halo2

From first principles to Halo2 proofs

halo2

Understand Halo2

Start with finite fields and elliptic curves. Follow the mathematics into polynomial commitments, PLONK, and a working Halo2 proof.

Explore the curriculum 18 modules

Contents

Your learning path

120–150 hours, with practical exercises, review checkpoints, and explicit security assumptions.

3 topic groups

Build the foundations

Modules 1–6 · Learn the arithmetic and cryptographic vocabulary from scratch.

Module 01–03𝔽

Fields and curves

Statements, witnesses, finite fields, groups, and elliptic-curve arithmetic.

Open section

Module 04–05G

Encryption and commitments

ElGamal, homomorphic operations, Pedersen commitments, and hash assumptions.

Open section

Module 06↔

Interactive proofs

Schnorr proofs, transcript challenges, and the Fiat–Shamir transformation.

Open section

3 topic groups

Understand the protocol

Modules 7–14 · Follow computation through constraints, polynomials, and verifier checks.

Module 07–09f(X)

Arithmetization

Circuit equations, interpolation, evaluation domains, and quotient identities.

Open section

Module 10–11⟨a,b⟩

Polynomial openings

Commit to a polynomial and prove evaluations with inner-product arguments.

Open section

Module 12–14π

PLONK and Halo2

Gates, copy constraints, lookups, blinding, and the complete proof transcript.

Open section

3 topic groups

Build and explain a proof

Modules 15–18 · Implement circuits, test failures, and connect the theory to a working proof.

Module 15–16{ }

Circuit engineering

Learn the Rust API, bind public inputs, and discover missing constraints.

Open section

Module 17✓

Private bounded value

Prove a hidden value satisfies a public bound and matches a public commitment.

Open section

Module 18∞

Beyond the first proof

Understand recursion, curve cycles, and the differences between IPA and KZG.

Open section