Groth16 Explained The Groth16 algorithm enables a quadratic arithmetic program to be computed by a prover over elliptic curve points derived in a trusted setup, and quickly checked by a verifier. It...

Finite Fields and Modular Arithmetic for ZK Proofs This article is the third in a series. We present finite fields in the context of circuits for zero-knowledge proofs. The previous chapters are P vs...

Elliptic Curves over Finite Fields What do elliptic curves in finite fields look like? It’s easy to visualize smooth elliptic curves, but what do elliptic curves over a finite field look like? The...

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...

Circom language tutorial with circomlib walkthrough This tutorial introduces the Circom language and how to use it, along with common pitfalls. We will also explain a significant portion of the...

ZK-addition-dapp with Noir and Nextjs !ZK Dapp Game built with Noir and Next.js We will demonstrate a step-by-step exploration of a basic zk-dapp designed for verifying additions. This application...

Zero knowledge programming languages !Zero knowledge proof moon math Zero knowledge proof moon math Zero knowledge proofs demonstrate you executed a computation correctly without revealing the inputs...