Technical educational content related to ZK, cryptography, and blockchains.
Technical content
The development and use of integrity/zero-knowledge (ZK) proofs has accelerated over the past few years. The introduction of general purpose ZK virtual machines, which allow us to write and prove Rust code, has made developing verifiable applications easier and faster. We have blockchains like Mina that prove every block
Technical content
Polynomial commitment schemes (PCS) are at the core of proof systems. They determine key properties such as proof size, verification time, and whether the system is post-quantum secure. The Kate-Zaverucha-Goldberg (KZG) is a popular PCS, first appearing in 2010. Learn more: Polynomial commitment schemes allow us to commit to a
Technical content
Plonk is one of the most widely used proof systems. It is at the core of the proof systems used by ZKsync, Mina, Halo2 (by Zcash), Plonky2 (Polygon), and Succinct Labs SP1’s compression proof, gnark, due to its versatility and efficient prover. Since it's introduction, the Plonk
Technical content
Mina is a layer 1 (L1) blockchain that uses zero-knowledge proofs (ZKP) to maintain its size at 22 kB. Its vibrant community and technology make it unique and developers and users from other ecosystems could benefit from their interaction with Mina. To this end, Aligned will support the technology needed
Technical content
Recently, Vitalik Buterin wrote on binary fields and their potential to generate zero-knowledge proofs. Binary fields are finite fields with characteristic equal to two. We can view them as polynomials whose coefficients can only take the values 0 and 1, so 1 + x^2 + x^6 are elements in some
Technical content
Aligned is designed to verify any proof system efficiently and for a fraction of the cost in Ethereum. Kimchi is the proof system at the heart of Mina. Do you want to know what makes Kimchi special? Mina is a succinct blockchain. It generates proofs for each block, allowing any
Technical content
The future of crypto is increasingly multi-chain. Blockchains are a powerful new platform for developers to build decentralized and trustless applications, but their properties place limits on scalability. To address this, we have seen an explosion in the number of blockchains, which has increased the global supply of blockspace and
Technical content
Aligned is a ZK verification layer for Ethereum. But what does a ZK verification layer do? Why is it needed? Read on to find out! Ethereum is achieving scalability through a rollup-centric roadmap. There are two types of rollups: optimistic and ZK. Basically, we move execution to rollups, which inherit
Technical content
Aligned is designed to verify every proof system. Groth16 was one of the first efficient proof systems. It's used by projects like Zcash, Worldcoin, RISC Zero, and SP1 by Succinct Labs. At the core of Groth16 lie pairing-friendly elliptic curves, such as BN254 and BLS12-381. These curves allow
Technical content
Aligned is designed to verify zk proofs cheaply, with high throughput and low latency. However, any existing mechanism that can guarantee computation integrity can be used in Aligned. For example, trusted Execution Environments (TEEs) like SGX, can also provide an efficient way to guarantee a computation was done correctly. This
Technical content
In recent months, we have witnessed the development and enhancement of general proving virtual machines such as Risc0, Valida, Jolt, and SP1. These innovations allow users to write ordinary code in languages like Rust or C and generate proofs demonstrating the integrity of computations. This evolution is poised to transform
Technical content
Elliptic curve pairings play an important role in Ethereum’s Proof of Stake and in proof systems such as Groth16 and Plonk. They allow us to perform some sort of encrypted multiplication, crucial to aggregatable signatures and some polynomial commitment schemes. However, pairings seem shrouded in mystery and complexity. Read