darkfi/doc/src/spec/crypto/merkletree.md

Merkle-tree

Append only merkle-tree tree

Merkle-node

A node node is a field element on the elliptic curve

Merkle root

Hash of leaf up to certain depth root(tree, depth), hash the leafs including the empty nodes up to given depth,

Witness

Authentication path to given depth, and bridge frontier, or position.

Sparse merkle tree

Is a merkle-tree with leafs stored in a search tree, has advantage over merkle-tree that is a allow non-inclusion proof, through membership proof to index of data in the search tree.

Membership proof

Given index the proof is a path from the leaf at index to the root.