Participants and Notations Clause Samples

Participants and Notations. Let P be a set with polynomial-size of potential protocol participants. Each participant in P has an identity and a private key. Any subset U = {U1, ..., Un} ⊆ P may decide at any point to establish a confidential channel among them. We use Ππ to represent instance π of participant U involved with partner participants {U , ..., U , U Ui , U } in a session. Each instance Ππ i + 1 n Ui holds the variables pidπ , sidπ , msπ , ekπ , dkπ and stateπ which are defined below: Ui Ui Ui Ui Ui Ui – pidπ is the partner ID of instance Ππ . It is a set containing the identities of the partici- Ui π Ui pants in the group with whom ΠUi intends to establish a session key including Ui itself. For simplicity, we assume that the identities in pidπ are lexicographically ordered. – sidπ Ui is the session ID of instance Ππ . We folUloi w [21] in assuming that unique session IDs Ui are provided by some higher-level protocol when the group key-exchange protocol is first initiated. Therefore, all members taking part in a given execution of a protocol will have the same session ID. – msπ Ui is the concatenation of all messages sent and received by Ππ Ui during its execution, where the messages are ordered by round, and within each round lexicographically by the identities of the purported senders. – ekπ – dkπ is the encryption key held by Ππ . is the decryption key held by Ππ . – Ui π Ui π state i represents the current (internal) state of instance Π i . When an instance has ter- has been successfully terminated (accepted) in the instance Ππ if it possesses ekπ ( dkπ (ƒ= null), pidπ and sidπ . Ui Ui Ui Ui Ui Definition 1 (Partnering). We say instances Ππ and Ππj (with i ƒ= j) are partnered iff (1) j Ui Uj j they are successfully terminated; (2) pidπ = pidπ ; and (3) sidπ = sidπ .