Course Syllabus


General Information

Class Time and Location: Tues/Thurs 3:40pm - 5pm, WEB 1248 

Office Hours: Tues 11am-12pm in WEB 2863 (or by appointment)

Important Dates:

  1. Mid-term exam (in class): 10/5/23, 3:40pm - 5:00pm
  2. Student project presentations (in class): 11/14/23 - 12/07/23 
  3. Final project reports due: 12/7/23



Course Description

 Modern Cryptography is used at scale to secure information at rest and/or in transit, and recently to also secure our computations. This course is a graduate-level introduction to the foundations of modern cryptography. It is also open to advanced undergraduates. We will cover basic cryptographic tools, discuss their applications and instantiations, and introduce a formal mathematical framework to rigorously argue about security. 

 In particular, the tools covered will include pseudorandom generators, pseudorandom functions, symmetric-key encryption, message-authentication codes, digital signatures, public-key encryption, and hash functions, along with a small sampling of advanced topics like zero-knowledge proofs and fully-homomorphic encryption. For each of these tools, will learn how to mathematically define security and discuss their use-cases in practice. We will also study their constructions from different computational hardness assumptions like the discrete-log problem, the factoring problem, and the plausibly quantum-hard problem of learning-with-errors. We may briefly cover applications of these tools for blockchain settings.

Pre-requisites: There are no formal pre-requisites and the course will not assume any prior background in cryptography. However, basic mathematical maturity is expected; exposure to undergraduate-level probability, elementary number/group theory, proofs by contradiction, and hardness reductions (in complexity theory) is highly recommended. Please discuss with the instructor in case of any gaps in your background.

Course Materials: The class will be self-contained, but the following is a continually expanding list of good resources for supplementary reading:

  1. A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup.
  2. A Course in Cryptography by Rafael Pass and abhi shelat.
  3. Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell.
  4. Lecture notes on Introduction to Cryptography by Vipul Goyal, and associated YouTube videos
  5. Foundations of Cryptography by Oded Goldreich. 



Credits breakdown: The credits (100%) are broken down as follows: 

  1. Four homework assignments (40%),
  2. In-class mid-term exam (15%),
  3. Final project (35%),
  4. Class participation (10%).

Homework Assignments: The assignment will be posted on Fridays at 11:59pm and will be due within a week. The solutions must be typeset in LATEX and submitted as a pdf. Please see the schedule below for release and due dates for homeworks.

Final project: Students can form groups of two. Each group will be assigned a topic along with suggestions of 1-2 research papers on that topic. The group is expected to submit a 3-5 page report (typeset in LATEX) along with a 30 mins in-class presentation on their findings. The format for the report and presentations will be discussed in class. Students are encouraged to choose a topic from this pre-populated list. Students can propose their own topic but instructor approval is required.

Class participation: To encourage class participation, each student is required to provide reviews on three student presentations. Once the schedule for the presentations is out, students can sign up for presentations they want to review. Each review must be about 1000 words (less is acceptable), and must demonstrate your understanding of the presentation's content, highlight positive aspects about the presentation, and suggest improvements that can be undertaken by the group. The reviews will be made available to the presenters in anonymized form at the end of the semester. Please be positive and constructive in your reviews!

(Suggested) Grading Scale:

A 100%-94%
A- 93.9%-90%
B+ 89.9%–87%
B 86.9%–84%
B- 83.9% - 80%
C+ 79.9%–77%
C 76.9%–74%
C- 73.9% - 70%
D+ 69.9%–67%
D 66.9%–64%
D- 63.9% - 60%
E 59.9%–0%

NEW: The final grading for this semester was done using an adjusted grading scale.

Late Submissions: Late submissions are highly discouraged. In case of any emergencies, please immediately consult with the instructor. The decision on accepting late submissions and/or the penalty imposed will lie solely with the instructor. 

