Zero Knowledge

This requires sending n elements to the verifier (assuming a is of length n). In the previous chapter, we showed how to do this with zero knowledge.

An inner product argument is a proof that the prover carried out the inner product computation correctly.

Bulletproofs are a zero knowledge inner product argument, which enable a prover to convince a verifier that they correctly computed an inner product.

This article explains how the ECDSA (Elliptic Curve Digital Signature Algorithm) works as well as why it works.

When allocating storage space, the payer must pay a certain number of SOL per byte allocated. Solana calls this the "rent".

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

In previous tutorials, we've had to initialize an account in a separate transaction before we can write data to it.

In the Anchor framework for Solana, close is the opposite of init (initializing an account in Anchor) — it reduces the lamport balance to zero, sending…

Using the polynomial commitment scheme from the previous chapter, a prover can show that they have three polynomials l(x), r(x), and t(x) and prove that…

Tornado Cash is a cryptocurrency smart contract mixer that enables users to deposit crypto with one address and withdraw with another wallet without…

Nearly all ZK-Proof algorithms rely on the Schwartz-Zippel Lemma to achieve succintness. Let's consider a few examples.

Pedersen commitments allow us to encode arbitrarily large vectors with a single elliptic curve point, while optionally hiding any information about the…