# Merkle Tree High Tree

I'm reading Merkle tree signatures and I like know if the security of the that scheme depends, also, of the high of the tree or only depends that hash function is 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.