Game G7 definition
Game G7. We will now conclude, by dealing with sessions where some corruption happened before the second round. We will try not to make use of the knowledge of the password of the honest players. Due to the use of the split functionality model of [6], we can assume that all the players received the same values during the first round since we split the groups according to the first-round messages. In particular, no flow was modified, and £ can extract the password used in non-oracle-generated flow(1a) and flow(1b) (corrupted players, from the beginning), granted z∗ and the list Λε. This extraction is unique granted the collision-restriction included in the simulation (see G1). One can argue that this strategy may fail if A never asked the corresponding encryption query. However, in such a case, A has no control over the plaintext (and in particular no idea about the discrete logarithm), and we deal with this case as if A had an incorrect password with respect to its neighbors (see below). We compare each corrupted player with the neighbor-sets of “consecutive” honest players belonging to the same connected component (sharing the same password). Considering all the possible situations in which a non-corrupted Pi can be, with respect to its neighbors (see Figure 6), we thus distinguish 6 mutually exclusive situations. In the first scheme of this figure, “ =” means that the simulator knows that Pi has the same password as the two nearest (on the left and on the right) corrupted players (according to the passwords extracted from the encryption queries), whereas “/=” stands for different passwords and “?” for unknown relation between the passwords. Corrupted players are denoted by A. Some cases share the same index to denote the fact that they are actually symmetric and can be studied as a single case.
Game G7. In some cases, F generates a random session key when the other party is corrupted. Upon receiving a NewKey query (NewKey, sid, Pi, ki) from S, if there is a fresh record of the form (Pi, pwi), and this is the first NewKey query for Pi, Pi is honest and P1−i corrupted and there is a record (P1−i, pw1−i) with d(pwi, pw1−i) > δ, we let F pick a new random key k from Fq and send (sid, k) to Pi. The simulation ensures that the record ( i, pwi) is either compromised or interrupted (cf. description of the simulator in game G4). Thus, the modification has no effect since it only concerns fresh records. Game G8: F generates a random session key for an honest session. Upon receiving a NewKey query (NewKey, sid, Pi, ki) from S, if there is a fresh record of the form (Pi, pwi), and this is the first NewKey query for Pi, both parties are honest and the NewKey query is not due, we let F pick a new random key k from Fq and send (sid, k) to Pi.
Game G7. In this game, we consider Corrupt queries. Thus, fresh and semi-fresh oracles will only imply fs-fresh and semi-fs-fresh oracles, respectively, in this game. When a Corrupt query is made to a fresh or semi-fresh client, π will be answered, while to a fresh or semi-fresh server, γ' and ν will be answered. In each case, we will modify the games to the correspond- ing “corrupted” games. We define a corrupted game as a game where Execute queries and corresponding random oracle queries are only allowed to the adversary for our measurement. This game could model the notion of forward secrecy. We also define a semi-corrupted game as a game where Send(Sj, C, m ) queries and corresponding random oracle queries are only allowed to the adversary for our measurement. This game could model the resistance against server compromise. All disallowed or unexpected queries are answered by following the rules defined in the previous games as much as possible, while the modified game can be con- sidered as a kind of mini game without those queries. These will make our modified game indistinguishable from the previous games unless specific events occur in the corrupted games. Gq
Examples of Game G7 in a sentence
The advantage of in the obliviousness game will be exactly the same as that of the environment in distinguishing between Game G6 and Game G7.