The ZK Chronicles

Fundamentals

Finite fields, polynomials, and the sum-check protocol - the math that every proving system in this series builds on.

1. 01The ZK Chronicles: First Steps
2. 02The ZK Chronicles: Math Foundations
3. 03The ZK Chronicles: Sum Check

Circuits and Computation Models

Arithmetic circuits, multilinear extensions, the GKR protocol, and why circuits are a universal model of computation (Cook-Levin).

1. 04The ZK Chronicles: Circuits (Part 1)
2. 05The ZK Chronicles: Multilinear Extensions
3. 06The ZK Chronicles: Circuits (Part 2)
4. 07The ZK Chronicles: Computation Models

The Cryptographic Toolkit

Hashing and Merkle trees, groups and elliptic curves, Pedersen commitments, sigma protocols, the FFT, and pairings - the primitives every modern proving system is built from.

1. 08The ZK Chronicles: Enter Hashing
2. 09The ZK Chronicles: Groups
3. 10The ZK Chronicles: Commitment Schemes (Part 1)
4. 11The ZK Chronicles: Sigma Protocols
5. 12The ZK Chronicles: Fast Fourier Transform
6. 13The ZK Chronicles: Commitment Schemes (Part 2)

Zero Knowledge

Inner product arguments (Bulletproofs, Dory), and the formal definitions - simulators, extractors, and knowledge soundness - that make zero knowledge precise, including their security under Fiat-Shamir.

1. 14The ZK Chronicles: Inner Product Arguments
2. 15The ZK Chronicles: Zero Knowledge
3. 16The ZK Chronicles: The Random Oracle Model

SNARKs

Onto the frontier of practical ZK: small, fast-to-verify proofs that we can actually use for real systems

1. 17The ZK Chronicles: Arithmetization
2. 18The ZK Chronicles: SNARKs (Part 1)
3. 19The ZK Chronicles: SNARKs (Part 2)