Zokyo Auditing Tutorials
  • 🔐Zokyo Auditing Tutorials
  • 📚Tutorials
    • 🏃Tutorial 1: Front-Running
      • 🚀Prerequisites
      • 📘Understanding Front-Running
      • 👓Examples
      • ⚒️Mitigation Steps
      • 🏦Resource Bank to more front running examples
      • 🤝Front-Running Conclusion
    • 🧱Tutorial 2: Unsafe Casting
      • 🚀Prerequisites
      • 📘Understanding Casting
      • 👓Examples
      • 🤝Unsafe Casting Conclusion
    • 👍Tutorial 3: Approvals and Safe Approvals
      • 🚀Prerequisites
      • 📘Understanding Approvals
      • 👓Vulnerability Examples
        • 🔁ERC20 Approval Reset Requirement
        • 😴Ignoring Return Values from ERC20 approve() Function: Potential Miscount of Successful Approvals
        • 🚫Improper use of Open Zeppelins safeApprove() for Non-zero Allowance Increments
        • 🥾Omitted Approval for Contract Interactions Within a Protocol
        • 🤦‍♂️Failing to Reset Token Approvals in Case of Failed Transactions or other actions
        • 💭Miscellaneous
        • ERC20 Approve Race Condition Vulnerability
      • ⚒️Spot the Vulnerability
      • 🤝Approvals and Safe Approvals Conclusion
    • ⛓️Tutorial 4: Block.chainid, DOMAIN_SEPARATOR and EIP-2612 permit
      • 🚀Prerequisites
      • 📘Understanding Block.chainid and DOMAIN_SEPARATOR
      • 👓Examples
      • ⚒️General Mitigation Steps
      • 🤝Tutorial 4 Conclusion
  • 💰Tutorial 5: Fee-On-Transfer Tokens
    • 🚀Prerequisites
    • 📘Understanding Fee-On-Transfer
    • 👓Examples
    • 📘Links to more fee-on-transfer vulnerability examples
    • 🤝Fee-On-Transfer Tokens: Conclusion
  • 🌴Tutorial 6: Merkle Trees
    • 🚀Prerequisites
    • 📘Understanding Merkle Trees
    • 🔎Verification within a Merkle Tree:
    • 📜Merkle Proofs Within Smart Contracts
    • 🖋️Merkle Proof Solidity Implementation
    • 🛑Vulnerabilities When Using Merkle Trees
    • 💀Example Vulnerabilities
    • 🧠Exercise
    • 🤝Merkle Trees Conclusion
  • 🌳Tutorial 7: Merkle-Patricia Trees
    • 🚀Prerequisites
    • 📘Understanding Merkle-Patricia Trees
    • 📕Understanding Merkle-Patrica Trees pt.2
    • 🔎Verification within a Merkle-Patricia Tree
    • 🛑Vulnerabilities When Using Merkle-Patricia Trees
    • 💀Example Vulnerability
    • 🤝Merkle-Patricia Trees: Conclusion
  • 🔁Tutorial 8: Reentrancy
    • 🚀Prerequisites
    • 📘Understanding Reentrancy
    • ⚒️Mitigation
    • 💀The DAO Hack: An In-depth Examination
    • 👓Examples
    • 🏦Resource Bank To More Reentrancy Examples
    • 🤝Conclusion: Reflecting on the Reentrancy Vulnerability
  • 🔂Tutorial 9: Read-Only Reentrancy
    • 🚀Prerequisites
    • 📘Understanding Read-Only Reentrancy
    • 🔨Mitigating Read-Only Reentrancy
    • 👓Real World Examples
    • 🏦Resource Bank To More Reentrancy Examples
    • 🤝Read-Only Reentrancy: Conclusion
  • 🚆Tutorial 10: ERC20 transfer() and safeTransfer()
    • 🚀Prerequisites
    • 📘Understanding ERC20 transfer() and safeTransfer()
    • 👓Examples
    • 🤝Conclusion
  • 📞Tutorial 11: Low level .call(), .transfer() and .send()
    • 🚀Prerequisites
    • 📘Understanding .call, .transfer, and .send
    • 🛑Understanding the Vulnerabilities of .transfer and .send
    • 👓Examples
    • 🤝Low level .call(), .transfer() and .send() conclusion
  • ☎️Tutorial 12: Delegatecall Vulnerabilities in Precompiled Contracts
    • 🚀Prerequisites
    • 📳Understanding Delegatecall
    • ⛰️EVM, L2s, Bridges, and the Quest for Scalability
    • 🏗️Understanding Precompiles in the Ethereum Virtual Machine (EVM)
    • 💻Custom Precompiles
    • 💀Potential Vulnerabilities in EVM Implementations: Overlooked DelegateCall in Precompiled Contracts
    • 👓Real World Examples
    • 🤝Delegatecall and Precompiles: Conclusion
  • 🌊Tutorial 13: Liquid Staking
    • 🚀Prerequisites
    • 📘Understanding Liquid Staking
