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I am studying about the AES encryption standard, and as I know from the theory there is no known weaknesses today about this block-cipher.

I would like to find out or at least to understand what "classification" of secureness is AES.

As I know there are several classifications:

  1. Perfectly secure. Which is not able to break and an example is the One-Time-Pad.
  2. Provably secure that is we can proof that the complexity of the algorithm is closed to a known theoretical assumption like the NP-hard.
  3. Practically secure when an encryption algorithm is tested for long time and there is no sucesful attack so far.

With this in mind I will say that the AES is provably secure because as I know (correct me if I am wrong) the AES is able to crack but to test all the possible keys will take trillion (?) years to achieve that so that my answer.

So I am wrong?

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    $\begingroup$ More concretely, "perfectly secure" means that mathematically, the ciphertext contains no information about the message unless you have the key (except for a maximum possible length). That said, it's a poor choice of terminology, because one-time pads are susceptible to some forms of attack (for instance, they are malleable). $\endgroup$ – Stephen Touset May 28 '15 at 22:51
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I think you meant brute force when you mention, it would take trillions(?) years to break AES. So your "provably secure" category boils downs to brute forcing the algorithm which is not considered "breaking" the algorithm.

AES is kind of a successor to DES (at least for an initial understanding) which had been in use for quite a long time and was not broken until it was easy to brute force it. So it's safe to say DES is "practically secure" and so is AES. Although I doubt you one categorize crpto Algos like these but I think i get your point.

There have been unconfirmed reports of breaking AES so it can be categorized to be practically secure for the basic understanding. http://en.wikipedia.org/wiki/Advanced_Encryption_Standard#Known_attacks

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AES is not provably secure, for the simple reason that there is no security proof for it. We suspect that AES is secure in practice, but there is no proof of that.

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