user of the D2D communication. In the proposed system model, UE refers to the personal smartphone of users.