In this two-part series, we’ll explore building a Zero Knowledge circuit using the Halo 2 zkSNARK proving system and subsequently how we can compile it to WebAssembly to be used in a web app. Introduction There’s no shortage of ways in which Zero Knowledge apps that can be built these days…

Final article in PLONK series. Here we will implement Prover and the Verifier. In the previous article we coded trusted setup, gate and permutations polynomials, now we are ready to start generating proof. Under the hood of zkSNARKs — PLONK protocol: part 5 Previous articles in the PLONK series served as preparations before we got our hands dirty and started implementing the…medium.com The Prover In the PLONK protocol, the prover is required to complete five rounds in a specified order. This…

This article will discuss the permutation check in PLONK, which I believe is the second most challenging aspect of the protocol. The most challenging part, in my opinion, is debugging and identifying errors in the code. Under the hood of zkSNARKs — PLONK protocol: part3 Many materials available online explain the basics of the PLONK protocol, often referencing Vitalik’s example…medium.com In our previous discussion, we delved into the complexities of arithmetization in PLONK, exploring…

This is the first part of the series that takes you from absolute ground zero in ZKPs to a fairly advanced level. We will start from the absolute basics and then move onward and upward. Subscribe to get regular updates! Learning ZKPs is hard. No doubt about that. The math…

Many materials available online explain the basics of the PLONK protocol, often referencing Vitalik’s example P(x)=x³+x+5=35 from his article: Understanding PLONK Very recently, Ariel Gabizon, Zac Williamson and Oana Ciobotaru announced a new general-purpose zero-knowledge proof…vitalik.ca To offer a different perspective, this article will explore a modified equation that introduces additional complexities. We will use the equation f(x,y)=2x²−x²y²+3 and set it to equal -25, with x=2 and…

In the previous article of the PLONK series, we covered the core of the protocol, the KZG commitment scheme, and how polynomial linear independence can aid in evaluating multiple polynomials within a single equation. Under the hood of zkSNARKs — PLONK protocol: Part 1 PLONK is one of the zero-knowledge proving systems that belong to the SNARK group. Compared to Groth16, which is an…medium.com Here, I want to discuss another important optimization used in PLONK, which is related to the…

PART I: Recursive SNARKs and Incrementally Verifiable Computation — This is the first of a sequence of blog posts on Nova, a recursive proof system based on a clever folding scheme for R1CS statements (more precisely relaxed R1CS statements, these and their generalizations will be defined in the next blog posts). We will start gently and later on in…

This is a blog series in which we explore ZK folding schemes and NOVA. Read the first part here. In our previous article, we introduced the idea of recursive proof composition, where a SNARK (an outer SNARK) is used to prove that the proof provided by another SNARK (an inner…

PLONK is one of the zero-knowledge proving systems that belong to the SNARK group. Compared to Groth16, which is an older system, PLONK offers advantages such as a universal and updatable trusted setup. In Groth16, a circuit-specific (or task-specific, for those unfamiliar with the term) trusted setup is required, whereas…

TL;DR: StarkWare and Herodotus have created a way to prove Ethereum blocks all the way back to genesis This is accomplished using the power of cryptographic proofs and block hashes It achieves the goals of EIP-2935 — a way to access historical block hashes older than 256 blocks in a chain-native…

Basic concepts and properties — Introduction Welcome to this guide on how to build zk-SNARKs! Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) is a cutting-edge technology that provides privacy and security in blockchain systems. It allows for verifying the authenticity of transactions without revealing the details. …

A primer for understanding the mathematical insights used to build ZK. — Part 1 (Proof systems & NP proofs) Part 2 (Computational complexity) Part 3 (Interactive Proofs) Part 4 (Negligible & Gain in Knowledge) Part 5 (Honest verifier zero-knowledge) Questions to answer - HVZK is a weak-notion of zero-knowledge. How can we modify HVZK to make our zk protocol more robust against malicious counterparties? …

A primer for understanding the mathematical insights used to build ZK. — Part 1 (Proof systems & NP proofs) Part 2 (Computational complexity) Part 3 (Interactive Proofs) Part 4 (Negligible & Gain in Knowledge) Questions to answer 1. How is zero-knowledge implemented as a protocol? (Read 1 and 2) 1. Honest Verifier Zero-Knowledge (HVZK) In the last part we defined zero-knowledge as “Bob (Verifier V) has gained no knowledge if…

Recently, I had two business students attending my applied cryptography lectures. Why? Because they were interested in blockchain and wanted to know more about how cryptography worked. In fact, they asked more questions in the lecture than all the other students in the whole class. To me, when you get…

A primer for understanding the mathematical insights used to build ZK. — Part 1 (Proof systems & NP proofs) Part 2 (Computational complexity) Part 3 (Interactive Proofs) Questions to answer This part will address 2 questions that need to be understood before we start the technical discussions on zero-knowledge. 1. We saw how randomness/probability was used in computationally hard problems (probabilistic polynomial time, IP). But…

A primer for understanding the mathematical insights used to build ZK. — The purpose of this series is to follow the trail of insights that led to the development of various zero-knowledge protocols. The series will focus on real-life applications and implications of these protocols. While reading, focus on the questions posed. Questions to answer - What is the need for zero-knowledge proof systems? …

A primer for understanding the mathematical insights used to build ZK. — Part 1 (Proof systems & NP proofs) Part 2 (Computational complexity) Questions answered in this part: - What happens when even the verification process becomes inefficient or slow? (Read 1, 2 and 3) - How can Interactive Proofs help us verify NP problems? (Read 4) 1. Super Polynomial Problems In the last post, we saw examples of three membership…

A primer for understanding the mathematical insights used to build ZK. — The purpose of this series is to follow the trail of insights that led to the development of various zero-knowledge protocols. The series will focus on real-life applications and implications of these protocols. Before reading this article, go to part 1. Questions to Answer - How do we measure the efficiency of a…

Zero Knowledge Proofs (ZKP) is a concept that has garnered much attention in the blockchain industry. Many, including myself at one point, view it as a mysterious “black box”. In this article, and the subsequent series, I will be sharing what I have learnt about one of ZKP protocols and…

This is a series of articles. Part 7,​ ​ PDF version Zero-Knowledge Proof of Computation Since the introduction of the general-purpose computation protocol (Proof of Operation section) we had to let go of the zero-knowledge property, to make the transition simpler. Until this point, we have constructed a verifiable computation protocol. Previously to make…