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