When you have a Merkle tree, what is the minimal number of hashes needed to verify a change to one leaf node?
Am I correct in my understanding that, at first, only the top hash (the Merkle tree root or hash of the Merkle tree root) is needed? And then once a leaf is modified, you need to obtain the hashes of each row "visited" while descending to the leaf node that got modified?
So if a root has, say, ten children and one grand-children that is modified and I want to verify that particular grand-children, I need to obtain the new merkle root hashes, the hashes of the ten children and the hashes of the children of the parent of the grand-children.
So at every modification you always need to obtain, at least, all the hashes from the first row? (otherwise how do you reconstruct and verify the merkle root hash?)