To show that E Sample Clauses

To show that E. 2.1.1 cannot happen with non–negligible probability, we modify the simulation in the analysis of E.1.1.3 to take as input a ∈R [1, q − 1] and X0, B ∈R G∗ (Aˆ’s key pair is set to (a, Ga), and Bˆ’s public key to B); S aborts if A activates a session matching the t–th session at Aˆ. The simulation remains perfect, except with negligible probability. And if S guesses correctly the test session, and A succeeds with a forgery σ0, S outputs σ0 as a FDCR–1 forgery, on messages Aˆ and Bˆ with respect to the public keys A and B. S succeeds with probability ((n − n1)2m)−1 Pr(E.2.1.1), and contradicts Proposition 3, unless Pr(E.2.1.1) is negligible.
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To show that E. 2.1 cannot happen with non-negligible probability, the simulation proceeds i0 j0 i q(k)

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