Zero Knowledge
Browse all Zero Knowledge articles.
18 min read
Succinct proofs of a vector commitment
Succinct proofs of a vector commitment If we have a Pedersen vector commitment $A$ which contains a commitment to a vector $\mathbf{a}$ as $A = a_1G_1 + a_2G_2+\dots + a_nG_n$ we can prove we know...
8 min read
A Zero Knowledge Proof for the Inner Product
A Zero Knowledge Proof for the Inner Product An inner product argument is a proof that the prover carried out the inner product computation correctly. This chapter shows how to construct a zero...
10 min read
Introduction to ZK Bulletproofs
Introduction to ZK Bulletproofs Bulletproofs are a zero knowledge inner product argument, which enable a prover to convince a verifier that they correctly computed an inner product. That is, the...
22 min read
The intuition behind elliptic curve digital signatures (ECDSA)
The intuition behind elliptic curve digital signatures (ECDSA) This article explains how the ECDSA (Elliptic Curve Digital Signature Algorithm) works as well as why it works. We will incrementally...
6 min read
Cost of storage, maximum storage size, and account resizing in Solana
Cost of storage, maximum storage size, and account resizing in Solana !Solana account rent When allocating storage space, the payer must pay a certain number of SOL per byte allocated. Solana calls...
7 min read
Init_if_needed in Anchor and the Reinitialization Attack
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...
5 min read
Deleting and Closing Accounts and Programs in Solana
Deleting and Closing Accounts and Programs in Solana !Hero image showing Close accounts and programs In the Anchor framework for Solana, is the opposite of (initializing an account in Anchor) — it...
9 min read
Solana Sysvars Explained
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...
10 min read
Zero Knowledge Multiplication
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 $l(x)$,...
30 min read
How Tornado Cash Works (Line by Line for Devs)
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...
12 min read
What are Pedersen Commitments and How They Work
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...
4 min read
The Schwartz-Zippel Lemma and its application to Zero Knowledge Proofs
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...