Zero Knowledge

Why another set theory tutorial? The target audience for this piece is the sort of folks who don’t care about abstract math unless they see a direct…

In the context of zero-knowledge proofs, an arithmetic circuit is a system of equations that models a problem in NP.

Abstract Algebra is the study of sets that have one or more operators on that set.

Sometimes also called bilinear mappings, bilinear pairings allow us to take three numbers, a, b, and c, where ab = c, encrypt them to become E(a), E(b)…

This article is the third in a series. We present finite fields in the context of circuits for zero-knowledge proofs.

This article provides several examples of algebraic groups so that you can build an intuition for them. We also discussed abelian groups.

P vs NP asks if every problem that is quick to verify is also quick to solve. A plain explanation with Boolean formulas, and what it means for ZK proofs.

The Groth16 algorithm enables a quadratic arithmetic program to be computed by a prover over elliptic curve points derived in a trusted setup, and…

This article is explains how to turn a set of arithmetic constraints into Rank One Constraint System (R1CS).

A quadratic arithmetic program is an arithmetic circuit, specifically a Rank 1 Constraint System (R1CS) represented as a set of polynomials.

To make the transformation from R1CS to QAP less abstract, let’s use a real example.

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.