Description.

The second solution is also straightforward (see Figure 6). It consists in sending to the card all elements of the ``black list'' one by one, each of them signed by the group manager. It is yet necessary to add a revocation number (a sequence number: number 1 corresponds to the first revoked member, etc.) to prevent some attacks (for example addition or substitution of some identifiers). In addition, GM signs the date of his updating of the ``black list'' $D_{GM}$ and the number of revoked members.

Figure 6: Second Approach - Second Solution