Verkle trees are shaping up to be an important part of Ethereum's upcoming scaling upgrades. They serve the same function as Merkle trees: you can put a large amount of data into a Verkle tree, and make a short proof ("witness") of any single piece, or set of pieces, of that data that can be verified by someone who only has the root of the tree. The key property that Verkle trees provide, however, is that they are much more efficient in proof size. If a tree contains a billion pieces of data, making a proof in a traditional binary Merkle tree would require about 1 kilobyte, but in a Verkle tree the proof would be less than 150 bytes - a reduction sufficient to make stateless clients finally viable in practice.
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