Merkle Proofs and Simplified Payment Verification (SPV) in Bitcoin

A Merkle Proof allows a lightweight client to verify that a transaction is included in a block without downloading the entire block.

How it works:

1. SPV clients store only the block headers, which include the Merkle Root.
2. To verify a transaction Tx3, the client requests the Merkle path from a full node:

• H3 → H4 (sibling hash) → H12 (parent hash)

3. The client reconstructs the Merkle Root using the hashes along the path and checks if it matches the root in the block header.

Example – SPV Verification:

• Alice wants to verify her Bitcoin transaction in block #100,000.
• SPV client knows the Merkle Root from the block header.
• Alice provides Tx3 and its Merkle path (H4, H12).
• Client calculates:
  • H34 = SHA256(H3 || H4)
  • Root = SHA256(H12 || H34)
• If this equals the Merkle Root in the block header → Transaction verified without downloading all transactions in the block.

Benefits for Blockchain:

• Saves storage and bandwidth.
• Enables mobile/lightweight wallets to participate securely.
• Ensures trustless verification using cryptography instead of relying on a full node.

Summary:

• Merkle Tree: Binary tree of transaction hashes; root summarizes all transactions.
• Transaction Integrity: Any modification in a transaction changes the root, allowing tamper detection.
• Merkle Proofs & SPV: Lightweight clients can verify inclusion of a transaction using only the Merkle path, not the full block.
• Widely used in Bitcoin, Ethereum, and many other blockchains to improve efficiency, security, and scalability.