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

Change Log (maintenance of the change log began June 2022)

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).