Course Description

This course is a two-part exploration of modern-day cryptography, or the science of secret writing.  On the one hand, we will attempt to answer questions such as “What makes an internet credit card transaction safe?” which will lead us to the mathematics behind modern public-key ciphers like Diffie-Hellman and RSA.  In order to understand what makes these crypto-systems virtually unbreakable, we will start with simple concepts like prime numbers and divisibility and quickly develop powerful number-theoretic machinery.  The emphasis in this part of the course will be placed on mathematical rigor, with elegance, conciseness, and the validity of the mathematical proof as the underlying theme.  Because of the fast pace of this part of the course, a certain level of mathematical maturity is required.  This means that you will be occasionally required to read and understand challenging mathematics on your own and learn how to write up logically sound mathematical arguments.
In parallel, we will look at the seemingly unrelated questions of the type “Why is the National Security Agency the largest employer of mathematicians in the world?”  Such questions will quickly lead into considerations of the various ethical and political aspects of privacy and secrecy.  Because of the internet, we transmit more and more easily intercepted (and therefore often encrypted) information to one another than ever before.  The issues surrounding dissemination of information and its regulation have consequently come to the forefront of the public discourse and have been subject to much debate in recent years.  One side argues, for example, that everyone should have the opportunity to transmit information in a way that nobody but the intended audience can read it.  The other side says that the advantage of being able to intercept and decode an encrypted message which is for example known to contain the time and place of the next terrorist attack is clear.  Some obvious questions immediately arise:  Should the government impose export regulations for new crypto-systems?  And if so, how can it prevent an upload of a new crypto-system to the internet for everyone around the world to download and use?  Should the National Security Agency regulate cryptographic standards and have access to private information?  The goal of this course will not be to find definitive answers to these questions but to understand and recognize that the issue of privacy is delicate and relevant and that it is being passionately debated in the background of our routine daily interactions through technology.