# 𝒫𝔩𝔬𝔫𝒦: A Hands-On Deep Dive - **Authors**: MartΓ­n Ochoa - **Date**: August 05, 2025 - **Tags**: educative, zk, plonk ![PLONK](https://blog.zksecurity.xyz/posts/plonk-tutorial/plonk.jpg) Understanding 𝒫𝔩𝔬𝔫𝒦 can be daunting given its multiple building blocks. Selector polynomials, wiring permutations, quotient tests, random challenges, and KZG commitments can be overwhelming at first sight. At zkSecurity, we have created [a hands-on tutorial](https://plonk.zksecurity.xyz) to demystify each piece through a progressive running example: you'll build tables of intermediate values, interpolate low-degree polynomials over the BN254 field, encode gate and wiring constraints, and perform both deterministic and probabilistic zero-tests. [πŸ“– Access the tutorial](https://plonk.zksecurity.xyz) Whether you are already familiar with the protocol or curious to learn more about it, this tutorial helps you understand the inner workings of 𝒫𝔩𝔬𝔫𝒦, turning a complex proof system into an accessible, step-by-step learning journey. **Choose how to solve**: Download a Jupyter Notebook version of the tutorial and solve with [Sage](https://doc.sagemath.org/html/en/installation/launching.html) or on [Cocalc](https://cocalc.com/). But you may also solve in some other programming language, we guide you with test cases along the way! **Deep Dives into building blocks**: Each algebraic construction is motivated through the running example, from vanishing polynomials to the grand-product argument, bridging theory and practice. **Progressive Complexity**: Start with a simple circuit, then incrementally introduce selectors, quotient polynomials, random challenges, and KZG commitments, culminating in a full non-interactive Fiat–Shamir 𝒫𝔩𝔬𝔫𝒦 proof. --- This article was published on the [ZK/SEC Quarterly](https://blog.zksecurity.xyz) blog by [ZK Security](https://www.zksecurity.xyz), a leading security firm specialized in zero-knowledge proofs, MPC, FHE, and advanced cryptography. ZK Security has audited some of the most critical ZK systems in production, discovered vulnerabilities in major protocols including Aleo, Solana, and Halo2, and built open-source tools like [Clean](https://github.com/Verified-zkEVM/clean) for formally verified ZK circuits. For more articles, see the [full list of posts](https://blog.zksecurity.xyz/llms.txt).