    • 💀Understanding Liquid Staking Vulnerabilities
    • 🛑Example Vulnerability
    • 🐜Example Vulnerability 2
    • 🕷️Example Vulnerability 3
    • 🤝Liquid Staking: Conclusion
  • 🚿Tutorial 14: Slippage
    • 🚀Prerequisites
    • 📘Understanding Slippage in Automated Market Makers (AMMs)
    • 💀Understanding the "Lack of Slippage Check" Vulnerability in Automated Market Makers (AMMs) and DEXs
    • 😡On-Chain Slippage Calculations Vulnerability
    • 📛0 slippage tolerance vulnerability
    • 👓Real World Examples
    • 🏦Resource bank to more slippage vulnerabilities
    • 🤝Slippage Conclusion
  • 📉Tutorial 15: Oracles
    • 🚀Prerequisites
    • 📘Understanding Oracles
    • 📈Types of price feeds
    • 😡Flash Loans
    • 💀Understanding Oracle Vulnerabilities
      • ⛓️The Danger of Single Oracle Dependence
      • ⬇️Using Deprecated Functions
      • ❌Lack of return data validation
      • 🕐Inconsistent or Absent Price Data Fetching/Updating Intervals
    • 🔫Decentralized Exchange (DEX) Price Oracles Vulnerabilities
    • 🛑Found Vulnerabilities In Oracle Implementations
      • ⚖️Newly Registered Assets Skew Consultation Results
      • ⚡Flash-Loan Oracle Manipulations
      • ⛓️Relying Only On Chainlink: PriceOracle Does Not Filter Price Feed Outliers
      • ✍️Not Validating Return Data e.g Chainlink: (lastestRoundData)
      • 🗯️Chainlink: Using latestAnswer instead of latestRoundData
      • 😭Reliance On Fetching Oracle Functionality
      • 🎱Wrong Assumption of 18 decimals
      • 🧀Stale Prices
      • 0️⃣Oracle Price Returning 0
      • 🛶TWAP Oracles
      • 😖Wrong Token Order In Return Value
      • 🏗️miscellaneous
    • 🤝Oracles: Conclusion
  • 🧠Tutorial 16: Zero Knowledge (ZK)
    • 🚀Prerequisites
    • 📚Theory
      • 🔌Circom
      • 💻Computation
      • 🛤️Arithmetic Circuits
      • 🚧Rank-1 Constraint System (R1CS)
      • ➗Quadratic Arithmetic Program
      • ✏️Linear Interactive Proof
      • ✨ZK-Snarks
    • 🤓Definitions and Essentials
      • 🔑Key
      • 😎Scalar Field Order
      • 🌳Incremental Merkle Tree
      • ✒️ECDSA signature
      • 📨Non-Interactive Proofs
      • 🏝️Fiat-Shamir transformation (or Fiat-Shamir heuristic)
      • 🪶Pedersen commitment
    • 💀Common Vulnerabilities in ZK Code
      • ⛓️Under-constrained Circuits
      • ❗Nondeterministic Circuits
      • 🌊Arithmetic Over/Under Flows
      • 🍂Mismatching Bit Lengths
      • 🌪️Unused Public Inputs Optimized Out
      • 🥶Frozen Heart: Forging of Zero Knowledge Proofs
      • 🚰Trusted Setup Leak
      • ⛔Assigned but not Constrained
    • 🐛Bugs In The Wild
      • 🌳Dark Forest v0.3: Missing Bit Length Check
      • 🔢BigInt: Missing Bit Length Check
      • 🚓Circom-Pairing: Missing Output Check Constraint
      • 🏹Semaphore: Missing Smart Contract Range Check
      • 🔫Zk-Kit: Missing Smart Contract Range Check
      • 🤖Aztec 2.0: Missing Bit Length Check / Nondeterministic Nullifier
      • ⏸️Aztec Plonk Verifier: 0 Bug
      • 🪂0xPARC StealthDrop: Nondeterministic Nullifier
      • 😨a16z ZkDrops: Missing Nullifier Range Check
      • 🤫MACI 1.0: Under-constrained Circuit
      • ❄️Bulletproofs Paper: Frozen Heart
      • 🏔️PlonK: Frozen Heart
      • 💤Zcash: Trusted Setup Leak
      • 🚨14. MiMC Hash: Assigned but not Constrained
      • 🚔PSE & Scroll zkEVM: Missing Overflow Constraint
      • ➡️PSE & Scroll zkEVM: Missing Constraint
      • 🤨Dusk Network: Missing Blinding Factors
      • 🌃EY Nightfall: Missing Nullifier Range Check
      • 🎆Summa: Unconstrained Constants Assignemnt
      • 📌Polygon zkEVM: Missing Remainder Constraint
    • 💿ZK Security Resources
  • 🤝Tutorial 17 DEX's (Decentralized Exchanges)
    • 🚀Prerequisites
    • 📚Understanding Decentralized Exchanges
    • 💀Common Vulnerabilities in DEX Code
      • 🔎The "Lack of Slippage Check" Vulnerability in Automated Market Makers (AMMs) a
