What is erkel tree in ethereum

What is Handshake? Rebalancing data structures are no good, since they're not history independent Merkle Patricia Tree, right? But proof sizes are too large, and storage requirements are too large Sparse Merkle Tree?

Didn't cut it in terms of performance, requires a bunch of DB lookups Way too many rounds of hashing per insertion What can we use instead? Urkel Tree: an optimized and cryptographically provable key value store for decentralized naming Intended to be stored in append-only flat files Base-2 Merkleized trie Based on the Merkle Set, invented by Bram Cohen Two types of nodes: internal nodes and leaf nodes Storing 4 types of nodes like in Patricia Trees sucks Append only files gives you crash-consistency How does it work?

Basically involves a lot of tombstone nodes and common hash prefixes Simplicity - Maintains only two types of nodes: internal nodes and leaf nodes. Storage - Internal nodes are small a constant size of 76 bytes on disk. This is important as internal nodes are frequently rewritten during updates to the tree.

Proof Size - Sibling nodes required for proofs are a constant size of 32 bytes, similar to a typical merkle tree proof. This results in an extremely compact proof size. The final benefit was the primary focus of the Handshake protocol. As name resolutions are a frequently requested operation, Handshake required proof sizes less than 1kb even after hundreds of millions of leaves are present in the tree.

History independence and non-destruction are also inherent properties of the urkel tree, just the same as the Ethereum trie. Note that urkel should only be used with uniformally distributed keys i. Compaction, while available, is currently inefficient and requires user intervention. This will be optimized in a future C implementation of the urkel tree. In the meantime, we don't see this as a problem as long as frequent commissions are avoided in consensus applications of the tree i.

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While traversing a path one nibble at a time, as described above, most nodes contain a element array. One index for each possible value held by the next hex character nibble in the path, and one to hold the final target value if the path has been fully traversed. These element array nodes are called branch nodes. Merkle Patricia Trie However, radix tries have one major limitation: they are inefficient.

If you want to store just one path,value binding where the path is in the case of the ethereum state trie , 64 characters long number of nibbles in bytes32 , you will need over a kilobyte of extra space to store one level per character, and each lookup or delete will take the full 64 steps. The Patricia trie introduced here solves this issue. Optimization Merkle Patricia tries solve the inefficiency issue by adding some extra complexity to the data structure.

It would be naive to require such a node to have empty values in every index one for each of the 16 hex characters besides the target index next nibble in the path. As a result of this, we can only safely commit to bit strings of at most bits, otherwise the field overflows. We chose a branching factor width of for the verkle tree, which means each commitment can commit to up to values of bits each or to be precise, integers up to p - 1.

Layout of the verkle tree One of the design goals with the verkle tree EIP is to make accesses to neighbouring positions e. In order to do this, a key consists of a stem of 31 bytes and a suffix of one byte for a total of 32 bytes. The key scheme is designed so that "close" storage locations are mapped to the same stem and a different suffix.

For details please look at the EIP draft. The verkle tree itself is then composed of two types of nodes: Extension nodes, that represent values with the same stem but different suffixes Inner nodes, that have up to children, which can be either other inner nodes or extension nodes. The commitment to an extension node is a commitment to a 4 element vector; the remaining positions will be 0. The reason we need to commitments is that values have 32 bytes, but we can only store bits per field element.

A single commitment would thus not be enough to store values. Figure 1 Representation of a walk through a verkle tree for the key 0xfeabcd.. Note that stem is actually the first 31 bytes of the key, including the path through the internal nodes. Commitment to the values leaf nodes Each extension and suffix tree node contain values. Because a value is bits wide, and we can only store bits safely in one field element, four bits would be lost if we simply tried so store one value in one field element.

To circumvent this problem, we chose to partition the group of values into two groups of values each. Each byte value in a group is split into two byte values. No value ever gets deleted from a verkle tree. This is needed for upcoming state expiry schemes.

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