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 16: Zero Knowledge (ZK)
  2. Theory

ZK-Snarks

In this we will outline the theory of the Pinocchio protocol in particular as an example

PreviousLinear Interactive ProofNextDefinitions and Essentials

Last updated 1 year ago

Zero-knowledge proofs allow one party (the prover) to convince another party (the verifier) that a statement is true, without revealing any specific details of the statement. Linear Interactive Proofs (LIP) are a class of zero-knowledge proofs. zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge) are a specialized form of zero-knowledge proofs that are both succinct and non-interactive. In this document, we explore the transition from the LIP model to zk-SNARKs, specifically focusing on the Pinocchio Protocol.

Linear Interactive Proofs (LIP)

In LIPs, the prover and verifier engage in an interaction, where:

Polynomial Encoding:

The prover encodes their secret witness as the values of polynomials A(x),B(x), and C(x) at a secret point s.

Verification:

The verifier issues random challenges, and based on the responses, verifies if the prover knows the polynomial without revealing the specific value of s or the polynomial evaluations at s.

Structured Reference String (SRS)

Secret s chosen by the Prover:

In our earlier discussions on zk-SNARKs, there is a phase where the prover chooses a secret

s to evaluate their polynomials. This secret evaluation demonstrates to the verifier that the prover knows the polynomial without revealing any specifics about it.

The prover hides the evaluation at this secret point to prove they genuinely know the whole polynomial.

Structured Reference String (SRS):

The SRS, which includes commitments to powers of τ, is part of the setup phase of zk-SNARKs and is a separate concept from the secret s chosen by the prover. The "Powers of Tau" setup is a method to create an SRS for zk-SNARKs. During this process, a secret value τ is chosen and then discarded after the setup. It's crucial that

τ remains secret, and no one should ever know it. The generated SRS, however, is public and is used by all participants in the protocol.The SRS provides public parameters that every prover and verifier in the system can use for their proofs and verifications. It is a common "reference" for all zk-SNARK proofs in a particular system.

Why do we need both?:

The secret s chosen by the prover is used to convince the verifier that they know a polynomial without revealing it. It's a dynamic value, chosen fresh for each proof instance.

The SRS is a static set of parameters. Think of it as a "foundation" or "infrastructure" for the zk-SNARK system. Every prover and verifier uses the same SRS for their proofs and verifications, but the individual proofs will still have their unique aspects (like the secret s).

In essence, zk-SNARKs require both a common reference (the SRS) for everyone in the system and individual secret values (like s) for each proof to ensure both the consistency of the system and the privacy/integrity of individual proofs.

Breakdown of Srs

Let's break down the use of the Structured Reference String (SRS) in the context of zk-SNARKs and the polynomials we discussed earlier.

1. SRS Generation: "Powers of Tau" setup

During the setup phase, an SRS is generated using a method like the "Powers of Tau." This involves:

Selecting a secret random value τ.

Computing powers of τ based on the degree of the polynomials, i.e., τ0, τ1, τ2,...,τd.

Creating commitments to these powers using a group G1. This results in:

srs=[τ^0]G1,[τ^1]G1,...,[τ^d]G1

These commitments are the public parameters available to all provers and verifiers, while τ itself remains a secret and is discarded.

2. Using the SRS in zk-SNARKs

Given the polynomials A(x),B(x), and C(x) that the prover possesses:

Evaluation Commitments: The prover evaluates these polynomials at a secret point s and then creates commitments to these evaluations using the SRS.For example, for A(x), the commitment might look like:

[A(s)]G1

The commitment effectively hides the value of

A(s) while still allowing for certain operations thanks to the properties of the group G1.

Verifier's Checks:

The verifier can then perform certain checks using the commitments received from the prover and the public SRS, without needing to know the exact values of the polynomial evaluations.

For instance, one such check might be to ensure that:

A(s)⋅B(s)−C(s)=Z(s)⋅H(s)

This becomes a pairing equation in the elliptic curve setting, like:

e([A(s)]1,[B(s)]2)−e([C(s)]1,[1]2)=e([Z(s)]1,[H(s)]2)

The verifier can verify this equation without knowing A(s),B(s), or C(s), using only the commitments and the SRS.

Benefits of the SRS:

The SRS, when used in the above manner, offers several advantages:

Hiding Information:

The SRS allows provers to hide specific information (like the secret evaluations of the polynomials) while still allowing verifiers to check the validity of certain claims.

Consistency Across Proofs:

The same SRS can be used across multiple proofs, ensuring consistency in the system.

Efficiency:

The SRS-based commitments and checks are efficient, allowing for quick proofs and verifications.

In summary, the SRS serves as a consistent set of public parameters that enable zk-SNARK proofs to be both private (hiding specific details like polynomial evaluations) and verifiable (allowing verifiers to check proof validity).

Necessity of SRS in zk-SNARKs

Non-interactivity: zk-SNARKs stand for Zero-Knowledge Succinct Non-Interactive Argument of Knowledge. To achieve the non-interactive feature, certain common reference parameters are required for the prover and verifier. SRS provides these parameters.

Randomness without Interaction: In traditional interactive proofs, randomness is introduced through challenges by the verifier. With zk-SNARKs, this randomness is inherently provided by the SRS, thus removing the need for an interactive challenge.

Security:

The SRS acts as a commitment scheme. It binds the prover to a specific statement without revealing the underlying secrets, ensuring the zero-knowledge property is maintained.

Efficiency:

The existence of a pre-established SRS accelerates the proof generation and verification process.

Usage of SRS in zk-SNARKs

The SRS is employed in two primary phases:

Proof Generation: The prover utilizes the SRS to generate commitments to their polynomial evaluations. These commitments are sent to the verifier.

Proof Verification:

The verifier, equipped with the SRS, performs pairing-based checks on the received commitments to validate the proof without the need for interactive challenges.

Conclusion

The Structured Reference String (SRS) is a cornerstone in the zk-SNARKs architecture, enabling non-interactivity, security, and efficiency in the proof systems. The "Powers of Tau" setup ensures that the SRS is generated in a universally trusted manner, forming a reliable foundation for zk-SNARKs operations.

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