Common use of B-GKAP Join Operation Clause in Contracts

B-GKAP Join Operation. During join operation, let the number of participants joining the group be K and participants be UN+1,UN+2,...,UN+K. As stated in Section 3.2, to join K participants into the group, K participants should fetch temporary public keys from the network, K + 1 participants should perform generateAndSendPublicKey(·) function and K + 2 participants should execute generateAndSendSecretKey(·). And finally, K + N partici- pants should perform querySecretKeys(·). For both B-GKAP1 and B-GKAP2 models, since computational complexity of each function is O(1)Texp, the complexity of join operation is Cc = O(1)Texp as well. While in join operation of K participants, the network participant should execute genera- teAndSendPublicKey(·) for K participants, veri f yPublicKeys(·) for K +1 participants, veri f y- SecretKeys(·) for K + 2 participants. And finally for K + N participants, the network should run querySecretKeys(·) function. As defined in key computation analysis, for B-GKAP1 and B-GKAP2 models, the total cost of these function execution for K joining participants is Cc = O(K + N)Texp.

B-GKAP Join Operation. During join operation, let the number of participants joining the group be K and participants be UN+1,UN+2,...,UN+K. UN+1,UN+2, . . . ,UN+K. As stated in Section 3.2, to join K participants into the group, K participants should fetch temporary public keys from the network, K + 1 participants should perform generateAndSendPublicKey(·) function and K + 2 participants should execute generateAndSendSecretKey(·). And finally, K + N partici- pants should perform querySecretKeys(·). For both B-GKAP1 and B-GKAP2 models, since computational complexity of each function is O(1)Texp, the complexity of join operation is Cc = O(1)Texp as well. While in join operation of K participants, the network participant should execute genera- teAndSendPublicKey(·) for K participants, veri f yPublicKeys(·) for K +1 participants, veri f y- SecretKeys(·) for K + 2 participants. And finally for K + N participants, the network should run querySecretKeys(·) function. As defined in key computation analysis, for B-GKAP1 and B-GKAP2 models, the total cost of these function execution for K joining participants is Cc = O(K + N)Texp.