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MD5 has a collision probability of $1 / 2^{64}$ under the Birthday Paradox. Does this apply to any input given to MD5? As explained in the other answer, $2^{64}$ is the birthday bound of messages until probable collision, not a collision probability. For two random messages you'd expect a $1/2^{128}$ probability of a collision with a 128-bit hash. ...

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