This is giving me a brain ache now... If I have AES-128, block is 128 bit, then every plaintext (128-bit) can be encrypted to some ciphertext that is also 128-bit. This is the block size. But: 128-bit ...
This answer points out that certain key and block lengths were a requirement for the AES submissions: The candidate algorithm shall be capable of supporting key-block combinations with sizes of ...
My intuition tells me it's a trade off between speed and security, but how did the standardisation process select these three seemingly arbitrary key lengths (namely, AES-128, AES-192, AES-256).
AES has several different variants (AES-128, AES-192, AES-256), but why would I use one over another?