# Min/max of hash function (Whirlpool)

The Whirlpool hash function generates a 128-digit hexadecimal number. Could that number ever be 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 or FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF?

• Probably, but it is very improbable: the probability should be roughly $2^{-127}$ to obtain either (assuming Whirlpool is a reasonable hash function, and an appropriate notion of random string). – Yuval Filmus Oct 16 '13 at 0:22
• I should clarify that by "improbable" I mean that it's highly improbable to obtain this hash value on any given input (more accurately, on a random input, say a random file of given length). Also, the probability should be $2^{-511}$ rather than $2^{-127}$. Why are you interested in this question? – Yuval Filmus Oct 16 '13 at 0:28
• @YuvalFilmus to be clear, it is not improbable that ${0}^{128}$ or ${F}^{128}$ is a valid hash of something. Rather it is improbable that you will ever find such an input to result in one of these hashes. – Realz Slaw Oct 16 '13 at 0:29