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What are the practical differences between 256-bit, 192-bit, and 128-bit AES encryption?
You would use AES 256 to protect against quantum brute force attacks; Grover's algorithm speeds up a brute force attack by the square root of n (see en.wikipedia.org/wiki/Grover's_algorithm)
Taking advantage of one-time pad key reuse?
This picture illustrates things beautifully. I guess the spirit of my question was "how would you actually do the statistical analysis once you have $m_1 \oplus m_2$"; a respectable cryptographer would probably say something like "that's trivial".