Tree Based Approach Sample Clauses

Tree Based Approach. The application of the tree structure to key agreement proto- cols has been proposed earlier [11], [12]. In [13], [14], they used one-way functions to enhance the security in protocols based on tree-liked structures. A group of members, participating in the key agreement protocol, has a group manager who maintains a binary tree. Each node x has two cryptographic keys, a node key A 00 α SA SB α SASB C 10 D (a) A 00 α SAB SCD C 10 D (b) kx and a blinded node key bx = g(kx), i.e., the blinded node key bx is computed from the node key kx using the one-way func- tion g. The key is blinded in the sense that an adversary with limited computational capability can know bx but cannot find kx. The application of key trees to a distributed environment has been proposed in the protocol Tree Group ▇▇▇▇-▇▇▇▇▇▇▇ (TGDH) [3] key agreement protocol. TGDH combines a binary tree structure with the group ▇▇▇▇-▇▇▇▇▇▇▇ technique. The TGDH protocol, uses the hierarchy in a binary tree to its advantage. The root is at the topmost level, given a value of 0 and all the leaves are at the lowest level h. Since the tree is a binary tree, each node is a leaf or a parent of two nodes. Each leaf node in the tree represents a group member Mi. The internal nodes are used for the key management and do not represent any individual member. Each node of the tree is represented by (l, v), where l is its level in the tree and v is the index of this node in level l. The key associated to node (l, v) is k(l,v) and its blinded key b(l,v) = αk(l,v) mod p. See [3] for detail. Each group member contributes equally to the group key. In other words, for each internal node (l, v), its associated key k(l,v) is derived from its children’s keys. In (a) Round 1: pairwise exchange in a d-cube. (b) Round 2: pairwise exchange in a d-cube. For simplicity, we assume that the number of members is n = 2d. Each member is assigned a vertex and a unique d-bit address from the set Zn. The protocol runs for d rounds. In the jth round, neighbors along the jth dimension of the hypercube participate in a 2-party ▇▇▇▇-▇▇▇▇▇▇▇ protocol. After d rounds all members share the same key. ▇▇▇▇▇▇ and ▇▇▇▇▇ [15] gave a detailed study of the commu- nication complexities of the hypercube based protocol. They also discussed a protocol named octopus, in which members are divided into four disjoint subgroups, and each subgroup has a member as the header. Let A, B, C, D be such four group head- ers. Member A first builds a secure communicatio...