Let's say I have a large amount of files, say 20GB worth, all encrypted with the same AES key. Each file is encrypted individually.
Now, suppose I get ahold of 10GB of these files in decrypted format. And let's say I can even match up which files are which by using their sizes.
Seems I have a whole lot of information here - is it possible for me to crack the key and get the other 10GB of data out in unencrypted form?
Please help me understand why this is possible or not possible. I've searched the net extensively and I cannot find anyone discussing this topic. All I can find are generic statements about how AES is "unbreakable." But I am curious if this unbreakability holds in the event that a large amount of data has been compromised.
No, it is not (believed) possible.
The attack scenario you are referring to is a commonly studied scenario, called ''known-plaintext attack''.
A cipher is only considered secure if it is resistant against this (and many other) attacks. "Resistant" in this context means that having plaintext (no matter how much) does not make it any easier to find a key.
As to why this is the case, this is hard to understand without knowing a lot about the structure of AES and the possible attack modes. For an introduction, see e.g. the references of the Wikipedia article on AES, or have a look at The Design of RijndaeL: AES - The Advanced Encryption Standard (by Daemen & Rijmen themselves).
Related question: Why is AES resistant to known-plaintext attacks?
AES is not a stream cipher and the output varies a lot for a small input changes (avalanche effect)
Breaking AES encryption using decrypted data
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