Solana Anchor Program IDL !Hero Image showing Interface Definition Language The IDL (Interface Definition Language) is a JSON file that describes how to interact with a Solana program. It is...

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....

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...

Elementary Group Theory for Programmers !Group Theory Hero Image This article provides several examples of algebraic groups so that you can build an intuition for them. A group is a set with: a...

Elementary Set Theory for Programmers 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 use-case for...

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...

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,...

Evaluating a Quadratic Arithmetic Program on a Trusted Setup Evaluating a Quadratic Arithmetic Program (QAP) on a trusted setup enables a prover to demonstrate that a QAP is satisfied without...

Elliptic Curve Point Addition This article describes how elliptic curve addition works over real numbers. Cryptography uses elliptic curves over finite fields, but elliptic curves are easier to...

Trusted Setup A trusted setup is a mechanism ZK-SNARKs use to evaluate a polynomial at a secret value. Observe that a polynomial $f(x)$ can be evaluated by computing the inner product of the...