Zero Knowledge

Homomorphisms by Example A homomorphism between two groups exists if a structure preserving map between the two groups exists. Suppose we have two algebraic data structures $(A,\square)$ and $(B,...

Building a Zero Knowledge Proof from an R1CS Given an arithmetic circuit encoded as a Rank 1 Constraint System, it is possible to create a ZK-proof of having a witness, albeit not a succinct one....

Bilinear Pairings in Python, Solidity, and the EVM Sometimes also called bilinear mappings, bilinear pairings allow us to take three numbers, $a$, $b$, and $c$, where $ab = c$, encrypt them to become...

Arithmetic Circuits for ZK In the context of zero-knowledge proofs, an arithmetic circuit is a system of equations that models a problem in NP. A key point from our article on P vs NP is that any...

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...