# Preimage security of combined hash functions

I am struggling with a property of combined hash function and more precisely concatenation. I have seen that concatenating two collision resistant hash functions preserves this property (same for 2nd preimage resistance). But not always for the first preimage. Indeed, some explains that if the two concatenated hash functions are dependent, the result function could be first preimage weak even if the concatenated functions are preimage resistant. I don't see how it could happen.

First image resistance: From y=H(x), it is computationally infeasible to find any input which hashes to that output y.

• – kelalaka Nov 6 '20 at 17:59
• @kelalaka If I'm not wrong, this is about collision and second preimage attack but not first preimage attack – BMalone Nov 6 '20 at 18:57
• It mentions inside, As far as I remember. Could you provide links for some explains.. – kelalaka Nov 6 '20 at 19:03
• this is what I've understood from slide 38 homes.esat.kuleuven.be/~preneel/preneel_hash_tools_2012v1.pdf – BMalone Nov 6 '20 at 19:10
• and if we want to concatenate two first preimage resistant hash functions, the concatenation of the two needs to use depency between the two concatenated functions (if there is) otherwise it will be not computationally feasibe no? – BMalone Nov 6 '20 at 19:20