Batch Algorithm Clause Samples

Batch Algorithm. The Batch algorithm is based on the centralized approach in [13], which is now applied to a distributed system without a centralized key server. The pseudo-code of the Batch algorithm is given in Fig.

Batch Algorithm. We evaluate the expected number of secret key computa- tions involved in the Batch algorithm by breaking down the analysis into five cases. We let Batch,c be the number of secret key computations of the Batch algorithm under condition c. Case 1: J > L = 0 (pure join). Since the original key tree = E subtree T j of the newly joined members will be inserted at the root of the existing tree T . Thus, the (exact) number of secret key computations is given by require s ( J ) secret key computations. Let J j = L, and hence the expected number of secret key computations is E[E ] E | ∫ EBatch,J>L=0 (J) + (N + J). (14) = E[E s ] + (J mod L)E s (| J ∫ + 1) The first term corresponds to the exponentiation cost of creating a tree for the J new members. The term (N + J) is the secret key computations of the new root node in the resulting tree performed by the N + J members. Note that the value is deterministic, so the average representation is omitted. Case 2: L > J = 0 (pure leave). Consider a node v at level l. We first derive the probability of renewing a node in terms of the number of departed descendants. When there is no node promotion, node v is renewed if at least one but not all descendants of node v leave the communication group. With node promotion, we have to exclude the counting of the renewed nodes that are pruned due to the departure of all descendants of their left or right subtrees. The probability is thus given by P [node v is renewed] = Σ Σ N/2l−1 . lΣ. lΣ N −1 .N/2l+1Σ. N −N/2l Σ N −N/2 2l+1 ▇▇▇▇▇,▇▇ =L>0 Rebuild L

Batch Algorithm. The Batch algorithm is based on the centralized approach in [14], which is now applied to a distributed system without a