In identity-based encryption, users decrypt the ciphertext by using private keys.
Without private key, no one will be able to decrypt.
In security proofs like here, random oracles are used with the restriction that the attacker is not allowed for key extraction for target identities.
With this restriction, it is sure for security because attacker does not know the private key of target identities.
Then, why presents random oracles?

  • $\begingroup$ Are you talking about the random oracle model? Or about the Decisional-Diffie-Hellman oracle? $\endgroup$ – CodesInChaos Jul 13 '16 at 14:32
  • $\begingroup$ @CodesInChaos.random oracle model. $\endgroup$ – La Yate May Jul 13 '16 at 14:33
  • $\begingroup$ Could you point to the specific security proof you are talking about? $\endgroup$ – otus Jul 14 '16 at 4:40
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    $\begingroup$ @otus.Efficient Multi-Receiver Identity-Based Encryption and Its Application to Broadcast Encryption by J.Baek,R. Safavi-Naini, W.Susilo. $\endgroup$ – La Yate May Jul 14 '16 at 6:01
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    $\begingroup$ @otus.Authenticated identity-based encryption by Ben. Lynn $\endgroup$ – La Yate May Jul 14 '16 at 6:07

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