Game G5 definition

Game G5. In this game, we rst deal with the passive case, in which all the ows are oracle-generated. The simulation of the rst three rounds is done as in G4 and we then consider two cases. If all the ows were oracle-generated up to round 4, we require S to simulate the end of the execution of the protocol on behalf of all the players. Otherwise, it simply follows the protocol (as above). In the former case (with only oracle-generated ows up to round 4), the simulator starts round 4 by asking a SamePwd-query. Notice that since we are assuming that S knows all the passwords, this boils down to verify that all the passwords are actually the same. Now we distinguish two cases: If all passwords are the same, S asks a Delivery query with a random key and keyword yes to the functionality for each player. Otherwise, all the players receive an error message. A problem only appears if A asks the corresponding query to H0, but then it must have obtained the values hi and event AskH, as described below, appears. − H
Sample 1Sample 2
Game G5. In this game, we attempt to solve CDH if the adversary has been lucky in guessing the password before a Corrupt query and asks Execute(Ci, Sj) and random oracle queries. We achieve this aim by further modifying the random oracle queries to hi for i 2, 3, 4 and using the reduction from CDH. In other words, given a random Xxxxxx-Xxxxxxx instance X, Y such that X gx and Y gy, we construct an algorithm Ψ that attempts to solve CDH (i.e., find Z such that Z gxy) by running on the simulation changed in the following way. R R
Sample 1
Game G5. Game G5 is same as Game G4 except that instead of a DDH-tuple (g, gra , grb , grarb ), ∆ chooses a random tuple (g, gra , grb , grc ). ∆ continues answering the queries as in Game G4, except that the role of grarb is taken by grc . And now when answering the Reveal query or Test query (in case r rc bit b = 1), ∆ uses g a in computing the session key instead of g rb which the protocol demands. Thus the only difference between games G4 and G5 is the computational distance between a DDH-tuple and a random tuple, therefore: | Pr[W in4] - Pr[W in5]| ≤ AdvDDH(tj). where tj is bounded by t + |P|(qex + qs)(texp + tlkup), texp being the time to perform an exponentiation in G and tlkup the time to perform a look-up in tables L and Sessions.
Sample 1

Examples of Game G5 in a sentence

  • Game G6 is same as Game G5 except that irrespective of the value of the bit b, ∆ answers the Test query with a random value.

  • If b = 0, the challenger will return actual (Fi, Xi) values, and the environment’s view we will be that of Game G5.

  • The advantage of in the obliviousness game will be exactly the same as that of the environment in distinguishing between Game G5 and Game G6.

  • Also Pr[W in5] = Pr[W in6] because while in Game G5, ∆ answers with grarl as a response to the Test query, in Game G6 ∆ answers with grandom.

  • We can use any environment who can distinguish this game from Game G5 to build an adversary B that can break the obliviousness property of our garbling scheme.

  • B executes RFE’s simulation of 0 as in Game G5, but instead of generating (F0, X0) and (F1, X1) according to the protocol, it queries the obliviousness challenger on (f, (pw0, pw1)) to obtain (F0, X0).

Related to Game G5

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