[Updated 09/20/23]: Every student can submit one of the three remaining HWs upto two days after the actual deadline. Example, if the homework is due on Friday 11:59pm MT, you may submit it before Sunday 11:59pm MT. There is no penalty for the late submission but you can exercise this exception only once. Please let me know (e.g., by email) if you will be exercising this exception before the actual deadline (i.e., Fridays) of the corresponding HW.

Academic Integrity: For homework assignments, students are encouraged to discuss homework problems (in groups of at most two) but are expected to write solutions independently. The name of the collaborator must be indicated. Additionally, the students are expected to adhere to KSoC's academic code of conduct outlined here, Please also look at the semester guidelines by CoE and KSoC as outlined here and here.

Learning Outcomes

Throughout the course, we will make progress towards achieving the following five (+ two bonus) learning outcomes through lectures and other evaluation components:

  1. Recognize the important of having a formal framework for defining and arguing about security.
  2. Define the security for basic cryptographic objects like pseudo-random generators, pseudo-random functions, encryption schemes, and digital signatures.
  3. Understand the factoring assumption, discrete-log assumption, learning-with-error assumption, and their plausibility.
  4. Write security proofs for cryptographic algorithms covered in the class.
  5. Compare different constructions of cryptographic algorithms w.r.t. their (concrete/asymptotic) efficiency (e.g., is the RSA encryption scheme with 80-bit security more ``efficient" than the Elgamal encryption scheme with the same security level?).
  6. [Bonus]: Understand the security definitions for at least one of the following advanced cryptographic objects: zero-knowledge proofs, fully-homomorphic encryption, program obfuscation, CCA encryption.
  7. [Bonus]: Discuss the significance of cryptography in the context of blockchains/crypto-currencies. 

Class Communications

We will be using Canvas for all class-related activities including uploading homework assignments, final project report, and release of grades. To get in touch with the instructor, students can either use the Chat feature on Canvas or send an email by including "[CS6961]" in the subject. Additionally, students may use our Piazza account for discussions including posting questions (anonymously).


Following is a tentative schedule for the semester. It is meant to give you an idea of the topics, but note that some of the topics may be altered depending on the pace and comfort of the class.

Week Date Lecture Contents
1 8/22/23

Course Organization

  • What is Modern Cryptography?
  • Paradigms of "Provable Security".
  • Historic Ciphers and their insecurity.

Learn LATEX, Overleaf

Lecture 1 notes


Perfect Secrecy & One-time Pad Encryption Scheme

  • Defining perfect secrecy for encryption schemes.
  • One-time pad encryption scheme.
  • Shannon's theorem and implications.


Lecture 2 notes

2 8/29/23

Pseudorandom Generators - 1

  • Computational indistinguishability.
  • Defining pseudorandom generators (PRGs).
  • Examples of PRGs and non-PRGs.
  • Introduction to hybrid arguments.


Lecture 3 notes


Pseudorandom Generators - 2

  • Review of hybrid arguments via an example.
  • Modular arithmetic in Z*_N.
  • The factoring assumption.
  • Blum-Blum-Shub PRG from factoring.

HW1 open

Lecture 4 notes

3 9/5/23

PRG Applications: Coin-tossing and Stream Ciphers

  • Bit commitments and coin-tossing from PRGs
  • Stream Ciphers from PRGs and Semantic Security
  • Attacks on Stream Ciphers in Practice (two-time pad, malleability) 


Lecture 5 notes


Block Ciphers and PRFs

  • Introduction to Block Ciphers
  • An abstraction: Pseudorandom Functions and Permutations
  • (Non)-examples of PRFs
  • Block cipher encryption modes: ECB and DCM

HW1 due

Lecture 6 notes

4 9/12/23

More Block Ciphers

  • Brief history of DES design and attacks
  • Feistel construction and its security for 1, 2, and 3 rounds
  • Review of Assignment 1 and discussion of hybrid arguments 


Lecture 7 notes

A Note on Hybrid Arguments


Chosen Plaintext Attack (CPA) Security for Encryption

  • Switching Lemma: Is a block-cipher a good PRF?
  • Motivation for CPA security and its definition
  • Deterministic Encryption is not CPA secure

HW2 open

Lecture 8 notes

5 9/19/23

Constructions of CPA-secure encryption schemes

  • From semantically-secure encryption scheme and a PRF.
  • From block-cipher in CTR mode.
  • From block-cipher in CBC mode.
  • An efficiency and security comparison of CTR and CBC modes.


