Group Key Agreement. A comprehensive group key agreement solution must handle adjustments to group secrets subsequent to all membership change operations in the underlying group communication system. The following membership changes are considered: We distinguish among single and multiple member operations. We also distinguish between additive and subtractive member operations. Single member changes include member join or leave, and multiple member changes include group merge and group partition. • Join occurs when a prospective member wants to join a group • Leave occurs when a member wants to leave (or is forced to leave) a group. There might be different reasons for member deletion such as voluntary leave, involuntary disconnect or forced expulsion. We believe that group key agreement must only provide the tools to adjust the group secrets and leave the rest up to the local security policy. • Partition occurs when a group is split into smaller groups. A group partition can take place for several reasons, two of which are fairly common:
Group Key Agreement. A comprehensive group key agreement solution must handle adjust- ments to group secrets subsequent to all membership change operations in the underlying group communication system. The following member- ship changes are considered: Join occurs when a prospective member wants to join a group. Leave occurs when a member wants to leave (or is forced to leave) a group. There might be different reasons for member deletion such as voluntary leave, involuntary disconnect or forced expulsion. Partition occurs when a group is split into smaller groups. A group partition can take place for several reasons, two of which are fairly com- mon: Network failure – this occurs when a network event causes disconnec- tivity within the group. Consequently, a group is split into fragments. Explicit partition – this occurs when the application decides to split the group into multiple components or simply exclude multiple members at once. Merge occurs when two or more groups merge to form a single group: Network fault heal – this occurs when a network event causes previ- ously disconnected network partitions to reconnect. Explicit merge – this occurs when the application decides to merge multiple pre-existing groups into a single group. At first glance, events such as network partitions and fault heals might appear infrequent and dealing with them might seem to be a purely academic exercise. In practice, however, such events are common owing to network misconfigurations and router failures. In addition, in mobile ad hoc (and other wireless) networks, partitions are both common and expected. Xxxxx et al. present compelling arguments in support of these claims [MAMSA94]. Hence, dealing with group partitions and merges is a crucial component of group key agreement.
Group Key Agreement. Group Key Agreement means that multiple parties want to create a common secret key that to be used to exchange information securely. This group key should be updated when there are membership change occurs due to node mobility (when the new member joins or current member leaves) in the group. This can be done either periodically or at the time of every membership changes.
Group Key Agreement. A comprehensive group key agreement method must handle adjustments to group secrets subse- quent to all membership change operations in the underlying group communication system. Mem- bership changes can involve single or multiple members. Single member changes include member join or leave, and multiple member changes include group merge and group partition. They can also be additive or subtractive in nature: join and merge are additive, while partition and leave are subtractive. Join occurs when a prospective member wants to join a group Leave occurs when a member wants to leave (or is forced to leave) a group. There might be different reasons for member deletion such as voluntary leave, involuntary disconnect or forced expulsion. We believe that group key agreement must only provide the tools to adjust the group secrets and leave the rest up to the local security policy. Partition occurs when a group is split into smaller groups. A group partition can take place for several reasons, two of which are fairly common:
Group Key Agreement. The security of a group key agreement protocol P is defined in the following context. The adversary executes the protocol exploiting as much parallelism as possible and any queries allowed in the security model. During executions of the protocol, the adversary , at any time, asks a Test query to a fresh oracle, gets back an A-bit string as the response to this query, and at some later point, outputs a bit bj as a guess for the hidden bit b. Let CG (Correct Guess) be the event that bj = b. Then we define the advantage of A in attacking protocol P to be AdvA,P (k) = 2 · Pr[CG] − 1. A We say that protocol P is secure against an adversary if AdvA,P (k) is negligible. Fur- thermore, we say that protocol P is a secure group key agreement protocol if it is secure against all probabilistic polynomial time adversaries A. G S V Signature Scheme. A digital signature scheme Γ = ( , , ) is defined by the following triple of algorithms: – A probabilistic key generation algorithm , on input 1k, outputs a pair of matching public and private keys (PK, SK). S – A signing algorithm is a (possibly probabilistic) polynomial time algorithm that, given a message m and a key pair (PK, SK) as inputs, outputs a signature σ of m. – A verification algorithm is a (usually deterministic) polynomial time algorithm that on input (m, σ, PK), outputs 1 if σ is a valid signature of the message m with respect to PK, and 0 otherwise. A A We denote by SuccA,Γ (k) the probability of an adversary succeeding with an existential forgery under adaptive chosen message attack [18]. We say that a signature scheme Γ is secure if SuccA,Γ (k) is negligible for any probabilistic polynomial time adversary A. We denote by SuccΓ (t) the maximum value of SuccA,Γ (k) over all adversaries running in time at most t. G DDH Assumption. Let G = (g) be any finite cyclic group of prime order q and let x, y, z be randomly chosen elements in Zq. Informally, the DDH assumption is that it is difficult to distinguish between the distributions of (gx, gy, gxy) and (gx, gy, gz). More formally, if we define Advddh(A) as G . . Advddh(A) = Pr[A(g, gx, gy, gxy) = 1] − Pr[A(g, gx, gy, gz) = 1] , G we say that the DDH assumption holds in G if Advddh(A) is negligible for any probabilistic polynomial time adversary A. We denote by Advddh(t) the maximum value of Advddh(A) G G over all adversaries A running in time at most t.
Group Key Agreement. The group key agreement with an arbitrary connectivity graph, where each user is only aware of his neighbors and has no information about the existence of other users. Further, he has no information about the network topology. Under this setting, a user does not need to trust a user who is not his neighbor. Thus, if one is initialized using PKI, then he need not trust or remember public- keys of users beyond his neighbors.
