Introduction to Cryptography

Computer Science 281/481
University of Rochester
Fall 2014

Instructor: Muthu Venkitasubramaniam

Time: TR 12:30-13:45
Place: CSB 632
Course Web page:

Office Hours: M 11:00-12:00 (Room 632)

TA: Mark Mullock



Modern cryptography studies techniques for facilitating interactions between distrustful entities. Today, with the advent of the Internet, these techniques become indispensable – enabling, for instance, anonymous electronic elections, privacy-preserving electronic auctions, internet banking and more. In this course we introduce some of the fundamental concepts of this study.

Topics Include: one-way functions, private-key/public-key encryption systems, digital signatures, zero-knowledge, secure-multiparty computation and its applications.  


CS 280 (or equivalent), MTH150 (or mathematical maturity), or permission of instructor.
The main skills that will be assumed from these courses are: 1) the ability to understand and write formal mathematical definitions and proofs and 2) comfort with reasoning about algorithms, such as proving their correctness and analyzing their running times. It is also important that you are familiar with basic probability.

Course Administration

We will be using Piazza for this course. If you have not been invited please send an email to Mark <>


There will be roughly 4-5 homeworks and 2 exams. Students taking the graduate course will be expected to do a final project. The grade will be based on homework assignments, exams and class participation.

Homework Policy

You are free to collaborate with other students on the homework, but you must turn in your own individually written solution and you must specify the names of your collaborators. Additionally, you may make use of published material, provided that you acknowledge all sources used. Note that it is a violation of this policy to submit a problem solution that you are unable to explain orally to me. Typed problem sets are strongly preferred.


Lecture notes covering a large fraction of the course can be found here (course notes developed by Rafael Pass and abhi shelat).

There is no required text for the course other than lecture notes. You may find the following two books to be useful references. Note, however, that we will not always be following the same notational conventions as these books.

For a more applied treatment of cryptography, I suggest the following book which is available on-line.

For background reading on probability, algorithms, and complexity theory, I recommend:


Lectures Outline

9/2 Lecture 1: What Crypt can do for you? the match-making game and zero-knowledge

9/9 Lecture 2: Basics of Number Theory and Number Theoretic Algorithms

9/16 Lecture 3: Kerchoff's principle, Historical Ciphers (Chapter 1 from Pass-shelat Notes)

9/18 Lecture 4: Shannon's definition of secrecy and One-Time Pad (Chapter 1 from Pass-Shelat Notes)

9/19 Lecture 5: One-way functions (OWF), Worst-Case and Strong OWF(Chapter 2 from Pass-shelat Notes)

9/23 Lecture 6: Weak OWF based on the Factoring Assumption (Chapter 2 – 2.3)

9/25 Lecture 7: Strong OWF based on the Factoring Assumption (Chapter 2 – 2.4.2)

9/30 Lecture 8: Basics of Computational Number Theory (Chapter 2 – 2.6.4,2.6.5)

10/2 Lecture 9: OWF based on the Discrete Logarithm Assumption(Chapter 2 – 2.8)

10/7 Lecture 10: OWF based on the RSA Assumption(Chapter 2 – 2.9)

10/9 Lecture 11: Computational Indistinguishability, Properties of Indistinguishability – Closure under Efficient Operations / Transitivity (Chapter 3 – 3.1, 3.1.1)

10/14 Lecture 12: Pseudorandom Generators (PRG), 1-bit to poly-bit expansion of PRGs (Chapter 3 – 3.3,3.3.1,3.3.5)

10/16 Lecture 13: Hard-Core predicates, PRGs from OWFs and Hard-Core predicates (Chapter 3 – 3.3.3,3.3.4)

10/21 Lecture 14: Hard-core predicate for the Discrete Logarithm OWF (Chapter 3 – 3.4.1)

10/23 Lecture 15: Single-message semantic-security, Multi-message semantic-security, Random Functions (Chapter 3 – 3.6,3.7,3.8)

10/25 Lecture 16: Pseudorandom Functions (PRF) and Multi-message semantic-secure encryption scheme (Chapter 3)

10/28 Lecture 17: Multi-message secure encryption scheme using Random Functions and Functional/Oracle-Indistinguishability

10/30 Mid-Term

11/4 Lecture 18: Multi-message secure encryption from PRFs and Public-Key Encryption.

11/6 Lecture 19: RSA and El-Gamal encryption scheme

11/11 Lecture 20: Block ciphers and Stream ciphers

11/13 Lecture 21: MACs and Digital Signatures

11/18 Lecture 22: Collision-resistant Hash Functions and Bitcoins

11/20 Lecture 23: Key Management and Public-Key Infrastructure Transfer

11/21 Lecture 24/25: Extra Class: 6:00p-9:00p Zero-Knowledge, Oblivious Transfer and Secure Computation

11/25 Lecture 26: Stronger/Alternate notions of Encryption: Zero-Knowledge, CPA/CCA1/CCA2

11/27 Thanksgiving

12/2 Lecture 27: Network Security I

12/4 Lecture 28: Network Security II

12/9 Lecture 29:

12/11 Lecture 30:

Presentation Schedule

9/23 Adam Scrivener – Enigma and World War II

9/25 Amelia Norvell – SQL Inject Attack

11/6 Cameron Caswell – Attacks on Encryption Schemes

11/11 Eric Podsaidly – TOR

11/13 Invited Speaker

11/18 Justin Fraumeni

11/20 Priya Thomas

11/25 Annie Zhang

12/2 Grace Heard

12/4 Eric Campbell

Related Course

MTH 233: Introduction to Cryptography