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Give a 256 bit key space and 128 message space would AES block cipher as the encryption scheme be CPA secure?

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AES is just a primitive. You should describe how you use it to build an actual encryption scheme. And how do you use the IV? – CodesInChaos Nov 26 '12 at 21:33
@CodesInChaos Reading this back (a comment pointed to it) I think the AES block cipher is an encryption scheme. One that only accepts 128 bit messages, but that seems to be the defined message space in the question. – Maarten Bodewes Jul 15 '14 at 20:41

You are mistaken about what an encryption scheme is. As CodeInChaos pointed out AES is a primitive and we assume that it is a preudo random permutation. That is an assumption since the way AES is built means that we won't be able to formally prove that it is one. With that PRP we try to build modes of encryption that might or might not be CPA-secure I encourage you to read Mihir Bellare course notes and especially the chapters about Symmetric encryption and pseudo random functions

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Using AES with a random oracle IV as in CBC mode or using a unique nonce as in CTR constrction will result in a CPA secure construction. You cannot play with the size of the key. The key is strictly defined in each mode.

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