Jeffrey Scholz
AliasCheck and Num2Bits_strict in Circomlib
An alias bug in Circom (or any ZK circuit language) occurs when a binary array of signals encodes a number larger than the field element...
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Web3 Blockchain Blogs & Tutorials
Learn more about the blockchain world
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- Oct 18, 2023
- 9 min
How arithmetic circuits are used to verify zero knowledge proofs
Zk circuits form a set of constraints that if satisfied, prove a computation was carried out correctly. Zk circuits are sometimes called...
4,522 views1 comment
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- Oct 13, 2023
- 8 min
What are Pedersen Commitments and How They Work
Pedersen commitments allow us to represent arbitrarily large vectors with a single elliptic curve point, while optionally hiding any...
3,037 views4 comments
Jeffrey Scholz
- Aug 31, 2023
- 8 min
Groth16 Explained
The groth16 algorithm enables a quadratic arithmetic program to be computed by a prover over elliptic curve points derived in a trusted...
7,750 views1 comment
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- Aug 28, 2023
- 4 min
Encrypted Evaluation of a Quadratic Arithmetic Program
We start with a quadratic arithmetic program which was derived from an Rank 1 Constraint System (R1CS) of the form Ls ⊙ Rs = Os where...
2,552 views0 comments
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- Aug 26, 2023
- 4 min
Building a Zero Knowledge Proof from an R1CS
Given a circuit encoded as a rank 1 constraint system, it is possible to create a zk-proof of having a witness, albeit not a succinct...
3,318 views3 comments
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- Aug 23, 2023
- 20 min
Quadratic Arithmetic Programs
A Quadratic Arithmetic Program (QAP) is a system of equations where the coefficients are monovariate polynomials and a valid solution...
4,366 views3 comments
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- Aug 1, 2023
- 11 min
Elementary Group Theory for Programmers
In our previous tutorial, we introduced set theory and made the journey from sets to defining a group in set-theoretic terms. Now it’s...
5,530 views0 comments
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- Jul 26, 2023
- 5 min
Encrypted Polynomial Evaluation
Encrypted Exponentiation In our article about bilinear pairings, we explained how to do (partially) homomorphic encryption for...
2,610 views0 comments
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- Jul 25, 2023
- 21 min
Elementary Set Theory and Abstract Algebra for Programmers
Why another set theory tutorial? The target audience for this piece are the sort of folks who don’t care about abstract math unless they...
14,302 views1 comment
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- Jul 22, 2023
- 3 min
Why elliptic curve point addition in prime finite fields always lands on integers
One thing that seems incredibly remarkable about elliptic curve addition (in the context of cryptography), is that when a line is drawn...
725 views0 comments
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- Jul 18, 2023
- 12 min
Bilinear Pairings in Python, Solidity, and the EVM
Sometimes also called bilinear mappings, bilinear parings allow us to take three numbers, a, b, and c, where ab = c, encrypt them to...
6,393 views1 comment
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- Jul 11, 2023
- 13 min
Converting Algebraic Circuits to R1CS (Rank One Constraint System)
The goal of this article is to explain how to turn a set of polynomial constraints into rank one constraint system (r1cs). The focus of...
7,260 views1 comment
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- Jun 27, 2023
- 24 min
How Tornado Cash Works (Line by Line for Devs)
Introduction to Tornado Cash Tornado cash is a cryptocurrency smart contract mixer that enables users to deposit crypto with one address...
16,392 views1 comment
tanim0la
- May 28, 2023
- 6 min
ZK-addition-dapp with Noir and Nextjs
We will demonstrate a step-by-step exploration of a basic zk-dapp designed for verifying additions. This application enables users to...
1,026 views0 comments
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- Dec 22, 2022
- 8 min
Zero knowledge programming languages
Zero knowledge programming language proofs demonstrate you executed a computation correctly without revealing the inputs to the computation
4,497 views0 comments
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