Proofs, Arguments, and Zero-Knowledge

You may download the draft manuscript by clicking on this link.

This manuscript is not in final form, but the technical content has stabilized as of mid-April 2022. Feedback is welcome and can be sent via email to

Supplementary Video Resources

Readers may find it useful to watch the following three videos in order:

The following two links (each about one hour) cover much of Chapters 2-4: Interactive Proofs Part I and Interactive Proofs Part II

The following video (about 90 minutes) covers much of Chapters 7-10: SNARKs from Polynomial IOPs

Note: Chapter numbering has changed since the above video was recorded. Chapter 4 on interactive proofs and the Fiat-Shamir transformation was split into two separate chapters (now Chapters 4 and 5), and Chapter 13 on polynomial commitments was split into 3 separate chapters (now Chapters 14-16).