COMS W4261:   Introduction to Cryptography

    Fall 2016

SyllabusLecture Summaries | Required and Suggested Reading | Prerequisites | Grading and Policies | Homework | Courseworks


  • 12/14/16 The exam location tomorrow is in the usual classroom: 1024 Mudd, 10am-12noon. Good luck!
  • 12/6/16 Office hours for next week:
    • Mon 12/12:
      • 3:30-5:00 Ghada
    • Tue 12/13:
      • 1:00-3:00 Luke
      • 5:00-7:00 Edo
    • Wed 12/14:
      • 10:00-12:00 Prof Malkin
      • 2:00-4:00 Edo
  • 12/6/16 Homework 5 is on the Homework page. It is due next Tue by 11pm electronically on courseworks. No late days will be accepted. This homework is shorter and counts as half a homework for grading purposes.
  • 12/6/16 Reminder: the exam will take place Thursday December 15 10am-12noon (location to be determined). The exam is open book open notes, but no electronic equipment and no sharing of materials during the exam. Students are responsible for everything covered in class starting with lecture 15 and on the homework starting with HW 3.
  • 12/3/16 Office hours change this week: Prof Malkin's office hours on Wednesday 12/7 will be 8:50am-9:50am (instead of 1-2). Other office hours will be held as usual.
  • 11/30/16 Edo will lead a recitation on Friday 12/2 from 12-1:15 in our usual classroom, focusing on the number theoretic material that we are using.

General Information

This is a three-credit graduate level course. It can be credited to all degree programs, subject to advisor approval.  It is also a theory elective for the PhD program in computer science, a suitable elective for the MS foundations or security tracks, and a suitable class for undergrads as well.  
We meet Tuesday and Thursday, 10:10-11:25am at 1024 Mudd.

Questions?  Email the instructors and/or the TAs.  


Tal Malkin (tal at cs)
Office hours: Wednesday 1:00pm-2:00pm, Thursday 11:30am-12:30pm, 514 CS Building

Teaching Assistants

Ghada Almashaqbeh (ghada at cs)
Office hours: Monday 3:30-5:00pm, DSI Mudd 4th floor

Luke Kowalczyk (luke at cs)
Office hours: Tuesday 1:00-3:00pm, DSI Mudd 4th floor

Edo Roth (enr2116 at columbia)
Office hours: Wednesday 2:00-4:00pm, TA room Mudd 1st floor

Class Description and Syllabus 

Lectures and Readings

This course is an introduction to modern cryptography.  In general, cryptography aims to construct efficient schemes achieving some desired functionality, even in an adversarial environment.  For example, the most basic question in cryptography is that of secure communication across an insecure channel: Can Alice send a message to Bob so that Bob understands the message, but no eavesdropper does?   How can Bob be sure that the message received was sent by Alice?  Another question is that of secure computation in an insecure environment:  Can a group of parties perform some distributed computation (e.g., coordinate an attack, or tally a vote), so that an adversary controlling the communication channels and some of the parties cannot disrupt the computation or learn extra information?  

While cryptography is an ancient field, the emergence of modern cryptography in the last few decades is characterized by several important features distinguishing it from classical cryptography.  For one thing, the availability of computers and the wide spread of networked information systems and the Web, has dramatically increased both the need for good cryptography, and the possibilities that it can offer.  In addition to the classical military and national security applications, a wide scope of financial, legal, and social cryptographic applications has emerged, from using a credit card on-line or sending an encrypted email, to more ambitious goals of electronic commerce, electronic voting, contract-signing, database privacy, and so on.  The most important characteristic of modern cryptography is its rigorous, scientific approach, based on firm complexity-theoretical foundations.  In contrast to the classical approach based on ad-hoc solutions (design a scheme that seems very hard to break, and hope for the best), modern cryptography aims for specific, rigorously quantifiable security guarantees,  based on precise mathematical definitions and provably secure protocols.

What You Will Learn in This Class (Hopefully!)

The principles and techniques underlying the above will be illustrated through specific examples drawing from the basic cryptographic primitives.  Through these examples, which are very important on their own, you will also learn to critically evaluate and interpret cryptographic definitions and security proofs (i.e., what is and what is not guaranteed?).  
While the class will focus on the theoretical foundations, we will discuss the relation to how things are actually done in practice.
The material covered in the class should prepare you to make sense of some current research papers in cryptography, and to study further on your own (or take an advanced class).  Opportunities for research under my supervision may be available for interested students who do well in the class.

Tentative List of Topics 

The following is an ambitious list of topics to be covered.  Depending on time, some of the topics may be omitted.

What You Will Not Learn in This Class

The following topics are outside of the scope of this class.  Some aspects of these topics are taught in COMS W4180 (Network Security), COMS 4187 (Security Architecture and Engineering), COMS E6184 (Anonymity and Privacy), and COMS W3995 Computers and Society classes.  

Required Text

We will use the book “Introduction to Modern Cryptography” by Jonathan Katz and Yehuda Lindell, Chapman and Hall/CRC Press, 2nd edition. This book will be on reserve in the engineering library, and available from the Columbia bookstore.   Additional papers and handouts may occasionally be distributed in class.  Recommendations for some other textbooks (not required) appear here


The following skills will be assumed:

It will also help to have background in at least some of the following areas:

These topics will be briefly covered in class as needed, but if you do not have any background in any of them, you are likely to find it hard to keep up.

The appendix of the textbook reviews some background, and additional references for background reading can be found here

Grading and Policies

The grading will be based on homework (50%) a midterm (25%) and a final (25%).
The midterm will take place November 3rd during class, and the tentative date for the final is during finals week (as scheduled by registrar).
Students are expected to attend class.
No laptops or other electronic equipment are to be used during class, unless you have obtained prior approval from the instructor.
See the Homework page for homework policies.

All students are presumed to be aware of the departmental policy regarding academic honesty.