      • 😡On-Chain Slippage Calculations Vulnerability
      • 📛Slippage tolerance vulnerability
      • 😵How Pool Implementation Mismatches Pose a Security Risk to Decentralized Exchanges (DEXs)
      • 🏊‍♂️Vulnerabilities in Initial Pool Creation - Liquidity Manipulation Attacks
      • 🛑Vulnerabilities In Oracle Implementations
        • ⚖️Newly Registered Assets Skew Consultation Results
        • ⚡Flash-Loan Oracle Manipulations
        • ⛓️Relying Only On Chainlink: PriceOracle Does Not Filter Price Feed Outliers
        • ✍️Not Validating Return Data e.g Chainlink: (lastestRoundData)
        • 🗯️Chainlink: Using latestAnswer instead of latestRoundData
        • 😭Reliance On Fetching Oracle Functionality
        • 🎱Wrong Assumption of 18 decimals
        • 🧀Stale Prices
        • 0️⃣Oracle Price Returning 0
        • 🛶TWAP Oracles
        • 😖Wrong Token Order In Return Value
        • 🏗️miscellaneous
      • 🥶Minting and Burning Liquidity Pool Tokens
      • 🎫Missing Checks
      • 🔞18 Decimal Assumption
        • 📌Understanding ERC20 Decimals
        • 💀Examples Of Vulnerabilities To Do With Assuming 18 Decimals
      • 🛣️Incorrect Swap Path
      • The Importance of Deadline Checks in Swaps
    • 🤝Conclusion
  • 🤖Tutorial 18: Proxies
    • 🚀Prerequisites
    • 📥Ethereum Storage and Memory
    • 📲Ethereum Calls and Delegate Calls
    • 💪Upgradability Patterns in Ethereum: Enhancing Smart Contracts Over Time
    • 🔝Proxy Upgrade Pattern in Ethereum
    • 🌀Exploring the Landscape of Ethereum Proxies
      • 🪞Transparent Proxies
      • ⬆️UUPS Proxies
      • 💡Beacon Proxies
      • 💎Diamond Proxies
  • 🔞Tutorial 19: 18 Decimal Assumption
    • 🚀Prerequisites
    • 📌Understanding ERC20 Decimals
    • 💀Examples Of Vulnerabilities To Do With Assuming 18 Decimals
    • 🤝Conclusion
  • ➗Tutorial 20: Arithmetic
    • 🚀Prerequisites
    • 🕳️Arithmetic pitfall 1: Division by 0
    • 🔪Arithmetic pitfall 2: Precision Loss Due To Rounding
    • 🥸Arithmetic pitfall 3: Erroneous Calculations
    • 🤝Conclusion
  • 🔁Tutorial 21: Unbounded Loops
    • 🚀Prerequisites
    • ⛽Gas Limit Vulnerability
    • 📨Transaction Failures Within Loops
    • 🤝Conclusion
  • 📔Tutorial 22: `isContract`
    • 🚀Prerequisites
    • 💀Understanding the 'isContract()` vulnerability
    • 🤝Conclusion
  • 💵Tutorial 23: Staking
    • 🚀Prerequisites
    • 💀First Depositor Inflation Attack in Staking Contracts
    • 🌪️Front-Running Rebase Attack (Stepwise Jump in Rewards)
    • ♨️Rugability of a Poorly Implemented recoverERC20 Function in Staking Contracts
    • 😠General Considerations for ERC777 Reentrancy Vulnerabilities
    • 🥏Vulnerability: _lpToken and Reward Token Confusion in Staking Contracts
    • 🌊Slippage Checks
    • 🌽The Harvest Functionality in Vaults: Issues and Best Practices
  • ⛓️Tutorial 24: Chain Re-org Vulnerability
    • 🚀Prerequisites
    • ♻️Chain Reorganization (Re-org) Vulnerability
    • 🧑‍⚖️Chain Re-org Vulnerability in Governance Voting Mechanisms
  • 🌉Tutorial 25: Cross Chain Bridges Vulnerabilities
    • 🚀Prerequisites
    • ♻️ERC777 Bridge Vulnerability: Reentrancy Attack in Token Accounting
      • 🛑Vulnerability: Withdrawals Can Be Locked Forever If Recipient Is a Contract
    • 👛The Dangers of Not Using SafeERC20 for Token Transfers
    • Uninitialized Variable Vulnerability in Upgradeable Smart Contracts
    • Unsafe External Calls and Their Vulnerabilities
    • Signature Replay Attacks in Cross-Chain Protocols
  • 🚰Tutorial 26: Integer Underflow and Overflow Vulnerabilities in Solidity (Before 0.8.0)
    • 🚀Prerequisites
    • 💀Understanding Integer Underflow and Overflow Vulnerabilities
    • 🤝Conclusion
  • 🥏Tutorial 27: OpenZeppelin Vulnerabilities
    • 🚀Prerequisites
    • 🛣️A Guide on Vulnerability Awareness and Management
      • 🤝Conclusion
  • 🖊️Tutorial 28: Signature Vulnerabilities / Replays
    • 🚀Prerequisites
    • 🔏Reusing EIP-712 Signatures in Private Sales
    • 🔁Replay Attacks on Failed Transactions
    • 📃Improper Token Validation in Permit Signature
  • 🤝Tutorial 29: Solmate Vulnerabilities
    • 🔏Lack of Code Size Check in Token Transfer Functions in Solmate
  • 🧱Tutorial 30: Inconsistent block lengths across chains
    • 🕛Incorrect Assumptions about Block Number in Multi-Chain Deployments
  • 💉Tutorial 31: NFT JSON and XSS injection
    • 📜Vulnerability: JSON Injection in tokenURI Functions
    • 📍Cross-Site Scripting (XSS) Vulnerability via SVG Construction in Smart Contracts
  • 🍃Tutorial 32: Merkle Leafs
    • 🖥️Misuse of Merkle Leaf Nodes
  • 0️Tutorial 33: Layer 0
    • 📩Lack of Force Resume in LayerZero Integrations
    • ⛽LayerZero-Specific Vulnerabilities in Airdropped Gas and Failure Handling
    • 🔓Understanding the Vulnerability of Blocking LayerZero Channels
    • 🖊️Copy of Understanding the Vulnerability of Blocking LayerZero Channels
  • ♻️Tutorial 34: Forgetting to Update the Global State in Smart Contracts
  • ‼️Tutorial 35: Wrong Function Signature
  • 🛑Tutorial 36: Handling Edge Cases of Banned Addresses in DeFi
  • Tutorial 37: initializer and onlyInitializing
  • ➗Tutorial 38: Eigen Layer
    • 📩Denial of Service in NodeDelegator Due to EigenLayer's maxPerDeposit Check
    • 📈Incorrect Share Issuance Due to Strategy Updates in EigenLayer Integrations
    • 🔁nonReentrant Vulnerability in EigenLayer Withdrawals
  • ⚫Tutorial 39: Wormhole
    • 📩Proposal Execution Failure Due to Guardian Set Change
  • 💼Tutorial 40: Uniswap V3
    • 📩Understanding and Mitigating Partial Swaps in Uniswap V3
    • 🌊Underflow Vulnerability in Uniswap V3 Position Fee Growth Calculations
    • ➗Handling Decimal Discrepancies in Uniswap V3 Price Calculations
  • 🔢Tutorial 41: Multiple Token Addresses in Proxied Tokens
    • 🔓Understanding Vulnerabilities Arising from Tokens with Multiple Entry Points
  • 🤖Tutorial 42: abiDecoder v2
    • 🥥Vulnerabilities from Manipulated Token Interactions Using ABI Decoding
  • ❓Tutorial 43: On-Chain Randomness
    • Vulnerabilities in On-Chain Randomness and How It Can Be Exploited
  • 😖Tutorial 44: Weird ERC20 Tokens
    • Weird Token List
  • 🔨Tutorial 45: Hardcoded stable coin values
  • ❤️Tutorial 46: The Risks of Chainlink Heartbeat Discrepancies in Smart Contracts
  • 👣Tutorial 47: The Risk of Forgetting a Withdrawal Mechanism in Smart Contracts
  • 💻Tutorial 48: Governance and Voting
    • Flash Loan Voting Exploit
    • Exploiting Self-Delegation
    • 💰Missing payable Keyword in Governance Execute Function
    • 👊Voting Multiple Times by Shifting Delegation
    • 🏑Missing Duplicate Veto Check
  • 📕Tutorial 49: Not Conforming To EIP standards
    • 💎Understanding EIP-2981: NFT Royalty Standard
    • 👍Improper Implementation of EIP-2612 Permit Standard
    • 🔁Vulnerabilities of Missing EIP-155 Replay Attack Protection
    • ➡️Vulnerabilities Due to Missing EIP-1967 in Proxy Contracts
    • 🔓Vulnerability of Design Preventing EIP-165 Extensibility
    • 🎟️The Dangers of Not Properly Implementing ERC-4626 in Yield Vaults
    • 🔁EIP-712 Implementation and Replay Attacks
  • ⏳Tutorial 50: Vesting
    • 🚔Vulnerability of Allowing Unauthorized Withdrawals in Vesting Contracts
    • 👊Vulnerability of Unbounded Timelock Loops in Vesting Contracts
    • ⬆️Vulnerability of Incorrect Linear Vesting Calculations
    • ⛳Missing hasStarted Modifier
    • 🔓Vulnerability in Bond Depositor's Vesting Period Reset
  • ⛽Tutorial 51: Ethereum's 63/64 Gas Rule
    • 🛢️Abusing Ethereum's 63/64 Gas Rule to Manipulate Contract Behavior
  • 📩Tutorial 52: NPM Dependency Confusion and Unclaimed Packages
    • 💎Exploiting Unclaimed NPM Packages and Scopes
  • 🎈Tutorial 53: Airdrops
    • 🛄Claiming on Behalf of Other Users
    • 🧲Repeated Airdrop Claims Vulnerability
    • 🍃Airdrop Vulnerability – Merkle Leaves and Parent Node Hash Collisions
  • 🎯Tutorial 54: Precision
    • 🎁Vulnerabilities Due to Insufficient Precision in Reward Calculations
    • Min-Shares: Fixed Minimum Share Values for Tokens with Low Decimal Precision
    • Vulnerability Due to Incorrect Rounding When the Numerator is Not a Multiple of the Denominator
    • Vulnerability from Small Deposits Being Rounded Down to Zero Shares in Smart Contracts
    • Precision Loss During Withdrawals from Vaults Can Block Token Transfers Due to Value < Amount
    • 18 Decimal Assumption Scaling: Loss of Precision in Asset Conversion Due to Incorrect Scaling
  • Tutorial 55: AssetIn == AssetOut, FromToken == ToToken
    • 🖼️Vulnerability: Missing fromToken != toToken Check
  • 🚿Tutorial 56: Vulnerabilities Related to LP Tokens Being the Same as Reward Tokens
    • 🖼️Vulnerabilities Caused by LP Tokens Being the Same as Reward Tokens
  • Tutorial 57: Unsanitized SWAP Paths and Arbitrary Contract Call Vulnerabilities
    • 📲Arbitrary Contract Calls from Unsanitized Paths
  • Tutorial 58: The Risk of Infinite Approvals and Arbitrary Contract Calls
    • 🪣Exploiting Infinite Approvals and Arbitrary Contract Calls
  • Tutorial 59: Low-Level Calls in Solidity Returning True for Non-Existent Contracts
    • Low-Level Calls Returning True for Non-Existent Contracts
  • 0️⃣Tutorial 60: The Impact of PUSH0 and the Shanghai Hardfork on Cross-Chain Deployments > 0.8.20
    • PUSH0 and Cross-Chain Compatibility Challenges
  • 🐍Tutorial 61: Vyper Vulnerable Versions
    • Vyper and the EVM
  • ⌨️Tutorial 62: Typos in Smart Contracts — The Silent Threat Leading to Interface Mismatch
    • Vyper and the EVM
  • ☁️Tutorial 63: Balance Check Using ==
    • The Vulnerability: == Balance Check
  • 💍Tutorial 64: Equal Royalties for Unequal NFTs
    • Understanding the Problem: Equal Royalties for Unequal NFTs
  • 🖼️Tutorial 65: ERC721 and NFTs
    • The Risk of Using transferFrom Instead of safeTransferFrom in ERC721 Projects
    • ❄️Why _safeMint Should Be Used Instead of _mint in ERC721 Projects
    • The Importance of Validating Token Types in Smart Contracts
    • 📬Implementing ERC721TokenReceiver to Handle ERC721 Safe Transfers
    • NFT Implementation Deviating from ERC721 Standard in Transfer Functions
    • NFT Approval Persistence after Transfer
    • 🎮Gameable NFT Launches through Pseudo-Randomness
    • 2️⃣Protecting Buyers from Losing Funds Due to Claimed NFT Rewards on Secondary Markets
    • ♻️Preventing Reentrancy When Using SafeERC721
    • 🖊️Preventing Re-use of EIP-712 Signatures in NFT Private Sales
  • 2️⃣Tutorial 66: Vulnerability Arising from NFTs Supporting Both ERC721 and ERC1155 Standards
  • 📷Tutorial 67: ERC1155 Vulnerabilities
    • ♻️Preventing Reentrancy in OpenZeppelin's SafeERC1155
    • 🛫Vulnerabilities in OpenZeppelin's ERC1155Supply Contract
    • Understanding Incorrect Token Owner Enumeration in ERC1155Enumerable
    • Avoiding Breaking ERC1155 Composability with Improper safeTransferFrom Implementation
    • 💍Ensuring Compatibility with EIP-2981 in ERC1155 Contracts
  • 🪟Informational Vulnerabilities
  • ⛽Gas Efficiency
  • 💻Automation Tools
  • 🔜Out Of Gas (Coming Soon)
  • 🔜DEX Aggregators (Coming Soon)
  • 🔜Bribes (Coming Soon)
  • 🔜Understanding Compiled Bytecode (coming soon)
  • 🔜Deployment Mistakes (coming soon)
  • 🔜Optimistic Roll-ups (coming soon)
  • 🔜Typos (coming soon)
  • 🔜Try-Catch (coming soon)
  • 🔜NFT Market-place (coming soon)
  • 🔜Upgrade-able Contracts (coming soon)
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  1. Tutorial 6: Merkle Trees

Verification within a Merkle Tree:

PreviousUnderstanding Merkle TreesNextMerkle Proofs Within Smart Contracts

Last updated 1 year ago

Understanding Merkle Proofs in Blockchain

In the world of blockchain, the validity and integrity of transactions are paramount. This is where Merkle proofs come into play. These proofs allow participants in the network, even those operating "lightweight" or "partial" nodes, to verify the existence of a specific transaction in a block without having to download and inspect the entire blockchain, saving resources and ensuring scalability.

Recap: what is a Merkle Tree?

A Merkle tree is a binary tree wherein each leaf node represents a transaction's hash and each non-leaf node is the hash of its child nodes. Consider eight transactions, labelled A to H. A basic visual representation of the resulting Merkle tree would look like this:

Each of the transactions (A to H) is hashed individually, and these hashes form the leaf nodes of the tree. Each non-leaf node is created by hashing the concatenation of its child nodes. For instance, the parent node of A and B (denoted as AB) is obtained by hashing Hash(A) and Hash(B) together. This process is repeated until we reach the root of the tree. The Merkle root is a unique hash representing all the transactions in the block. again To construct this tree, each transaction (A through H) is hashed individually, creating the leaf nodes. Parent nodes are then created by hashing the concatenation of the hashes of their respective child nodes. This process is repeated up the tree until reaching the Merkle root, a unique hash representing all transactions in the block. Crafting a Merkle Proof for Transaction Verification

Suppose we wish to confirm that transaction C occurred and is included in the block represented by the tree above. For this, we would create a Merkle proof for transaction C Transaction C (or any other transaction in the blockchain) represents an action taken by a user in the blockchain network. This could be anything from sending cryptocurrency like Bitcoin or Ethereum to another user, executing a smart contract, or interacting with a decentralized application. The details of that action, such as the amount of cryptocurrency sent and the sender and recipient's addresses, are what make up the content of transaction C.

So, when we talk about constructing a Merkle proof for transaction C, it means that we're trying to verify an action that a user claims to have taken on the blockchain. Maybe they say they've sent some cryptocurrency to another user, and we want to confirm whether this is true.

By creating and validating a Merkle proof, we can definitively confirm that the user's action (in this case, transaction C) was recorded in a specific block in the blockchain. This is important not just for transparency and accountability, but also for the functionality of many blockchain applications. For example, a decentralized financial service might need to confirm that you really do own the cryptocurrency you're trying to deposit To create a Merkle proof for transaction C, we do as follows:

Let's delve deeper into the process of crafting a Merkle proof for a specific transaction, Transaction C, in this case. We will break down each step, clarifying the 'why' behind every action.

First, to understand the necessity of a Merkle proof, we need to remember that in a blockchain network, many participants (or nodes) may not hold a complete copy of all transactions. These participants, especially lightweight or mobile nodes, want to verify transactions without downloading the entire blockchain, which can be gigabytes or even terabytes in size. That's where the Merkle proof comes into play.

The Initial Steps

We start with the raw data of the transaction, transaction C in this case. The raw data of a transaction, such as the sender's address, recipient's address, and the amount transferred, is the direct output of a user's action on the network.

This raw data is then processed through a cryptographic hash function to create Hash(C), which is a unique representation of transaction C. This transformation serves two primary purposes. First, it secures the transaction's details because the hashing process is one-way - you can't derive the original data from the hash value. Second, it standardizes the data size, making it easier to manage and process, regardless of how much data is in the original transaction.

Sibling and Parent Nodes

Next, we identify the sibling of Hash(C), which is Hash(D) in our Merkle tree. This is crucial because Hash(D), as a neighbor to Hash(C), forms part of the 'path' or 'trail' to the root.

After that, we identify the sibling of the parent node, which is Hash(AB). Including Hash(AB) in our Merkle proof is crucial because, as with Hash(D), it is part of the 'path' to the root.

We include the information about the position of the siblings because the order of inputs matters in cryptographic hashing. Hash(AB) is not the same as Hash(BA). Knowing which sibling hash was on the left or right is important for correctly reconstructing the path to the root.

Reconstructing the Root

(Note, on the diagram above H(A-D) represents Hash(ABDC) and H(E-H) represents Hash(EFGH))

With these pieces of information - Hash(C), Hash(D), Hash(AB), and Hash(EFGH) - any participant can reconstruct the path from transaction C to the root:

  1. First, the node computes Hash(CD) by hashing Hash(C) and Hash(D) together, remembering that D was on the right. This gives us the parent node of Hash(C), which we'll call Hash(CD).

  2. Next, it computes Hash(ABCD) by hashing Hash(AB) and Hash(CD) together, recalling that AB was on the left. This gives us the parent node of Hash(AB), which we'll call Hash(ABCD).

  3. Finally, the participant computes the root by hashing Hash(ABCD) and Hash(EFGH) together, giving us the Merkle root.

After this, the participant has a computed root hash, a replica of what the Merkle root would look like if transaction C indeed happened and was included in the block.

By performing these steps, we've demonstrated that with Hash(AB), Hash(D), Hash(EFGH), and the original transaction C, any participant can validate the inclusion of transaction C in the block, demonstrating the power and efficiency of Merkle Proofs.

The Final Check

But, how do we ensure the accuracy of this process? This is where the 'known' Merkle root comes into play. Each block in the blockchain comes with a 'known' Merkle root - the root that results from hashing all transactions in the block. This known root is widely accepted as the truthful representation of all transactions within that block.

Now, if the root derived from our Merkle proof calculations matches the known Merkle root, it verifies that transaction C did take place and was recorded in the block. This is the crucial final check that validates the accuracy of the Merkle proof.

The need to submit a Merkle proof, therefore, arises from the need for efficient, secure transaction verification in a distributed system like a blockchain. It provides a way for participants to confirm the existence and integrity of specific transactions without needing to store or process all transactions in a block. This enhances the scalability of blockchain technology, allowing it to support vast numbers of transactions while maintaining security and transparency.

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H(A-D) represents Hash(ABDC) and H(E-H) represents Hash(EFGH)