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As CodesInChaos notes in the comments, having more ciphertext–plaintext pairs doesn't help with brute force guessing attacks. Well, that is, except for the minor issue of unicity. Basically, to narrow the results of your brute force attack down to a single key, you do need to have enough ciphertext–plaintext pairs that the length of the known plaintext ...


EDIT: I realised that I assumed an IND-CPA game where the adversary has pre- and post-challenge access to the encryption oracle and not only pre-challenge access. I'll edit my answer soon. I'll give the idea and leave the concrete analysis to you. You want to show that single-query IND-CPA implies multi-query IND-CPA or in other words if there is an ...


The Game described in #1 is equivalent to IND-CPA security according the CRYPTUTOR wiki from UIUC (The section on modifications). This may explain why Mikero had trouble coming up with a counter example.


The oracle in step 3 is absolutely necessary. Check the answer to this question for an example that would break IND-CPA security otherwise. On the other hand, the oracle in step 5 may be unnecessary for IND-CPA security according to the alternate formulations of IND-CPA suggested in the CRYPTUTOR wiki from UIUC.

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