Finite Fields and Modular Arithmetic for ZK Proofs This article is the third in a series. We present finite fields in the context of circuits for zero-knowledge proofs. The previous chapters are P vs NP and its Application to Zero Knowledge Proofs and Arithmetic Circuits. In the previous chapter on arithmetic circuits, we pointed out […]
Arithmetic Circuits for ZK An arithmetic circuit (in the context of zero knowledge proofs) is a system of equations whose solution models a problem in NP. One key point from our article on P vs NP was that any solution to a problem in P or NP can be verified by modeling the problem as […]
Uniswap V2: Calculating the Settlement Price of an AMM Swap This article explains how to determine the price settlement of a trading pair in an Automated Market Maker (AMM). It answers the question of “How many token X can be swapped for token Y from the AMM?”. The swap() function on Uniswap V2 requires you […]
P vs NP and its application to zero knowledge proofs The P = NP problem asks: “If we can quickly verify a solution to a problem is correct, can we also quickly compute the solution?” Most researchers believe the answer is no, i.e., P ≠ NP. By understanding the P vs NP problem, we can […]
![#[derive(Accounts)] in Anchor: different kinds of accounts](https://www.rareskills.io/wp-content/uploads/2024/08/935a00_05694389f65848dfb3dee8af7aa05874mv2-1024x576.jpg)
[derive(Accounts)] in Anchor: different kinds of accounts #[derive(Accounts)] in Solana Anchor is an attribute-like macro for structs that holds references to all the accounts the function will access during its execution. In Solana, every account the transaction will access must be specified in advance One reason Solana is so fast is that it executes transactions […]
Three ways to detect if an address is a smart contract This article describes three methods in Solidity for determining if an address is a smart contract: Check if msg.sender == tx.origin. This is not a recommended method, but because many smart contracts use it, we discuss this method for completeness. The second (and recommended […]
ERC-1363 Standard Explained ERC-1363 enables a smart contract to detect and respond to an incoming transfer of tokens. What problem does ERC-1363 Solve? Suppose a user transfers an ERC-20 token to a contract. The smart contract cannot credit the user for the transfer because it has no mechanism to see who made the transfer. Although […]
Creating Raw Ethereum Interactions in Go: Blob Transactions, Tracing Transactions, and Others. The ethclient package from Go-Ethereum (Geth) provides an API wrapper for JSON-RPC requests to the Ethereum network, similar to web3.js and ethers.js. However, some capabilities of the JSON-RPC, like transaction tracing, are not exposed in API of ethclient (and web3.js and ethers.js). This […]
Understanding the Function Selector in Solidity The function selector is a 4 byte id that Solidity uses to identify functions under the hood. The function selector is how a Solidity contract knows which function you are trying to call in the transaction. You can see the 4 byte id using the .selector method: pragma solidity […]