Introduction
You’ve been in crypto for years. You trade, you hold, you follow the chaos on Crypto Twitter. But now you want more than surface-level understanding. You’re already sold on the vision that blockchain will become fundamental infrastructure for finance and beyond. You’ve watched Bitcoin transform how we think about money. You’ve seen Ethereum and smart contracts unlock entirely new categories of self-custodial financial applications. And maybe you’ve stumbled onto ZK proofs as the next frontier worth understanding.
This course is built for you. We’ll move quickly through the blockchain fundamentals you probably already grasp, then dig into the ZK concepts that actually matter. By the end, you’ll understand not just what zero knowledge proofs are, but how they’re being deployed in production systems today.
What Blockchain Actually Does
You’ve heard it countless times: blockchain is a giant ledger with special properties like transparency, decentralization, and immutability. All true, but there’s a more useful way to think about it.
Think of blockchain as an aspiring world computer. Not your laptop, but a machine that anyone can access and share. A computer that doesn’t live in one place, controlled by one entity, but operates across thousands of nodes simultaneously. A computer that executes programs where the results can’t be faked or reversed.
Bitcoin was V1 of this computer. Powerful for what it did, recording who owns what without needing banks or intermediaries to verify transactions. But limited. Bitcoin’s blockchain could really only do one thing well: track ownership transfers of its native currency. You couldn’t build much else on top of it. The world computer could barely run one application.
The fundamental shift happened when someone asked: what if this shared computer could run arbitrary programs, not just track token transfers?
Ethereum and the Smart Contract Revolution
Ethereum introduced smart contracts, which are exactly what they sound like: contracts that execute themselves based on code rather than human enforcement. If X happens, then Y executes automatically. No lawyers, no judges, no trust required in any third party.
This unlocked entirely new possibilities. Suddenly you could build lending protocols, decentralized exchanges, prediction markets, DAOs, and thousands of other applications. All running on this shared world computer where the rules couldn’t be changed mid-game and execution was guaranteed.
The trust model shifted fundamentally. Before blockchains, you trusted humans and institutions: banks, brokers, payment processors. With Bitcoin, you trusted the protocol and its incentive structure. With Ethereum and smart contracts, you could trust code itself. Write the rules into a program, deploy it to the blockchain, and those rules become immutable and self-executing.
This was genuinely transformative. DeFi protocols now hold billions in value with no CEO, no board of directors, no customer service department. Just code executing exactly as written.
But there was a catch.
The Constraints Emerge
The world computer had a problem: it was expensive and limited. Every operation costs gas. Every piece of data stored on-chain costs gas. Running complex computations costs a lot of gas. And the blockchain, by design, needs every node to verify every transaction, which means everything needs to be relatively simple and lightweight.
Take Ethereum as an example. It transitioned from Bitcoin’s Proof of Work (where miners compete to solve complex mathematical puzzles to validate blocks) to Proof of Stake (where validators lock up collateral and are randomly selected to propose blocks) in 2022. This shift dramatically improved energy efficiency and reduced hardware requirements for participation. But even with this upgrade, Ethereum’s consensus model still relies on about a 1 million validators who must independently verify every block. When a new block is proposed, other validators receive it and re-execute all the transactions locally to ensure the proposed state change is valid. Every validator redundantly processes the same computations to maintain security and decentralization.
This redundancy is fundamental to how blockchains achieve trustlessness. But it creates hard constraints on what smart contracts can actually do:
They can’t access their own history. A smart contract on Ethereum can see its current state, but can’t efficiently look back at what happened 1,000 blocks ago, or even 10 blocks ago, without prohibitively expensive operations. The data is there on-chain, technically public, but practically inaccessible to the contract itself.
They can’t see other chains. Ethereum contracts can’t natively read data from Polygon, Arbitrum, Base, or any other chain. Each blockchain is isolated. Cross-chain communication requires trusted intermediaries or complex bridge infrastructure.
They can’t do heavy computation. Want to run a complex algorithm? Train a model? Process large datasets? Too expensive. The gas costs would be astronomical, and you’d hit block gas limits anyway. If a million validators need to re-execute your computation, it better be simple.
They operate in a trust vacuum. If you need information from outside the blockchain (price feeds, weather data, sports scores), you need an oracle. And oracles reintroduce the exact trust assumptions that blockchains were supposed to eliminate.
So the pendulum started swinging back. Applications that wanted to do anything sophisticated had to process data off-chain and ask users to trust the results. We started rebuilding the very intermediaries and trust dependencies that blockchain was meant to eliminate.
But what if there was a way to prove that off-chain computation was done correctly without anyone having to trust the party that did it? What if you could verify massive amounts of work with a tiny, cheap check?
That’s where cryptographic proofs come in. And to understand how they solve these problems, we first need to understand what makes any proof valuable in the first place.
Read Part 2: Cryptographic Proofs next.
Brevis Network© 2023 