Definitions of Security. The security of the protocol P is defined using the A,B following game, played between an adversary F and a collection of Πs oracles for players A, B and s ∈ N. ∈ { } – In the initialization phase, each player i A, B is assigned a long-term key related to the security parameter. F – In the running phase, an adversary may ask some queries and get back the answers from the corresponding oracles. F – At some point, the adversary asks a Test query to a fresh oracle, and outputs its guess bj for the bit b involved in the Test query. Success of F in the game is quantified in terms of F ’s advantage in distin- guishing whether F receives a real session key or a random value, i.e., its ability guessing b. We define F ’s advantage as P Advaka(F ) = |2 × Pr[b = bj] − 1| where the probability space is over all the random coins of the adversary and all the oracles. We say that the protocol P is secure if Advaka(F ) is negligible in the security parameter. P
Definitions of Security game is terminated. The advantage of the adversary A is measured by the ability of distinguishing a session key from a random value, i.e., its ability is guessing b. We de- fine Succ to be the event that A correctly guesses the bit b which is chosen in the Test query. The advan- tage of the adversary A in the attacked scheme P is To demonstrate the security of the ID-based MAKA scheme for multi-server environment, we defined as Adv A,P
Definitions of Security. We define the security of the protocol by following game between the adversary A and an infinite set of oracles Πs for IDi ∈ ID and s ∈ N.
