## An Efficient Protocol For Authenticated Key Agreement

(ii) Requests. To deal with, and sessionKeyReveal C queries, the challenger first manages the corresponding empty lists, and . Then the challenger responds S to all C queries as below: (1). In the set-up phase, where the long-term secret key of each party is set, S inserts the entry in. If a query about Opponent C sent by Opponent C already exists in, S returns the corresponding entry to C. Otherwise, S randomly selects and adds the new entry to the list. S then returns the random value. (2) When C launches a query, S first searches for the corresponding entry in the entire list. If S discovers the entrance, S transmits to C.

Conversely, S calculates and verifies whether this value is already in or not. If this one has the corresponding value, the challenger gives C. Otherwise, S chooses at random. Then S inserts the entry into the opposing C and returns to opponent C. (3). Before this query, S performs an empty table whose entries are the shape of. i) When the corresponding entry is found in, challenger S responds to the query. (ii) If not, S reviews the entire list.

If i has the right B value and the target item is stored, S uses the oracle to check if, and . If all of them are correct, put and store S entry in . When the entry is found in the list, the Challenger S equation is created and the corresponding item is added to. But if the list doesn`t have the corresponding entry or if the oracle checks are wrong, S selects this new data at random and lists it. In the final, S returns the matching to opponent C. (4) EphemeralKeyReveal (). If this is the session, the challenger stops. Otherwise, the temporary private key is sent to S by opponent C. (5) StaticKeyReveal (). If i-B, S stops.

Otherwise, it is the challenger C. (6) MasterPrivateKeyReveal (). Challenger S stops. (7) EstablishParty (). For this request, the challenger chooses S at random. Then S ranks the value of and calculates. Finally, S sends C as his long-term secret key. Therefore, the opponent can completely control C because the long-term secret key of C.(8)SessionKeyReveal () is known. If the session is or is, S stops. Otherwise, S searches the entire list for value and sends it to C.(9) Send (, M). An empty table is held by S, whose element is for the issue request. i) If and , the opponent receives C X returned by challenger S.

(ii)If the value of i B and is, S randomly selects and returns it to C. In addition, S checks if, and. If, and are correct, S specifies the entry in the list and inserts it. However, if the list does not contain the entry or one of and is incorrect, S randomly selects and writes new information in . iii) If B is not the correct value for i, S responds to this query in accordance with the protocol rule. (10) Test (). If the session is , selects S at random and this data is returned to Opponent C. On the contrary, S does not play this game.

W. Diffie, P. van Oorschot and M.Wiener, Authentication and authenticated key exchanges, Designs, Codes and Cryptography, Vol. (ii) Requests. As before, S contains four empty tables, and to deal with the corresponding queries. S responds to these C queries as follows. (1) Challenger S has a blank list in the form of . i) If the list already has matching input, S returns to C. (ii) Otherwise S checks the entire table.

If the item is found, S will enter the new entry into the list. If this is not the case, it is randomly selected by S and the corresponding data are written in. (2) StaticKeyReveal (). is revealed by S an C.(3)MasterPrivateKeyReveal. Challenger S responds to this request with . (4) EphemeralKeyReveal (). If so, stop. Otherwise, S returns the volatile key of C. (5) Send (, M). S manages a blank list in the form of . i) If , S X returns to C.

(ii) Si , S Y returns to C. Then looks for the corresponding entry in .