Group Key Distribution.

The most simple solution to manage group key distribution for our proposal is to share a secret key with each group member and to encrypt the new group-shared key with each secret key. Each valid member can decrypt one of the encrypted values to obtain the new group-shared key.
The identifier of the group member can be appended to each encrypted value. The group member only has to test if it is his own identifier and to decrypt the corresponding value if it is the case (see Figure 3).

Figure 3: First Approach - Getting the Key

There are some other solutions in the literature that are more interesting than this simple one. For example, Wong et al. [16] propose a solution based on a tree, where each leaf corresponds to a group member and where each node corresponds to a secret key. Each group member shares with the group manager all keys that are in the path between their leaf and the root. As every member knows the key root, this latter is chosen as the group-shared key. Consequently, for a particular revocation phase, the GM only has a limited number of values to encrypt, instead of many in the naive method.