# PQC: XMSS L-Trees

I understand how WOTS+ signing works: I create a secret key and put it into leaves of my binary tree and hash it with some random values in the binary tree with my chaining function until the root is created, which is the public key.

But how do I combine that with the XMSS L-Trees?

The XMSS tree is constructed using the W-OTS keys. Each leaf of the XMSS tree corresponds to a distinct W-OTS key. The W-OTS keys have length $$ln$$, but each node of the XMSS tree should have length $$n$$.
In order to make the size of the W-OTS keys compatible with the XMSS tree, the L-tree is used to first reduce the W-OTS key from $$ln$$ to $$n$$ bits.The L-tree divides the W-OTS key into $$l$$ $$n$$-bit strings, which then form the $$l$$ leaves of the L-tree. The root of the L-tree is $$n$$ bits and can be used as a leaf in the XMSS tree.