The discovery and study of probabilistic proof systems, such as PCPs and IPs, have had a tremendous impact on theoretical computer science. These proof systems have numerous applications (e.g., to hardness of approximation) but one of their most compelling uses is a direct one: to construct cryptographic protocols that enable super fast verification of long computations. This course will introduce students to the foundations of probabilistic proof systems, covering both classical results as well as modern efficient constructions.
This course requires knowledge of basic algorithms and complexity.
Completing the course for credit requires weekly homeworks and endofterm project. Class attendance is important.
This course has no required textbook. Each lecture will have specific references.
TBD.
#  Date  Topic  Reading 

1  2022.02.22  Interactive Proofs 1

Formulation of interactive proofs:
Video:

2  2022.02.23  Interactive Proofs 2

The sumcheck protocol: 
3  2022.03.01  Interactive Proofs 3

Shamir's protocol: Additional: 
4  2022.03.02  Interactive Proofs 4

The result presented in class: A survey: Additional on implementations of GKR's protocol:
Additional on doublyefficient interactive proofs: 
5  2022.03.08  Interactive Proofs 5

On zero knowledge:
Video:

6  2022.03.09  Probabilistically Checkable Proofs 1

Video: New York Times article about the PCP Theorem: 
7  2022.03.15  Probabilistically Checkable Proofs 2

The exponentialsize constantquery PCP is the inner PCP in this paper: 
8  2022.03.16  Probabilistically Checkable Proofs 3

Main: Additional:
Video: 
9  2022.03.22  Probabilistically Checkable Proofs 4

Main: 
10  2022.03.23  Probabilistically Checkable Proofs 5

Main: Additional: 
11  2022.03.29  PCPs with Sublinear Verification 1

Main: 
12  2022.03.30  PCPs with Sublinear Verification 2

Main: 
13  2022.04.05  Interactive Oracle Proofs 1

IOP model and its compilation into noninteractive arguments: 
14  2022.04.06  Interactive Oracle Proofs 2

IOPs for R1CS(𝔽): Aditional on IOPs for CSAT(𝔽_{2}): 
15  2022.04.12  Interactive Oracle Proofs 3

FRI protocol: 
16  2022.04.13  Interactive Oracle Proofs 4

FRI protocol: Additional reading: 
X  2022.04.19  No class (on break). 

X  2022.04.20  No class (on break). 

17  2022.04.26  IOPs with Sublinear Verification

Main: 
18  2022.04.27  Holographic Proofs

Main: 
19  2022.05.03  Proof Composition 1

Main:

20  2022.05.04  Proof Composition 2

Robustification: Additional on O(1)query tests: 
21  2022.05.10  Proof Composition 3

Main: 
22  2022.05.11  Limitations 1

GoldwasserSipser transformation:
Additional:

23  2022.05.17  Limitations 2

The results presented in class: Additional results: 
24  2022.05.18  Limitations 3

Main:
Towards the sliding scale conjecture: 
25  2022.05.24  Parallel Repetition

Main on parallel repetition: Counterexamples:
Additional on explicit bounds for Furstenberg–Katznelson: 
26  2022.05.25  Applications

Reading: 
27  2022.05.31  Class Project Presentations 1 

28  2022.06.01  Class Project Presentations 2 