Instructor: Dakshita Khurana

TA: Amit Agarwal

Time: WF 3.30 - 4.45 pm

Location: Siebel 0216


The Spring 2023 offering will be an advanced topics course discussing recent research in the theoretical foundations of cryptographic proofs, including zero-knowledge proofs and probabilistically checkable proofs.


This course will assume solid background knowledge of cryptography. In particular we will assume that you have already taken CS 407 (or an equivalent course).


We will expect participants to understand and present advanced technical papers. If you have previously taken a cryptography course that is equivalent to 407, please email the instructor ( asap with information about the course you've taken. If you have not previously taken a cryptography course, you will unfortunately not have the necessary pre-requisite background to participate in this course.


Rough breakdown of graded components:


Quiz: 10% of your grade

Participation: 10% of your grade

Presentation: 40% of your grade

Project: 40% of your grade


Tentative Schedule:

This is a tentative schedule and is subject to change. Please keep checking this page for updates to topics.

Many lectures will be in flipped classroom format, with links to videos posted below. Please watch these videos before class.

Date Topic H.W. Review Videos (to be reviewed before class) Papers

Introduction + Quiz


  • Introduction to Zero Knowledge
  • ZK for all of NP

Video 1:

Video 2:


  • Proofs of Knowledge
  • Constant round ZK for NP
  • Witness Indistinguishability
  • (Constant round) Statistical ZK for NP
  • Witness hiding

Video 1:

Video 2:

Video 3:

  • NIZK in the Hidden Bits Model
  • The Fiat-Shamir Transform

Video 1:

Video 2:


NIZK from bilinear maps - 1

Video 1:

Video 2:

NIZK from bilinear maps - 2

Video 3:

02/08 NIZK from Correlation Intractability/LWE - 1 Student presentation - Amit

NIZK and Correlation Intractability from Circular-secure LWE


NIZK from Correlation Intractability/LWE - 2

Student presentation - Amit

NIZK for NP from LWE


NIZK from subexponential DDH - 1

Student presentation - James NIZK from subexponential DDH

NIZK from subexponential DDH - 2

Student presentation - James NIZK from subexponential DDH
  • Lower bounds and limitations on ZK
  • Non-black-box ZK (Barak's protocol)
  • NBB ZK via Homomorphic Trapdoors - 1

Video 1:

Video 2:



NBB ZK via Homomorphic Trapdoors - 1

Student presentation - Kabir

Weak ZK beyond the black-box barrier

NBB ZK - 2

Student presentation - Kabir Weak ZK beyond the black-box barrier

(No class)


ZAPs from NIZK Proofs

Student presentation - Maria This paper on ZAPs

ZK with superpolynomial simulation

Student presentation - Maria This paper  

No class/spring break


No class/spring break


Interactive Proofs 

Video 1:

Video 2:

Video 3:

Video 4:


Probabilistically Checkable Proofs - 1

Video 1:

Video 2:


Probabilistically Checkable Proofs - 2

Video 1:

Video 2:

03/31 Probabilistically Checkable Proofs - 3

Video 1:

Video 2:



No-Signaling PCPs and Delegation - 1

Student presentation - Fangqi This paper

No-Signaling PCPs and Delegation - 2

Student presentation - Fangqi This paper

SNARGs via Correlation Intractability - 1

Student presentation - Ruta  

SNARGs via Correlation Intractability - 2

Student presentation - Ruta  

Connections with PPAD Hardness - 1

Student presentation - Cruz This paper

Connections with PPAD Hardness - 2

Student presentation - Cruz This paper

Open problems session - 1


Open problems session - 2


No class




The intent of this section is to raise student and instructor awareness of the ongoing threat of bias and racism and of the need to take personal responsibility in creating an inclusive learning environment.

The Grainger College of Engineering is committed to the creation of an anti-racist, inclusive community that welcomes diversity along a number of dimensions, including, but not limited to, race, ethnicity and national origins, gender and gender identity, sexuality, disability status, class, age, or religious beliefs. The College recognizes that we are learning together in the midst of the Black Lives Matter movement, that Black, Hispanic, and Indigenous voices and contributions have largely either been excluded from, or not recognized in, science and engineering, and that both overt racism and micro-aggressions threaten the well-being of our students and our university community.

The effectiveness of this course is dependent upon each of us to create a safe and encouraging learning environment that allows for the open exchange of ideas while also ensuring equitable opportunities and respect for all of us. Everyone is expected to help establish and maintain an environment where students, staff, and faculty can contribute without fear of personal ridicule, or intolerant or offensive language. If you witness or experience racism, discrimination, micro-aggressions, or other offensive behavior, you are encouraged to bring this to the attention of the course director if you feel comfortable. You can also report these behaviors to the Bias Assessment and Response Team (BART) ( Based on your report, BART members will follow up and reach out to students to make sure they have the support they need to be healthy and safe. If the reported behavior also violates university policy, staff in the Office for Student Conflict Resolution may respond as well and will take appropriate action.

All members of the Illinois Computer Science department - faculty, staff, and students - are expected to adhere to the CS Values and Code of Conduct. The CS CARES Committee is available to serve as a resource to help people who are concerned about or experience a potential violation of the Code. If you experience such issues, please contact the CS CARES Committee. The Instructors of this course are also available for issues related to this class.

Diminished mental health, including significant stress, mood changes, excessive worry, substance/alcohol abuse, or problems with eating and/or sleeping can interfere with optimal academic performance, social development, and emotional well-being. The University of Illinois offers a variety of confidential services including individual and group counseling, crisis intervention, psychiatric services, and specialized screenings at no additional cost. If you or someone you know experiences any of the above mental health concerns, it is strongly encouraged to contact or visit any of the University's resources provided below. Getting help is a smart and courageous thing to do -- for yourself and for those who care about you.

Counseling Center: 217-333-3704, 610 East John Street Champaign, IL 61820

McKinley Health Center:217-333-2700, 1109 South Lincoln Avenue, Urbana, Illinois 61801

University wellness center: