Imagine a large array (Megabytes) that is virtually empty, i.e. contains 0 in almost all locations. But also imagine there's 1000 pseudo random locations that contain a pseudo random byte. There is no correlation between bytes nor locations. So on average, there is a random byte > 1000 bytes apart. Then the entire array is hashed with a Merkle–Damgård type hash.
Is there a way to speed up the overall hashing time by knowing that the likely values ahead are 0? Certainly most of the time, the next input block will be all 0. Many times over. Can this statistical predictability be leveraged for speed?