Lecture 9 notes


Message Authentication

  • Motivating examples
  • Definition of a Message Authentication Code (MAC)
  • A short-input MAC from a PRF
  • Prefix-free PRFs: CBC and Cascade Constructions
  • Extension attacks on CBC and Cascade

HW2 due

Lecture 10 notes

6 9/26/23

Message Authentication II

  • Prefix-free PRFs to PRFs via prefix-free encodings
  • Prefix-free PRFs to PRF via encrypted method
  • Encrypted CBC (ECBC) and optimality of the bound, Nested MAC (NMAC), Parallel MAC (PMAC)
  • MAC Combiners


Lecture 11 notes


Collision-Resistant Hash Functions

  • Motivating example: File integrity checking
  • Definition
  • Application 1: MACs for longer messages
  • Application 2: Merkle trees (authenticated data structures)


Lecture 12 notes

7 10/3/23

Collision-Resistant Hash Functions II

  • The Merkle-Damgard Construction Paradigm
  • Case-studies: SHA1, SHA256/SHA512, SHA3
  • The HMAC standard


Lecture 13 notes

10/5/23 Mid-term Exam
8 10/10/23 Fall break
10/12/23 Fall break
9 10/17/23

Key Exchange Protocols

  • Diffie-Hellman Key Exchange
  • Hardness assumptions: DL, CDH, DDH
  • (Im)-possibility of efficient key-exchange from PRGs
  • Minicrypt and Cryptomania
Lecture 17 notes

Public-Key Encryption 1

  • Recap of DL, CDH, DDH
  • PKE motivation, applications
  • Semantic-security and CPA-security
  • Elgamal encryption

HW3 open

Lecture 18 notes

10 10/24/23

Public-Key Encryption 2

  • The RSA problem (and its relatives)
  • Key-agreement from RSA
  • PKE from RSA in the random oracle model
  • Accumulators from RSA (Self Study)


Lecture 19 notes


Public-Key Encryption 3

  • Security proof of the RSA encryption in the random oracle model

CPA-security proof of RSA

HW3 due

11 10/31/23

Chosen Ciphertext Security 1

  • examples of active attacks on CPA-secure schemes
  • defining CCA security
  • CCA insecurity of RSA and Elgamal
Lecture 21 notes

Chosen Ciphertext Security 2

  • RSA-PKCS1 standard
  • CCA attack on RSA-PKCS1 and SSL
  • RSA-OAEP standard (CCA-secure)
  • More on RSA's CCA-security


Lecture 22 notes

12 11/7/23

Digital Signatures

  • Motivating application: Software Distribution
  • RSA signatures (the full domain hash paradigm)
  • RSA PKCS1 standard (for signatures)
  • Bleichenbacher's attack (yet again)
  • Certificates and PKI
Lecture 23 notes

Zero-knowledge Protocols 1

  • Schnorr's ID protocol for proving knowledge of discrete-logs
  • Honest-Verifier Zero-knowledge (a special case of ZK)
  • More HVZK protocols: Chaum-Pederson, Guillou-Quiquater

HW4 open

Lecture 24 notes

13 11/14/23

Zero-knowledge Protocols 2

  • Proving properties of encrypted data:
    • Plaintext equality
    • Plaintext is a bit
  • Full ZK (strengthening of HVZK to malicious verifiers)
  • Proving properties about graphs in ZK:
    • Graph isomorphism
    • Graph 3-coloring
Lecture 25 notes

