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In authenticated identity-based encryption by Benn Lynn, in proof of security, I have a little difficulties in understanding.
In key extraction queries,if attacker request for guessed ID, then B fails. I think this is because B cannot generate private key for guessed ID.
When attacker challenges messages M0,M1 and two identities, if identities are not guessed ID, then B fails.
In this scenario, I think B cannot encrypt for guessed ID as it does not know private key. However, here, it fails when identities are not guessed ID.
Please guide me correct thinking.

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