Zero Knowledge from the Discrete Logarithm Problem

Explore the foundations of zero-knowledge proofs derived from the discrete logarithm problem in this comprehensive lecture by Dan Boneh from Stanford University. Delve into the current state of affairs, parameters of transparent succinct ZK arguments, and practical applications through examples like range proofs and polynomial commitments. Examine the R1CS representation of circuits, additive properties, and proof characteristics. Investigate Bulletproofs, multi-commitments, and the inner product argument, including its main idea, single-step process, and logarithmic round complexity. Gain insights into verifiable shuffles and the intricacies of proofs, consensus, and decentralizing society as part of the Simons Institute's boot camp series.

Intro
The current state of affairs
Parameters of a transparent succinct ZK argument
This talk
Proving knowledge of an assignment
Example 1: range proof
Example 2: polynomial commitment
verifiable shuffle
R1CS representation of circuits
R1CS with auxiliary commitments
Additive properties
Properties of proof
Bulletproofs
Multi-commitments
Inner product argument: main idea
Inner product argument: one step
Inner product argument: log (n) rounds