Ethereum Stateless Series #3: Verkle Tree Verification

1. Why Verkle Trees?

Vitalik’s roadmap for Ethereum statelessness highlights two approaches:

• State expiry
• Weak statelessness

Weak statelessness reduces the need for full nodes to store state by requiring only block proposers to maintain it. Validators can verify state transitions using proofs submitted with each block. However, traditional Merkle trees produce proofs that grow excessively large with tree depth and width. Verkle trees solve this by generating constant-sized proofs, making them ideal for Ethereum’s scalability.

2. The Importance of Proofs

Who needs proofs?

• Full nodes & archive nodes: Store complete state and don’t require proofs.
• Light clients: Rely on proofs to verify data without storing state.

Why end-users care:

• Wallets like MetaMask depend on RPC nodes for balance checks. A malicious node could report incorrect balances (e.g., showing no ETH deduction after a transfer).
• Proofs enable trustless verification, ensuring users receive accurate data even from untrusted nodes.

3. Merkle Tree Verification

How It Works:

• Leaf nodes: Store data (e.g., account balances).
• Internal nodes: Hash child nodes (e.g., H(A-B), H(C-D)).
• Proofs: Require sibling nodes at each level to recompute the root hash.

Problem:

• Ethereum’s hexary Merkle Patricia trees (16 children per node) produce large proofs due to multiple siblings.
• Example: Proving value C exists requires submitting D, H(A-B), and H(E-H)—inefficient for statelessness.

4. Verkle Tree Proofs

Key Innovation: Vector Commitments

• No sibling nodes: Verkle proofs omit siblings, keeping size constant.
• Pedersen/KZG commitments: Replace hashes with cryptographic commitments.

Visual Comparison:

• Merkle proof: Requires 3 hashes for 4ce → HORSE.
• Verkle proof: Single opening proves x_i = v under commitment C.

5. Verkle Tree Verification Methods

KZG Commitments:

1. Encode child nodes as polynomial coefficients.
2. Generate a constant-sized proof using polynomial evaluations.
3. Validators verify openings without storing siblings.

Pedersen Commitments:

• Current favorite for Ethereum.
• Leverages elliptic curves for efficient proofs.

Advantage:

• O(1) proof size regardless of tree width (e.g., 256–1024 children).

FAQs

Q1: Why switch from Merkle to Verkle trees?
A: Verkle trees reduce proof sizes from O(log n) to O(1), critical for stateless clients and rollups.

Q2: How do light clients verify Verkle proofs?
A: They check a single compressed proof against the root commitment, eliminating the need for sibling hashes.

Q3: Are Verkle trees backward-compatible?
A: Yes, but Ethereum will require a hard fork to transition from Merkle Patricia to Verkle trees.

👉 Explore Verkle Trees in Depth

This article simplifies complex cryptography for readability. For mathematical rigor, refer to academic papers on vector commitments.

### SEO Keywords:  
- Ethereum Verkle trees  
- Stateless client proofs  
- KZG commitments  
- Pedersen vector commitments  
- Light client verification