# Authenticated Multicast in Tiny Networks via an Extremely Low-Bandwidth Medium
## 6 Conclusions and Final Remarks  
Securing multicast communication poses a challenge if the size of digital signatures is excessive from the point of view of the narrow communication channel. Implicit authentication known from one-to-one communication no longer work in this setting, and it is not obvious how to efficiently construct authentication schemes from symmetric primitives only. The problem is compounded by advances in cryptanalysis, including quantum threats. Other channel characteristics, such as unreliability, may affect protection mechan \begin{table}
\begin{tabular}{l l c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Security Level**} & \multicolumn{3}{c}{**Number of Nodes in the Network**} \\ \cline{3-5}  & & **3** & **6** & **9** & **15** \\ \hline \multirow{4}{*}{**Basic by [PERSON] et al. [28]**} & \multirow{2}{*}{\(2^{10}\)} & \multicolumn{3}{c}{Number of MAC keys = 41} \\  & & \multicolumn{3}{c}{Communication overhead = 451 bits} \\ \cline{3-5}  & & & Number of MAC keys = 79 \\  & & \multicolumn{3}{c}{Communication overhead = 1659 bits} \\ \hline \multirow{4}{*}{**Low overhead by [PERSON] et al. [28]**} & \multirow{2}{*}{\(2^{10}\)} & \multicolumn{3}{c}{Number of MAC keys = 148} \\  & & \multicolumn{3}{c}{Communication overhead = 148 bits} \\ \cline{3-5}  & & \multicolumn{3}{c}{Communication overhead = 300 bits} \\ \hline \multirow{4}{*}{**Our construction (tag \(T_{1}\))**} & \multirow{4}{*}{\(2^{10}\)} & \(|\mathcal{SF}|=3\), & \(|\mathcal{SF}|=4\), & \(|\mathcal{SF}|=5\), & \(|\mathcal{SF}|=6\), \\  & & 3 MAC keys & 4 MAC keys & 5 MAC keys & 6 MAC keys \\  & & 30 bits & 40 bits & 50 bits & 60 bits \\ \cline{3-5}  & & \multicolumn{3}{c}{\(|\mathcal{SF}|=3\),} & \(|\mathcal{SF}|=4\), & \(|\mathcal{SF}|=5\), & \(|\mathcal{SF}|=6\), \\  & & 3 MAC keys & 4 MAC keys & 5 MAC keys & 6 MAC keys \\  & & 60 bits & 80 bits & 100 bits & 120 bits \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of communication overhead between [28] (for \(w=1\), i.e., a single compromised node) and our construction. For our scheme, we only count the \(t_{i}\) chunks corresponding to the \(T_{1}\) part of the tag (recall Section 4.6.1). nisms based on chaining and delayed disclosure of authentication keys (such as TESLA), making them ineffective. Solutions aimed specifically at tiny networks can take advantage of the small number of nodes, using methods that do not scale well but reduce the communication overhead. We have presented solutions aimed at a network where it is possible to preload a moderate number of symmetric keys with the goal of solving the following core problems:  
1. How to establish a shared key for a multicast group;
2. How to authenticate the source of multicast messages so as to prevent senders being impersonated by internal adversaries. To this end, we have provided fine-tuned schemes tailored for tiny networks. The presented schemes rely on some initial keys being preloaded prior to the network deployment. As this is done in a secure environment, the keys are automatically bound to the identities of either single nodes or groups of nodes, and knowledge of the keys implicitly authenticates the entities. A further research direction is to answer the question of how to handle two networks merging after deployment, e.g., when two fleets of UUVs rendezvous at sea. The choice of method, e.g., whether the keys for the new link should be established via the base stations of the individual networks or dynamically generated using physical-layer security protocols, might be dependent on the trust model. Our solutions use only standard assumptions about the underlying primitives, such as MACs and encryption schemes, and can be applied in both MAC-then-encrypt and encrypt-then-MAC configurations; in the latter case, the'message' \(m\) in (12) and (13) corresponds to the ciphertext. The proposed authentication scheme is generic in the sense that it does not make any assumptions about the nodes' mobility or frequency of transmission.