Reddit reviews The Design of RijndaeL: AES - The Advanced Encryption Standard (Information Security and Cryptography)
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Used Book in Good Condition
> Has AES been proven to be secure?
No. Proving AES is unconditionally secure would imply One-Way Functions exist which further implies P != NP.
So basically proving AES is unconditionally secure will net you at minimum $1000000. This is true about most cryptographic primitives.
On that note, we believe with overwhelming confidence^1 that AES is very much a family of PRPs.
It is worth reading the design of rijndaal.
^1: After years of cryptanalysis and public scrutiny.
I'd have to agree with /u/pint. The Design of Rijndael is basically the handbook on this. It explains the so called Wide Trail Strategy, which deals with exactly what you're after. You might be able to find some of this in Joan Daemen's PhD thesis as well (at the bottom of this page) - a lot of the stuff in The Design of Rijndael is from there.
It is really sad to see this shit upvoted.
The best cryptographers (and cryptanalysis) folks are pretty much in academia. Most if not all advocate the use of AES. AES has and continues to be cryptanalyzed. The best known attacks are intractable.
NSA may have a bigger budget, but it certainly doesn't have enough to tempt academic professionals that want to produce quality work.
Rijndael wasn't simply born out of a competition, but it was a cipher that evolved over time.
"We did not design Rijndael from scratch. In fact, prior to the design of Rijndael, we had already published three block ciphers that are similar to Rijndael. Each of these ciphers inherits properties from its predecessor and enriches them with new ideas. Moreover, since the publication of Rijndael and its predecessors, a substantial number of cryptographers have based block cipher designs on ideas that were introduced in the Rijndael family. Hence, Rijndael can be seen as a step in an evolution, with predecessors and successors."
I recommend before blabbering at how untrustworthy the NIST competition and AES is, read chapter 11 The Design of Rijndael, and first understand how the design came about.