Key Tree Notation Clause Samples
Key Tree Notation. Key tree is earliest proposed by ▇▇▇▇▇▇▇, ▇▇▇▇▇▇ and ▇▇▇▇ (1999) and emerged in group key agreement by ▇▇▇ et al. (2000;2004) in TGDH protocols and ▇▇▇▇▇ et al. (1998) in STR protocol. The tree structure is widely implemented to decrease the communication, computation and storage overhead. The number of communication rounds to form the group key can be reduced to the logarithm of the group size. The braid groups cannot implement with balanced key tree as TGDH protocol, because limitation of braid groups operations and properties. Therefore key tree in this research is based on unbalanced key tree similar to STR protocol. Key tree is implemented in protocol according to be suitable solution for contributory group key agreement in MANET because it does not require that the members are be serialized or structured in order to compute the group. The following section describes the notation and definition of key tree. A sample of key tree based on STR is shown in Figure 3.1. The binary tree, every node is either a leaf or a parent of two nodes, is used in key tree. Each node is represented as [h,v] what is associated with a secret key K[h, v] and a blinded key BK[h, v]. The blinded key is calculated as f(K[h, v]) where function f ( ) is braid groups key exchange what describe in next section. The members are located at the leaf node. The information of each intermediate node, key and blinded key, is computed from the information of two children nodes to achieve the subgroup key. The leaf node Mi, where 1 ≤ i ≤ n, knows every key along the path from node Mi to root node, this path is called the key-path. In Figure 3.1, M1 knows every key { K[3,0] , K[2, 0] ] , K[1, 0] ] , K[0, 0] } in key-path { [3,0], [2,0], [1,0], [0,0] }. The co-path is the set of sibling nodes of each node in the key-path of a member Mi. The sample in Figure 3.1, the co-path of M1 is set of node { [3,1], [2,1], [1,1] }. The group secret key is key at the root node, K[0, 0], what can be computed from all blind keys on the co-path and session random K[h, v] of a computing node (member). [1,1] M4 [2,0] [3,0] [3,1] M1 M2
Key Tree Notation. A key tree was earliest proposed by ▇▇▇▇▇▇▇, ▇▇▇▇▇▇, and ▇▇▇▇ (1997) as a tool in centralized group key distribution systems and was adapted by ▇▇▇, ▇▇▇▇▇▇, and ▇▇▇▇▇▇ (2000) for using in fully distributed, contributory key agreement. Figure
3.1 shows an example of key tree mentioned in Norranut Saguansakdiyotin and Pipat Hiranvanichakorn (2012). It is a binary tree which has only left subtree. The tree composes of both intermediate and leaf nodes. The root node is located at level 0 and the lowest leaf is at level h. Each node is represented as <l,v> where l and v are denoted as vth node at level l in a tree. As shown in Figure 3.1, a member node Mi where i ∈ (1…N) is located only at a leaf of the tree. Each member node is associated with a private keys pair (K<l,v>, K-1<l,v>) and a published braid g<l,v>. A public key of each member node PK<l,v> = K<l,v> g<l,v' > g<l,v> K-1<l,v> where v' is another node at the same level. For an intermediate node, which is not a member node K<l,v> = K<l+1, 2v> PK<l+1, 2v+1> K-1<l+1, 2v> or K<l,v> = K<l+1, 2v+1> PK<l+1, 2v> K-1<l+1, 2v+1>. A key K<l,v> and a public key PK<l,v> of an intermediate node is computed independently from the values of key and public key of child nodes to achieve a subgroup key.