# How to derive a hash function from another hash function?

Problem:

I'm trying to figure out how to solve this, apparently it's hashing the hash value itself. So G has two rounds of hashing the original message x. I tried searching for the relationship properties that I could use to achieve this

•Collision resistance implies 2nd-preimage resistance

•If the output values of 𝐻 are uniformly distributed, then collision resistance implies preimage resistance

•If the output values of 𝐻 are uniformly distributed, then 2nd-preimage resistance implies preimage resistance

•Preimage resistance does not imply 2nd-preimage resistance

•2nd-preimage resistance does not imply collision resistance

But I didn't find anything I could use, I'm really having trouble, so I'd appreciate any help.

• instead of an image, could you write the question, please? And use bullets. – kelalaka Oct 17 at 22:00
• Suppose you have a collision $G(x') = G(x), x' \neq x$ meaning that $H(H(x)) = H(H(x'))$. Can you construct a collision using that for $H$? – Carl Löndahl Oct 17 at 22:01
• Woud I need to use Merkle-Damgard to do this? I honestly am a little lost. – Jorge Oct 17 at 22:19
• @Jorge No. Carl gave you hint based on Contraposition – kelalaka Oct 18 at 5:49