Init_if_needed in Anchor and the Reinitialization Attack !Hero image showing Anchor init_if_needed In previous tutorials, we've had to initialize an account in a separate transaction before we can...

Solana Sysvars Explained !Solana Sysvars In Solana, sysvars are read-only system accounts that give Solana programs access to the blockchain state as well as network information. They are similar to...

Zero Knowledge Multiplication Zero Knowledge Multiplication of Polynomials Using the polynomial commitment scheme from the previous chapter, a prover can show that they have three polynomials $l(x)$,...

How Tornado Cash Works (Line by Line for Devs) !tornado cash tutorial by rareskills Introduction to Tornado Cash Tornado Cash is a cryptocurrency smart contract mixer that enables users to deposit...

The Schwartz-Zippel Lemma and its application to Zero Knowledge Proofs Nearly all ZK-Proof algorithms rely on the Schwartz-Zippel Lemma to achieve succintness. The Schwartz-Zippel Lemma states that...

What are Pedersen Commitments and How They Work Pedersen commitments allow us to encode arbitrarily large vectors with a single elliptic curve point, while optionally hiding any information about the...

P vs NP and its application to zero knowledge proofs The P = NP problem asks: "If we can quickly verify a solution to a problem is correct, can we also quickly compute the solution?" Most researchers...

Abstract Algebra Abstract Algebra is the study of sets that have one or more operators on that set. For our purposes, we only care about sets where the operator is a binary operator. Given a set with...

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...

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...