Overview of Cryptography in Blockchains

  • What is a blockchain?
  • Role of signatures, merkle-trees, ZK proofs in cryptocurrencies
  • Discussion

HW4 due

Talk by Prof. Dan Boneh

14 11/21/23

Fully-homomorphic Encryption (FHE) - 1

  • The Learning-with-errors (LWE) Problem; discussion on its security
  • SKE and PKE from LWE
  • PKE from LWE
  • Discussion on additive and multiplicative homomorphism of the PKE scheme


Lecture 27 notes

11/23/23 No Class due to Thanksgiving Day
15 11/28/23

Fully-homomorphic Encryption (FHE) - 2

  • Levelled FHE scheme
  • Discussion on additive and multiplicative homomorphism
  • Bootstrapping: Towards unbounded FHE via circular-security

Final Project Presentations:

  1. Sarabjeet on Homomorphic Encryption for Arithmetic of Approximate Numbers.



FHE Slides


Final Project Presentations:

  1. (Hemanth, Palguni) on Securing Secrets: The Double Ratchet Unveiled.
  2. Jackson on Attacks on RSA, DH, DSA in the Wild.

Double Ratchet Slides

Attacks on RSA,DH, DSA Slides

16 12/5/23

Final Project Presentations:

  1. (Albert, Phillip) on Zero knowledge Proofs for Proving Program Safety
  2. (Seng, Toshi) on Commitments to Polynomials and Their Applications


UNSAT in ZK Slides

Polynomial Commitment Slides


Final Project Presentations:

  1. Prashant on Circular-Secure Encryption from Decision Diffie-Hellman
  2. Ganesh on Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems

Circular-security from DDH

Circular-security from Learning Problems

Final reports due



University Policies

COVID-19 Information

COVID-19 Central @ The U


Drop/Withdrawal Policies

Students may drop a course within the first two weeks of a given semester without any penalties.

Students may officially withdraw (W) from a class or all classes after the drop deadline through the midpoint of a course. A “W” grade is recorded on the transcript and appropriate tuition/fees are assessed. The grade “W” is not used in calculating the student’s GPA.

For deadlines to withdraw from full-term, first, and second session classes, see the U's Academic Calendar.

Academic Honesty, Plagiarism and Cheating

It is assumed that all work submitted to your instructor is your own work. When you have used the ideas of others, you must properly indicate that you have done so.

It is expected that students adhere to University of Utah policies regarding academic honesty, including but not limited to refraining from cheating, plagiarizing, misrepresenting one’s work, and/or inappropriately collaborating. This includes the use of generative artificial intelligence (AI) tools without citation, documentation, or authorization. Students are expected to adhere to the prescribed professional and ethical standards of the profession/discipline for which they are preparing. Any student who engages in academic dishonesty or who violates the professional and ethical standards for their profession/discipline may be subject to academic sanctions as per the University of Utah’s Student Code:

Plagiarism and cheating are serious offenses and may be punished by failure on an individual assignment, and/or failure in the course. Academic misconduct, according to the University of Utah Student Code,

“...Includes, but is not limited to, cheating, misrepresenting one’s work, inappropriately collaborating, plagiarism, and fabrication or falsification of information…It also includes facilitating academic misconduct by intentionally helping or attempting to help another to commit an act of academic misconduct.”

For details on plagiarism and other important course conduct issues, see the U's Code of Student Rights and Responsibilities.

Course Materials Copyright

The Content is made available only for your personal, noncommercial educational, and scholarly use. You may not use the Content for any other purpose, or distribute, post or make the Content available to others unless you obtain any required permission from the copyright holder. Some Content may be provided via streaming or other means that restrict copying; you may not circumvent those restrictions. You may not alter or remove any copyright or other proprietary notices included in the Content.
Please see the Code of Student Rights and Responsibilities, Section III.A.5 regarding the use and distribution of class Content and materials. Section III.A.5. prohibits the following:
Sale or distribution of information representing the work product of a faculty member to a commercial entity for financial gain without the express written permission of the faculty member responsible for the course. (“Work product” means original works of authorship that have been fixed in a tangible medium and any works based upon and derived from the original work of authorship.)

