How can Deterministic Pseudo Random Number Generator generate 64 byte hash from 32 byte seed using SHA-256 hashing function?

Question

SHA-256 hashing function outputs 32 byte hash always. How can I, using 32 byte seed and SHA-256 hashing function to create an 64 byte hash output ?

I've heard that they use technique like this (pseudocode):

init_hash = SHA256 (seed)
next_hash = SHA256 (init_hash + 1)
next_hash_vol2 = SHA256 (next_hash + 2)
next_hash_vol3 = SHA256 (next_hash_vol2 + 3)
...
next_hash_volA = SHA256 (next_hash_vol9 + A)
...
next_hash_vol10 = SHA256 (next_hash_volF + 10)
...
...
next_hash_vol64 = SHA256 (next_hash_vol63 + 40)

This sounds really nice! But problem is that SHA-256 ALWAYS generates 32 byte output, but I need 64 bytes :(

Answer 1

If you are starting with a 32 byte seed and a 32 byte hash, you will end up with 32 bytes of entropy no matter how much you expand it.

Given that, then you have many options such as the one @David Schwartz suggested. Here is a different option in pseudocode:

hash64(inputString)
  hash1 = SHA256(inputString)
  hash2 = SHA256(hash1)
  return concatenate(hash1, hash2)
end hash64

Many other similar options are possible, such as:

hash64(inputString)
  gnirtStupni = reverse(inputString)
  hash1 = SHA256(inputString)
  hash2 = SHA256(gnirtStupni)
  return concatenate(hash1, hash2)
end hash64

Essentially, two separate hashes based on the same input, but tweaked so the hashes are not identical. Then concatenate the two hashes.