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...

Modeling the Stack Data Structure in ZK This tutorial shows how to create a stack in Circom. Be warned — this chapter is long. However, the strategy for creating ZK proofs about stacks will be...

Roots of unity ω have the property ω^(k/2) ≡ −1 In previous articles, we established that in the finite field $\mathbb{F}_q$, if $k$ divides $q-1$: There exists a unique subgroup of order $k$ - the...

Cairo for Solidity Developers Cairo is a Rust-inspired language that compiles to bytecode, which runs on the Cairo Virtual Machine. The Cairo virtual machine is a zero-knowledge virtual machine...

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...

Converting Algebraic Circuits to R1CS (Rank One Constraint System) This article is explains how to turn a set of arithmetic constraints into Rank One Constraint System (R1CS). The focus of this...

Components Part 2: OpenZeppelin ERC-20 Tutorial In Component Part 1, we learned how to create and use a component within a single file. We built a from scratch and integrated its storage, events, and...

Events in Starknet Events emit data from contract execution into the transaction receipt. The receipt holds metadata about what happened during the execution, which can be queried or indexed by...

Constructors in Cairo A constructor is a one-time-call function executed during contract deployment to initialize state variables, perform contract setup tasks, make cross-contract interactions and...

Access Control in Cairo Access control defines who can call specific functions or modify contract behavior. This article explains how Cairo implements access control using the macro. A Review of...

Cairo Components Part 1 Components in Cairo behave like abstract contracts in Solidity. They can define and work with storage, events, and functions, but they can’t be deployed on their own. The...