# Merkle–Damgård padded block concatenated outside the compression function hash?

I learned that the output of hash function from Merkle Damgard is

H(x) = ZB+1 = h(ZB || L) = h(ZB - 1 || XB || L) where XB = block of padded x and L = XB+1

and it is proven that H(x) is collision resistant. However, what if I tweak the H(x) by extracting L from the compression function h(x) s.t

H(x) = h(ZB - 1 || XB) || L

I feel like this makes H(x) to be not collision resistant, but I don't know how to design an attack for this hash function. Can someone give me an idea (perhaps hint) to design such attack?

NOTE: Before anyone screams at me about anything, I want to say YES this is a practice question from a cryptography textbook. That is why I asked for a HINT not an answer. Thanks :)

Why don't you look at it the other way; suppose you could find a collision with your modified H(x) = h(ZB - 1 || XB) || L; could you use that collision to find a collision in the original H?
• @ThomasWest: if you prove that, if you can find a collision in the new $H$, you can find a collision in the original $H$, then you've proven that the new $H$ is at least as collision resistant as the original. – poncho Nov 20 '17 at 18:17