## 2 Related Works
### Group Key Management Techniques  
SKDC follows a very simple approach, where all the existing participants of the group share an individual secret key with the KMS. When there is a change in the number of group members, the new group key is handed out by KMS to existing participants of the group individually, encrypted using the shared secret key, in sequential order. Hence, the communication cost is linear, which is highly inefficient for large dynamic groups. The group Diffie-Hellman (DH) proposed in [35] uses asymmetric encryption for key distribution, with higher computation overhead. Logical Key Hierarchy (LKH) [36] is a familiar centralized, hierarchy-based key management approach for dynamic groups. LKH uses a balanced binary tree-based data structure with member devices' keys as leaf nodes. The root node contains the group key. The intermediate nodes along the path of the member devices to the root hold the key encryption keys with which the devices can obtain the group key. The overall overhead of the approach is 2 log n.  
Yet another centralized, hierarchy-based key management approach for groups is the OFT, which reduces the communication cost to log n. Hence, the approach reduces bandwidth consumption considerably. The approach is similar to LKH, with the member device's individual keys as leaf nodes. The root key is the group key. The intermediate nodes hold the key-encryption key, which is calculated using a one-way and mixing function on the child node's keys. However, the approach fails to provide collusion resistance where two expelled members collide and can gain access to unauthorized group data. Several advancements to the OFT-based approach are proposed [37; 38] to enhance the collusion resistance property, but in turn, the advancements increase the overall overhead. To impart collusion resistance in OFT, two more approaches are proposed in [39]; both approaches successfully impart collusion resistance with the same communication cost as OFT but with higher computation costs. A centralized key management approach for the group that uses Diffie-Hellman for generating the key-encryption key is proposed in [40]. The group key can be decrypted using the key-encryption key. However, the use of public key cryptography increases the computation cost greatly. Moreover, without authentication, the use of Diffie-Hellman is liable to man-in-the-middle attack. A lightweight key management approach for groups formed in IoT applications is proposed in. The approach uses a hybrid technique with a combination of CRT and LKH. The intermediate node keys are calculated by hashing the device's ID. Although the ID of a device is unique, tracking the ID of the device is simple for malicious users to perform forgery-based attacks. Group key management using the Chinese Reminder Theorem (CRT) is proposed in. The approach is efficient, with the least communication cost of a single broadcast. When the group size exceeds the preset n value, the individual keys for the entire group must be renewed. A blockchain-based solution for key management in groups for autonomous aerial vehicles has earlier been proposed. The approach uses LKH along with blockchain for group key updating and reduces delay. The approach also assures forward and backward secrecy. However, the use of blockchain in a resource-constrained environment would be a problem. Another lightweight asymmetric group key management approach for VANETS is proposed in [41]. The approach uses a combination of CRT and asymmetric cryptography in contrast to the traditional symmetric group key management techniques. The scheme is comparatively scalable and has minimal computation overhead compared to its predecessor, CRT-based group key management techniques for VANETS. Still, the approach cannot use variable key sizes since the key sizes are chosen based on constraints. Further, a collusion-resistant approach to group key management is proposed in [42], which makes use of tokens to avoid collusions.