# Why and How zk-SNARK Works

arXiv: https://arxiv.org/abs/1906.07221 · HTML: https://mlsanity.com/paper/1906.07221/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Intelligent AI Delegation](https://mlsanity.com/paper/2602.11865/) (2026)
- [Trust the Process: Zero-Knowledge Machine Learning to Enhance Trust in Generative AI Interactions](https://mlsanity.com/paper/2402.06414/) (2024)
- [ZKTorch: Compiling ML Inference to Zero-Knowledge Proofs via Parallel Proof Accumulation](https://mlsanity.com/paper/2507.07031/) (2025)
- [VerifiableFL: Verifiable Claims for Federated Learning using Exclaves](https://mlsanity.com/paper/2412.10537/) (2024)
- [On-Chain Decentralized Learning and Cost-Effective Inference for DeFi Attack Mitigation](https://mlsanity.com/paper/2510.16024/) (2025)

## Abstract (arXiv)

Despite the existence of multiple great resources on zk-SNARK construction, from original papers to explainers, due to the sheer number of moving parts the subject remains a black box for many. While some pieces of the puzzle are given one can not see the full picture without the missing ones. Hence the focus of this work is to shed light onto the topic with a straightforward and clean approach based on examples and answering many whys along the way so that more individuals can appreciate the state of the art technology, its innovators and ultimately the beauty of math. Paper's contribution is a simplistic exposition with a sufficient and gradually increasing level of complexity, necessary to understand zk-SNARK without any prerequisite knowledge of the subject, cryptography or advanced math. The primary goal is not only to explain how it works but why it works and how it came to be this way.