research/rln-research/merkle-tree-update.md

Preliminaries

In a Merkle Tree with the capacity of n leaves , one can compute the root of the tree by maintaining the root nodes of log(n) number of complete Merkle trees. We use this fact and define F to be an array of size log(n) holding the root of complete Merkle trees (all positioned on the left side of the tree) for levels [0, d=log(n)+1]. Each entry of F at position i holds a pair (index, H) where H is the root of the complete subtree at level i, and index indicates the index of the leaf node whose insertion resulted in H.