Putting aside the math/confusion for a second, essentially, StarkWare uses STARK technology to scale Ethereum. Why do we need to do this? Ethereum can handle about 15 transactions per second (tps), Visa averages about 1700 tps. That’s a problem.
There are many proposals for how to scale Ethereum, a popular one is called rollups and the 2 most popular types of rollups are Optimistic rollups and ZK rollups.
ZK stands for zero-knowledge, it’s a concept in cryptography that dates back to the 1980s. A ZK-proof is one where a Verifier via an interaction can verify that a statement is true without gaining additional information (let that sink in, it’s pretty wild).
SNARKs and STARKs are both types of ZK-proofs. STARK proponents would argue it has nicer qualities than SNARKs including but not limited to being transparently set up, universal, scales in a quasi-linear way, and post-quantum resistant (for our purposes, you don’t need to know any of those words, just know it proves you can efficiently compute proofs in a privacy-preserving way)
Rollups “roll up” a bunch of transactions off-chain, and then update Ethereum’s main chain (remember: our whole goal is to scale Ethereum and the methodology is to do expensive stuff off-chain and then store minimal - but valid - data on-chain). Valid is the key word here, we’ve accomplished nothing if people can fraudulently change the blockchain.
Fraud avoidance in Optimistic rollups relies on a challenge period where users are financially incentivized to report fraud. Fraud avoidance in ZK-rollups uses Validity-Proofs (math). The rolled-up transactions are sent to a Prover that computes a validity proof and sends it to be verified by an on-chain Verifier. There are pros and cons to both approaches.
If that sounds very theoretical, it’s because this tech comes from theoretical computer science. StarkWare is an implemented version of this theory. StarkWare has many products, two of which are StarkEx and StarkNet. StarkEx is a permissioned (blockchain not available to the public) version of StarkNet, which is a general-purpose L2.
Transactions are batched off-chain by a Prover, once a certain batch size is reached or enough time has passed, a STARK proof is produced attesting to the validity of the batch, the proofs are verified through an on-chain Verifier and if valid, the new state root (the new state of the blockchain) is committed to Ethereum. Notably, unlike most blockchain experiences, since the gas cost is distributed across the batch, the more transactions there are, the cheaper each transaction is. This is one solution to the fundamental problem of scaling decentralized blockchains to the practical levels needed for daily transactions.
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