# Group Authentication Scheme for Neighbourhood Area Networks (NANs) in Smart Grids
## 2 Group Authentication
### Related Work  
[PERSON] _et al._, term the first scenario as a reverse single sign-on and succinctly describe a framework for group authentication which is applicable for mobile telecom networks and extendible to the M2M context, which is relevant to our discussion [9]. They introduce a gateway entity to coordinate/represent the group and this entity performs the required upstream authentication. The group authentication is based on a group challenge sent by the gateway to all devices. The devices individually respond to the gateway with their credentials. In the absence of the gateway, the upstream authentication server does the authentication and the overall saving in communication overhead remains one-sided (from the authentication server to the device group) [9]. The proposal in [9] is similar to our proposal in terms of having a gateway as an intermediary. In the scenario we consider, each node in the network authenticates with a central entity, the networkoperations centre (NOC). This includes all intermediate nodes (group leaders) that provide a path to the end nodes to reach the NOC. Operationally, each group leader has no autonomy to authenticate a group member, but it has sufficient information to validate that a group member attempting to relay packets through it has indeed been authenticated, centrally. There are a hierarchy of groups where necessary, functionally to reach the NOC, resulting in a multi-hop path from the end device to the NOC. [PERSON], _et al._[9] does not discuss an authentication requirement with multi-hop paths. [PERSON] proposed a Group Authentication Scheme (GAS), where the role of a group manager is responsible for registering all members of the group and issuing a distinct token to each member [10]. Subsequently, the members of the group authenticate and interact with each other without the need for the group manager's involvement. They propose a non-interactive basic t-secure m-user n-group authentication scheme ((t; m; n) GAS), where t is the threshold of the proposed scheme; m is the number of users participating; and n is the total number of group members. This scheme, based on [PERSON]'s secret-sharing [11], works for synchronous communications only. Therefore, they also propose an asynchronous (t; m; n) GAS, which can determine whether all users that participate in a group actually belong to that group [10]. The proposal in [10] is primarily for a many-to-many communication within a group (intra-group). It enables autonomous authentication within the group as well as detection of invalid members. The requirement for a SG scenario that we consider does not necessarily require a many-to-many characteristic. In addition, the limiting factor for the authentication scheme is the threshold t. There is no estimate of the scalability of t or the generic suitability of the scheme to resource-constrained devices. In the specific scenario we consider, the proposal in [10] is over-dimensioned. [PERSON] _et al._, present a Group Authentication scheme for IoT based on Threshold Cryptography-based Group Authentication (TCGA) [12]. They extend [10] to use Pallier Threshold Cryptography [13], using its properties; namely, homomorphic addition, indistinguishability, and self-binding. Primarily, they address the problem of different groups (applications) requiring communicating with each other. The authentication scheme has a pre-authentication phase where a group head does the key distribution and followed by a group authentication phases where a secret session key is distributed. The group members rely on the group head to initiate all group communication. They demonstrate that their scheme performs better than [10]. However, the implementation is on WiFi-based laptops and reflects a scaled performance of their scheme on IoT platforms. Our scenario does not require communication within the group. Group members do not need to communicate between themselves. The authentication is done centrally and the intermediate nodes verify that a downstream node is already authenticated.