The technical content top engineers rely on to level up.
4 min read
MD5 Hash In Circom In this tutorial, we will implement the MD5 hash in Circom both to compute the hash and to constrain in Circom that it was computed correctly. Although the MD5 hash function is not...
Last updated on Aug 20, 2025The Schwartz-Zippel Lemma and its application to Zero Knowledge Proofs Nearly all ZK-Proof algorithms rely on the Schwartz-Zippel Lemma to achieve succintness. The Schwartz-Zippel Lemma states that...
Last updated on Aug 20, 20254 min read
ZK Proof of Selection Sort Most computations of interest are generally “stateful” — that is, they need to go through a series of steps to produce the final result. Sometimes, we do not need to show...
Last updated on Aug 20, 20256 min read
ZK Friendly Hash Functions ZK-friendly hash functions are hash functions that require much fewer constraints to prove and verify than traditional cryptographic hash functions. Hash functions such as...
Last updated on Aug 20, 202510 min read
Zero Knowledge Multiplication Zero Knowledge Multiplication of Polynomials Using the polynomial commitment scheme from the previous chapter, a prover can show that they have three polynomials $l(x)$,...
Last updated on Aug 20, 202516 min read
Assembly revert Reverting transactions using inline assembly can be more gas-efficient than using the high-level Solidity or statement. In this guide, we’ll explore how the different types of reverts...
Last updated on Aug 20, 202516 min read
20 Common Solidity Beginner Mistakes Our intent is not to be patronizing towards developers early in their journey with this article. Having reviewed code from numerous Solidity developers, we’ve...
Last updated on Aug 20, 2025ERC-6551 Standard: Token Bound Accounts (TBA) Introduction NFTs were originally created to represent ownership of digital or physical assets, like collectibles. However, they were limited to tracking...
Last updated on Aug 20, 202520 min read
ERC-1155 Multi Token Standard The ERC-1155 standard describes how to create both fungible and non-fungible tokens then incorporate them into a single smart contract. This saves significant deployment...
Last updated on Aug 20, 20258 min read
Square and Multiply Algorithm The square and multiply algorithm computes integer exponents in $\mathcal{O}(\log n)$ (logarithmic time). The naive way to compute an exponent $x^n$ is to multiply $x$...
Last updated on Aug 20, 202510 min read
Introduction to Proxies Proxy contracts enable smart contracts to retain their state while allowing their logic to be upgraded. By default, smart contracts cannot be upgraded because deployed...
Last updated on Aug 20, 2025How Concentrated Liquidity in Uniswap V3 Works This article explains how Uniswap V3 implements concentrated liquidity. We assume the reader already understands Uniswap V2. To understand concentrated...
Last updated on Aug 20, 2025