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10 August 2021

Verkle Tree Gas Metering Impact

Dedaub was commissioned by the Ethereum Foundation to investigate the impact of Vitalik Buterin’s Verkle tree gas metering proposal on existing smart contracts.

The impact is not negligible, with a 26% gas cost increase on average. However, this will be gauged against the impact to the security and scalability of the consensus of the network, and Verkle trees could be a game-changer in this regard.


Dedaub was commissioned by the Ethereum Foundation to investigate the impact of Vitalik Buterin’s Verkle tree gas metering proposal on existing smart contracts. In order to appraise the impact of the proposed change, we performed extensive simulations of the proposed changes over past transactions; wrote a static analysis and applied it over most contracts deployed to the mainnet; examined bytecode, source, decompiled code, and low level traces of past transactions.

Vitalik Buterin’s proposal introduces new gas changes to state access operations that closely reflect the worst case witness size that needs to be downloaded by a stateless client that needs to validate a block. As described in the original proposal, a Verkle tree is a cryptographically secure data structure with a high branching factor. Unlike Merkle trees, trace witnesses in Verkle trees do not need to include the siblings of each node in a path to the root node, which means that trees with a high branching factor are more efficient. Verkle trees can still retain the security properties by making use of a polynomial commitment scheme. By leveraging these properties, gas costs can therefore more easily reflect the upper bound of the cost of transmitting these witnesses across stateless clients, assuming these are appropriately designed.

In addition to gas changes that the proposal introduces, the Verkle tree proposal may break protocols that are too tied to the existing implementation, such as protocols that use Keydonix Oracles like Rune, but this consideration is outside the scope of this report.

In the report we briefly summarize the proposal with respect to gas costs. We then delve into the impact to existing contracts using two techniques: path-sensitive static program analysis, and dynamic analysis by modifying an Erigon node with the new gas semantics and analyzing the data per internal transaction. Finally we state our recommendations for lessening the impact of this proposal.


The goal of the proposal [1] aims to make Ethereum _stateless clients _sustainable in terms of data transmission requirements.

Stateless clients should be able to verify the correctness of any individual block without any extra information except for the block’s header and a small file, called witness, that contains the portion of the state accessed by the block along with proofs of correctness. Witnesses can be produced by any state-holding node in the network. The benefits of stateless verification include allowing clients to run in low-disk-space environments, enabling semi-light-client setups where clients trust blocks by default but stand ready to verify any specific block in the case of an alarm, and secure sharding setups where clients jump between shards frequently without the need to keep up with the state of all shards.

Large witness sizes are the key problem for enabling stateless clients for Ethereum and the adoption of Verkle trees can reduce the witness sizes needed. More specifically, a witness accessing an account in the hexary Patricia tree is, in the average case, close to 3 kB, and in the worst case it may be three times larger. Assuming a worst case of 6000 accesses per block (15m gas / 2500 gas per access), this corresponds to a witness size of ~18 MB, which is too large to safely broadcast through a p2p network within a 12-second slot. Verkle trees reduce witness sizes to ~200 bytes per account in the average case, allowing stateless client witnesses to be acceptably small.

Finally, contract code needs to be included in a witness. A contract’s code can contain up to 24000 bytes, and so a 2600 gas CALL can add ~24200 bytes to the witness size. This implies a worst-case witness size of over 100 MB. The proposal suggests breaking up contract code into chunks that can be proven separately; this can be done simultaneously with a move to a Verkle tree. Since a contract’s code can contain up to 24000 bytes, and so a 2600 gas CALL can add ~24200 bytes to the witness size. This implies a worst-case witness size of over 100 MB. The solution is to move away from storing code as a single monolithic hash, and instead break it up into chunks that can be proven separately and adding gas rules1 that accounts for these costs2.

The small witness sizes described above are possible because Verkle trees rely on an efficient cryptographic commitment scheme, called Polynomial Commitments3 4. Polynomial Commitments allow for logarithmic-sized (in respect to the tree’s height) proof-of-inclusion of any number of leaves in a subtree – and this is independent to the branching factor of the tree. In comparison, traditional Merkle tree’s proofs depend on the branching factor of the tree in a linear fashion, since all siblings of a node-to-be-proved must be included in the proof.


The current proposal suggests new gas costs which have no counterpart in the previous versions of Ethereum. These is a gas cost for every chunk of 31 bytes of bytecode which are accessed and some additional access events that apply to the entire transaction. An improvement in gas cost can however be also achieved by lowering the cost for SLOAD/SSTORE for when fewer subtrees of the tree structure underpinning the state are accessed. The following is a summary of the gas cost changes between EIP-2929, which introduces the notion of “access lists” and the current proposal.

SLOAD, but location previously accessed within the same tx using SLOAD or SSTORE


SLOAD, but location previously unread within the tx using SLOAD or SSTORE

Verkle200 if previously visited subtree 2100 if subtree has not been visited (storage location is up to 64 / 256 elements away from the closest visited)

CALL an address for an account that has not been previously accessed within the tx

VerkleAccess list costs (typically 1900 + 200 + 200 + more if value bearing)

EIP-2929 mentions that precompiles are not charged COLD_ACCOUNT_ACCESS_COST but the Verkle specification omits this case at the time of writing.

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