What is the range of possible sha1hash results?

Question

What is the lowest and highest possible returns from sha1? (with respect that sha1 results are actualy 5 32 bit values rather than 1 true 160 bit value)

Answer 1

To create a secure hash the output of the hash must be indistinguishable from random. Many pseudo random number generators and key derivation methods actually use a hash as final calculation.

So the "highest" result consists of all zero's, the lowest consists of all ones. That is, if you interpret the result to be an unsigned integer of course. The chances of exactly getting those values is almost zero of course, as SHA-1 results should be evenly distributed. But the change of a number starting with 8 ones is still 1/2^8 == 1/256, which is certainly not insignificant.

Note that the result of SHA-1 should be interpreted as a bit string. Most runtimes don't have a very useful bitstring representation and use an octet string (aka byte array) instead. I would consider it very annoying of a SHA-1 implementation would return shorts instead of bytes. You don't want to annoy the user with differences in little-endian and big-endian representations, and most other primitives do expect their input represented as bytes.