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30 min read
P vs NP and its application to zero knowledge proofs
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...
11 min read
Homomorphisms by Example
Homomorphisms by Example A homomorphism between two groups exists if a structure preserving map between the two groups exists. Suppose we have two algebraic data structures $(A,\square)$ and $(B,...
12 min read
Abstract Algebra
Abstract Algebra Abstract Algebra is the study of sets that have one or more operators on that set. For our purposes, we only care about sets where the operator is a binary operator. Given a set with...
25 min read
Arithmetic Circuits for ZK
Arithmetic Circuits for ZK In the context of zero-knowledge proofs, an arithmetic circuit is a system of equations that models a problem in NP. A key point from our article on P vs NP is that any...
16 min read
Invariant Testing in Foundry
Invariant Testing in Foundry Introduction In this article, we will discuss invariants and how to perform an invariant test on Solidity smart contracts using Foundry test suites. Invariant testing is...
6 min read
Solidity Mutation Testing
Solidity Mutation Testing Mutation testing is a method to check the quality of the test suite by intentionally introducing bugs into the code and ensuring the tests catch the bug. The kind of bugs...
6 min read
Ethereum precompiled contracts
Ethereum precompiled contracts Ethereum precompiles behave like smart contracts built into the Ethereum protocol. The nine precompiles live in addresses 0x01 to 0x09. The utility of precompiles falls...
11 min read
How ERC721 Enumerable Works
How ERC721 Enumerable Works An Enumerable ERC721 is an ERC721 with added functionality that enables a smart contract to list all the NFTs an address owns. This article describes how functions and how...
7 min read
The interest rate model of Aave V3 and Compound V2
The interest rate model of Aave V3 and Compound V2 Interest rates in TradFi (traditional finance) are largely determined by central banks and influenced by market factors. In contrast, DeFi interest...
3 min read
The Fallback Extension Pattern
The Fallback Extension Pattern The fallback-extension pattern is a simple way to circumvent the 24 KB smart contract size limit. Suppose we have functions and in our primary contract and wish to add...
6 min read
EIP 1967 Storage Slots for Proxies
EIP 1967 Storage Slots for Proxies EIP 1967 is a standard for where to store information that proxy contracts need to execute. Both the UUPS (Universal Upgradeable Proxy Standard) and the Transparent...
12 min read
The staking algorithm of SushiSwap MasterChef and Synthetix
The staking algorithm of SushiSwap MasterChef and Synthetix The MasterChef and Synthetix staking algorithms distribute a fixed reward pool among stakers according to their time-weighted contributions...