# Merkle Tree Height

I'm reading about Merkle tree signatures, and I would like to know whether the security of that scheme depends on the height of the tree, or does it only depend on the hash function being resistant to collision?

If you look at exact security, the height matters. The reason is that it defines the number of OTS key pairs and hence the possible number of one time signatures per MSS key pair. To forge a MSS signature, it is enough to generate a forgery for 1 out of $2^h$ OTS signatures. Hence you get a reduction in the bit security of $h$ bits.