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I know for now practically it is impossible to crack AES 128 key by brute-force attack.

But is it still true if one has the key and can repeatedly use it to encrypt or decrypt arbitrary data block? In another word, given any clear text A, they can get the cipher encrypted with that key.

Is there a term referring to this kind of crack which is 'crack key with the ability to encrypt arbitrary data block by the key'?

Thanks

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Is there a term referring to this kind of crack which is 'crack key with the ability to encrypt arbitrary data block by the key'?

Yes. That's a Choosen Plaintext Attack. AES-128 is designed to resist that, and as far as we know does so very well. CPA is considered indispensable for any modern cipher or block cipher.

Beware however that in practice, an adversary might gather additional information (side channel attacks), like the power consumption during encryptions (Differential Power Analysis), the time it takes to make the encryption (timing attack), or the state of the data cache after that (cache as side channel), or the result of encryption when some of it is affected by errors (fault attack). An AES implementation could be vulnerable to these.

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