Common use of B-GKAP Join Clause in Contracts

B-GKAP Join. For the join operation of B-GKAP, when a new participant joins the group, the group key should be re-computed. Therefore, for joining K participants, K par- ticipants should receive temporary public key of the network, K + 1 participants should per- form generateAndSendPublicKey(·) function, K + 2 participants execute queryPublicKey(·) function, and K + 2 participants should perform generateAndSendSecretKey(·). Finally, all participants should perform querySecretKeys(·). Table 5.4. Communication cost of B-GKAP join operation for K joining participants. Function B-GKAP1 Ct B-GKAP2 Ct generateAndSendPublicKey(·) (2K + 1)|2q + p| (2K + 1)|2Mq + M p| queryPublicKey(·) (K + 2)|2q + p| (K + 2)|2q + p| generateAndSendSecretKey(·) (K + 2)|3q + p| (K + 2)|3q + p| querySecretKeys(·) (N + K)|(N + 1)q + p| (N + K)|(N + 2M — 1)q + M p| Based on Table 5.4, in B-GKAP1, 5 ⇥ K + N + 5 network transmissions occurs. Even- tually, the communication complexity of the join operation is Ct = O(N + K). For B-GKAP2, generateAndSendPublicKeyv2(·) and querySecretKeysv2(·) are exe- cuted for each organization. The transmission cost of other functions are same with B- GKAP1. Therefore, there are total M(3 ⇥ K + N + 1)+ 2 ⇥ K + 4 network transactions. If we consider that M is negligible against K and N, communication complexity is Ct = O(N + K).

B-GKAP Join. For the join operation of B-GKAP, when a new participant joins the group, the group key should be re-computed. Therefore, for joining K participants, K par- ticipants should receive temporary public key of the network, K + 1 participants should per- form generateAndSendPublicKey(·) function, K + 2 participants execute queryPublicKey(·) function, and K + 2 participants should perform generateAndSendSecretKey(·). Finally, all participants should perform querySecretKeys(·). Table 5.4. Communication cost of B-GKAP join operation for K joining participants. Function B-GKAP1 Ct B-GKAP2 Ct generateAndSendPublicKey(·) (2K + 1)|2q + p| (2K + 1)|2Mq + M p| Mp| queryPublicKey(·) (K + 2)|2q + p| (K + 2)|2q + p| generateAndSendSecretKey(·) (K + 2)|3q + p| (K + 2)|3q + p| querySecretKeys(·) (N + K)|(N + 1)q + p| (N + K)|(N + 2M — − 1)q + M p| Mp| Based on Table 5.4, in B-GKAP1, 5 ⇥ K ×K + N + 5 network transmissions occurs. Even- tually, the communication complexity of the join operation is Ct = O(N + K). For B-GKAP2, generateAndSendPublicKeyv2(·) and querySecretKeysv2(·) are exe- cuted for each organization. The transmission cost of other functions are same with B- GKAP1. Therefore, there are total M(3 ⇥ K ×K + N + 1)+ 1) + 2 ⇥ K ×K + 4 network transactions. If we consider that M is negligible against K and N, communication complexity is Ct = O(N + K).