Safety at the U

The University of Utah values the safety of all campus community members. You will receive important emergency alerts and safety messages regarding campus safety via text message.

For more safety information and to view available training resources, including helpful videos, visit (Links to an external site.).

To report suspicious activity or to request a courtesy escort, contact:

Campus Police & Department of Public Safety
801-585-COPS (801-585-2677)
1735 E. S. Campus Dr.
     Salt Lake City, UT 84112

Wellness at the U

Your personal health and wellness are essential to your success as a student. Personal concerns like stress, anxiety, relationship difficulties, depression, or cross-cultural differences can interfere with a student’s ability to succeed and thrive in this course and at the University of Utah.

Please feel welcome to reach out to your instructor or TA to handle issues regarding your coursework.

For helpful resources to manage your personal wellness and counseling options, contact:

Center for Student Wellness
2100 Eccles Student Life Center
     1836 Student Life Way
     Salt Lake City, UT 84112

Women's Resource Center
411 Union Building
     200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Addressing Sexual Misconduct

Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran’s status, or genetic information.

If you or someone you know has been harassed or assaulted, you are encouraged to report it to university officials: 

Title IX Coordinator & Office of Equal Opportunity and Affirmative Action
135 Park Building
     201 Presidents' Cir.
     Salt Lake City, UT 84112

Office of the Dean of Students
 270 Union Building
     200 S. Central Campus Dr.
     Salt Lake City, UT 84112

To file a police report, contact:

Campus Police & Department of Public Safety
801-585-COPS (801-585-2677)
1735 E. S. Campus Dr.
     Salt Lake City, UT 84112

If you do not feel comfortable reporting to authorities, the U's Victim-Survivor Advocates provide free, confidential, and trauma-informed support services to students, faculty, and staff who have experienced interpersonal violence.

To privately explore options and resources available to you with an advocate, contact:

Center for Student Wellness
328 Student Services Building
    201 S. 1460 E.
     Salt Lake City, UT 84112

Americans With Disabilities Act (ADA)

The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities.

All written information in this course can be made available in an alternative format with prior notification to the Center for Disability & Access (CDA). CDA will work with you and the instructor to make arrangements for accommodations. Prior notice is appreciated. To read the full accommodations policy for the University of Utah, please see Section Q of the Instruction & Evaluation regulations.

If you will need accommodations in this class, or for more information about what support they provide, contact:

Center for Disability & Access
162 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Diverse Student Support

Your success at the University of Utah is important to all of us here! If you feel like you need extra support in academics, overcoming personal difficulties, or finding community, the U is here for you.

Student Support Services (TRIO)

TRIO federal programs are targeted to serve and assist low-income individuals, first-generation college students, and individuals with disabilities.

Student Support Services (SSS) is a TRIO program for current or incoming undergraduate university students who are seeking their first bachelor's degree and need academic assistance and other services to be successful at the University of Utah.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Student Support Services (TRIO)
 Room 2075 
     1901 E. S. Campus Dr.
     Salt Lake City, UT 84112

American Indian Students

The AIRC works to increase American Indian student visibility and success on campus by advocating for and providing student-centered programs and tools to enhance academic success, cultural events to promote personal well-being, and a supportive “home-away-from-home” space for students to grow and develop leadership skills. 

