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

Merkle Proof Solidity Implementation

PreviousMerkle Proofs Within Smart ContractsNextVulnerabilities When Using Merkle Trees

Last updated 1 year ago

Blockchain developers often come across use cases where they need to confirm the presence of a particular transaction in a block, without having to handle the entire block's data. A classic example is within decentralized finance (DeFi) protocols, cross-chain bridges, Layer 2 solutions, and other DApps that require interaction with multiple blockchains or large datasets. It is in these scenarios that the use of Merkle proofs becomes vital.

Merkle proofs allow you to verify the existence of a specific transaction (leaf node) in a Merkle tree, without needing to know every transaction in the block. This property comes handy when you need to keep track of state across multiple chains, or when you need to scale your DApp to handle a larger number of transactions without increased cost or slower performance.

In this article, we'll take a closer look at how to implement a function for verifying Merkle proofs using the Solidity programming language. Below is the Solidity function that verifies a Merkle proof:

function verify(
    bytes32[] proof,
    bytes32 root,
    bytes32 leaf
  )
    internal
    pure
    returns (bool)
  {
    bytes32 computedHash = leaf;

    for (uint256 i = 0; i < proof.length; i++) {
      bytes32 proofElement = proof[i];

      if (computedHash < proofElement) {
        computedHash = keccak256(abi.encodePacked(computedHash, proofElement));
      } else {
        computedHash = keccak256(abi.encodePacked(proofElement, computedHash));
      }
    }

    return computedHash == root;
  }
}

The function, verify, accepts three parameters:

function verify(
    bytes32[] proof,
    bytes32 root,
    bytes32 leaf
  )
  • proof: An array of type bytes32, representing the sibling hashes on the branch from the leaf to the root of the Merkle tree.

  • root: A bytes32 hash representing the Merkle root of the tree.

  • leaf: A bytes32 hash representing the leaf node (the specific transaction) we're verifying.

The function's visibility is internal, meaning it can only be called from within the current contract or contracts that derive from it. The pure keyword indicates that the function will not alter any state variables and will not consume any gas apart from the execution cost. The function returns a boolean value, signifying the success or failure of the verification process.

The function operates by initializing a bytes32 variable, computedHash, to the value of the provided leaf. It then iterates through the provided proof, which is an array of hashes that constitute the Merkle proof.

In the context of our earlier example, we're aiming to validate that 'C' is indeed a legitimate leaf in the Merkle tree.

To do this, we provide a proof in the form of an array of type bytes32[] proof. This 'proof' array includes the sibling hashes of the path from the leaf to the root. In the case of verifying 'C', the array would be populated in the order of Hash(D), Hash(AB), and Hash(EFGH).

bytes32 leaf refers to the hash value of the specific leaf we are verifying, in this case, the hash of transaction 'C'.

Finally, bytes32 root is a representation of the root of the Merkle tree. It's the hash value that we'll use to compare against the result of our computed hash in order to validate the proof. In the context of our previous example, root would be the Hash(ABCDEFGH). Our verification function will compare this root hash with the final computed hash resulting from the proof verification process. If they match, the function will return true, indicating a successful Merkle proof verification.

The function operates by initializing a bytes32 variable, computedHash, to the value of the provided leaf. It then iterates through the provided proof, which is an array of hashes that constitute the Merkle proof.

bytes32 computedHash = leaf;

For each proofElement in the proof, the function computes a new hash that combines computedHash and the current proofElement. It takes into account the order of computedHash and proofElement in the tree when computing this new hash.

The Ethereum network, like many others, use the cryptographic hash function keccak256 (SHA-3 variant), and abi.encodePacked is used to concatenate computedHash and proofElement together. In other words, the function is essentially reconstructing the path from the leaf node up to the root of the Merkle tree.

if (computedHash < proofElement) {
  computedHash = keccak256(abi.encodePacked(computedHash, proofElement));
} else {
  computedHash = keccak256(abi.encodePacked(proofElement, computedHash));
}

Is crucial to maintaining the integrity of the original Merkle tree's structure. When the Merkle tree was first constructed, the sibling nodes were ordered based on their hash values. To ensure the verification process aligns with the original tree structure, the computation of new hashes needs to follow the same order.

That's why the comparison if (computedHash < proofElement) is performed. The order of the two values in the pairing matters when hashing because keccak256(abi.encodePacked(computedHash, proofElement)) will yield a different result from keccak256(abi.encodePacked(proofElement, computedHash)).

Here's a breakdown:

  1. computedHash < proofElement: If the computed hash is less than the current proof element, the function will concatenate the computed hash and the proof element in that order before performing the hash function.

  2. computedHash >= proofElement: If the computed hash is greater than or equal to the current proof element, the function will concatenate the proof element and the computed hash in that order before performing the hash function.

This ordering is essential because it ensures that the Merkle proof follows the same path as when the original Merkle tree was constructed. Without adhering to the correct order, the final computed root would not match the original Merkle root, and the proof would fail even if the transaction were valid.

The keccak256 function is a cryptographic hash function used by the Ethereum network, and abi.encodePacked is a function to concatenate two byte strings.

Note that concatenation is the process of appending one string to the end of another string. When you concatenate strings, you essentially link them together end-to-end to create a new, combined string. It's a fundamental operation in most programming languages for manipulating strings. abi.encodePacked is concatenating computedHash and proofElement into a single, contiguous byte array. This new byte array is then passed to the keccak256 function. For instance, if computedHash were "123" and proofElement were "456", abi.encodePacked(computedHash, proofElement) would result in "123456". So in summary this code is essentially reconstructing the path from the leaf node to the root of the Merkle tree, making sure to maintain the correct order of siblings in each pairing along the path. By keeping the order, the function ensures that it computes the same root hash as in the original Merkle tree, allowing for a valid comparison and successful proof verification.

Once the loop completes, computedHash should be equal to the root if the proof is valid. The function checks this by returning the result of computedHash == root. This will be true if the proof is valid, and false otherwise.

return computedHash == root;

It's worth noting that the given Solidity function verify is a pure, self-contained function, which means it doesn't read or write data from the blockchain's state. It simply computes a value based on the inputs it receives, and then returns that value. This is clear from the pure keyword in the function declaration.

function verify(
    bytes32[] proof,
    bytes32 root,
    bytes32 leaf
  )
    internal
    pure
    returns (bool)

This verify function returns a boolean value: true if the computed hash matches the provided root (meaning the proof is valid), and false otherwise. However, this returned value in itself doesn't have an effect on the blockchain state or any outside variables.

This means that it's the responsibility of the calling function, or the decentralized application (DApp) that utilizes this contract, to handle the inputs to this function and do something meaningful with the returned value.

For instance, a DApp might use this function as part of a larger operation like validating a transaction or verifying the integrity of a data set. If the verify function returns true, the DApp could proceed with the operation; if it returns false, the DApp could halt the operation and alert the user that the proof verification failed.

Ultimately, how this verify function is used—and how its return value is handled—depends on the specific requirements and logic of the DApp or smart contract that's using it.

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