ZK/SEC Research notes from zkSecurity
All posts
educative · zk · halo2

Become a Halo2 Hero: Master Zero-Knowledge Proofs with Our New Course

Halo2 course

In collaboration with the Zircuit development team, we are excited to announce the release of a course on Halo2 development. Unlike the excellent Halo2 book which focuses on the proof system itself, this course focuses on teaching Rust developers how to develop Halo2 circuits from scratch -- without any prior knowledge of Halo2, PlonK or developing circuits for zkSNARKs required. You don't need to be a cryptographer to follow along! We start from the very basics and build up to more complex circuits with lookups, challenges and more. At the end of the course, you should become a true Halo Hero!

All code in the course comes with complete runnable examples available in the accompanying GitHub repository. This means that any code snippet in the course can be run as a self-contained example!

Get started with Halo2 development today at halo2.zksecurity.xyz.

Keep reading
Recommended

Halo2's Elegant Transcript As Proof

In this blog post, we explore a clever design in Zcash's halo2 implementation for securing the Fiat-Shamir transformation. By using a mutable transcript, the process ensures that values are automatically absorbed, reducing potential bugs. You'll find explanations of the distinct roles of `write` and `read` functions for points and scalars, highlighting how this abstraction makes the prover-verifier interaction seamless and secure. If you're curious about the inner workings of cryptographic protocols, this is a fascinating read.

David Wong · September 30, 2025

Uncovering the Query Collision Bug in Halo2: How a Single Extra Query Breaks Soundness

We recently discovered a subtle but important soundness issue in Halo2, which we’ve named the query collision bug. It affects certain edge-case circuits and was present in widely used versions, including the main Zcash implementation and PSE’s fork. We disclosed the issue to the relevant teams, including Zcash, PSE, and Axiom, all of whom have since patched it. While no known production circuits were affected, the bug reveals a surprising vulnerability in the proving system that deserves attention.

Suneal Gong · July 09, 2025

𝒫𝔩𝔬𝔫𝒦: A Hands-On Deep Dive

𝒫𝔩𝔬𝔫𝒦’s many layers (selector polynomials, wiring permutations, quotient tests, random challenges and KZG commitments) can be overwhelming. Our zkSecurity tutorial uses a single running example to demystify them all. Build tables and interpolate low-degree BN254 polynomials, encode gate and wiring constraints, run deterministic and probabilistic zero-tests, then layer in randomness and KZG commitments to produce a full Fiat–Shamir proof. Grab the Jupyter Notebook (Sage or Cocalc), or work in your favorite language with our guided test cases.

Martín Ochoa · August 05, 2025
More to explore

Notes and Proofs for Divisor Techniques

Notes and proofs for the divisor-based ECIP protocol of Eagen, written with Diego F. Aranha and supported by MAGIC Grants. The document is self-contained: it works through the necessary algebraic geometry, the interactive proof and its soundness, the composition with a simulation-extractable NIZK, and the R1CS verifier circuit used by Parker's gadget in Monero's FCMP++.

Mathias Hall-Andersen · May 08, 2026

Sum-Check as an Algebraic Tensor Reduction: Part I

This post introduces algebraic tensor reductions as a unifying framework for understanding recursive proof protocols, using sum-check as the main motivating example. It walks through one recursive step of sum-check, showing how the prover sends a univariate summary, the verifier checks sum consistency, and the original claim is reduced to a smaller claim with one fewer variable. A small bivariate example illustrates how this “peel off one variable, check, then fold with randomness” pattern works concretely. The post sets up the rest of the series, which will introduce the tensor language needed to recover classical sum-check as an algebraic tensor reduction.

Marco Besier · April 27, 2026

Nine Years to Halve a Hash Function: RFC 9861 Is Out

After nearly a decade in the making, RFC 9861: KangarooTwelve and TurboSHAKE was officially published in October 2025, with zkSecurity among its editors. This post explains why these hash functions deserve to be far more widely used than they are today. Built on the same Keccak permutation as SHA-3 and SHAKE but with the round count halved, they do the same job at the same security level roughly twice as fast. We cover why halving the rounds is safe, what the RFC actually defines, the caveats around FIPS compliance and workload-dependent speedups, and why a standard like this took nine years to land.

David Wong · July 21, 2026