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

American Indian Resource Center
Fort Douglas Building 622
     1925 De Trobriand St.
     Salt Lake City, UT 84113

Black Students

Using a pan-African lens, the Black Cultural Center seeks to counteract persistent campus-wide and global anti-blackness. The Black Cultural Center works to holistically enrich, educate, and advocate for students, faculty, and staff through Black-centered programming, culturally affirming educational initiatives, and retention strategies.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Black Cultural Center
Fort Douglas Building 603
     95 Fort Douglas Blvd.
     Salt Lake City, UT 84113

Students with Children

Our mission is to support and coordinate information, program development, and services that enhance family resources as well as the availability, affordability, and quality of child care for University students, faculty, and staff.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Center for Childcare & Family Resources
408 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Students With Disabilities

The Center for Disability and Access is dedicated to serving students with disabilities by providing the opportunity for success and equal access at the University of Utah. They also strive to create an inclusive, safe, and respectful environment.

For more information about what support they provide and links to other resources, view their website or contact:

Center for Disability and Access
162 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Students of Ethnic Descent

The Center for Ethnic Student Affairs offers several programs dedicated to the success of students with varied cultural and ethnic backgrounds. Its mission is to create an inclusive, safe campus community that values the experiences of all students.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Center for Ethnic Student Affairs
 235 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

English as a Second/Additional Language (ESL) Students

If you are an English language learner, there are several resources on campus available to help you develop your English writing and language skills. Feel free to contact:

Writing Center

 (Links to an external site.)

2701 Marriott Library
     295 S 1500 E
     Salt Lake City, UT 84112

English for Academic Success (EAS) Program
 2300 LNCO
     255 S. Central Campus Dr.
     Salt Lake City, UT 84112

English Language Institute
801-581-4600 (Links to an external site.)
540 Arapeen Dr.
     Salt Lake City, UT 84108

Undocumented Students

Immigration is a complex phenomenon with broad impact—those who are directly affected by it and those who are indirectly affected by their relationships with family members, friends, and loved ones. If your immigration status presents obstacles that prevent you from engaging in specific activities or fulfilling specific course criteria, confidential arrangements may be requested from the Dream Center.

Arrangements with the Dream Center will not jeopardize your student status, your financial aid, or any other part of your residence. The Dream Center offers a wide range of resources to support undocumented students (with and without DACA) as well as students from mixed-status families.

For more information about what support they provide and links to other resources, view their website or contact:

Dream Center
801-213-3697 (Links to an external site.)

LGBTQ+ Students

The LGBTQ+ Resource Center acts in accountability with the campus community by identifying the needs of people with a queer range of [a]gender and [a]sexual experiences and responding with university-wide services.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

LGBTQ+ Resource Center
801-587-7973 (Links to an external site.)
409 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Veterans & Military Students

The mission of the Veterans Support Center is to improve and enhance the individual and academic success of veterans, service members, and their family members who attend the university; to help them receive the benefits they earned, and to serve as a liaison between the student veteran community and the university.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Veterans Support Center
801-587-7722  (Links to an external site.)
418 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112


The Women’s Resource Center (WRC) at the University of Utah serves as the central resource for educational and support services for women. Honoring the complexities of women’s identities, the WRC facilitates choices and changes through programs, counseling, and training grounded in a commitment to advance social justice and equality.

For more information about what support they provide, a list of ongoing events, and links to other resources, view their website or contact:

Women's Resource Center
411 Union Building
     200 S. Central Campus Dr.
     Salt Lake City, UT 84112

Inclusivity at the U

The Office for Inclusive Excellence is here to engage, support, and advance an environment fostering the values of respect, diversity, equity, inclusivity, and academic excellence for students in our increasingly global campus community. They also handle reports of bias in the classroom as outlined below:

Bias or hate incidents consist of speech, conduct, or some other form of expression or action that is motivated wholly or in part by prejudice or bias whose impact discriminates, demeans, embarrasses, assigns stereotypes, harasses, or excludes individuals because of their race, color, ethnicity, national origin, language, sex, size, gender identity or expression, sexual orientation, disability, age, or religion.

For more information about what support they provide and links to other resources, or to report a bias incident, view their website or contact:

Office for Inclusive Excellence
801-581-4600 (Links to an external site.)

Other Student Groups at the U

To learn more about some of the other resource groups available at the U, check out: