An introduction to cryptographic methods and ideas.

The first half of this paper concerns number theory, which provides the basis of cryptography and computer security. Famous problems include for example Fermat’s Last Theorem, the Riemann Hypothesis and the Goldbach Conjecture. Topics covered in the paper include sums of squares, finding rational points on curves, arithmetic functions, and Gauss' law of quadratic reciprocity.

The Cryptography half of this paper will cover the basics of both public and private key cryptosystems. We will touch on some simple cryptosystems, key exchange, trapdoor functions, Feistel and other block cyphers, Data Encryption Standard, R.S.A., Massey-Omura, and El Gamal. We will also look at some Information Theory, the notions of entropy, key equivocation and unicity distance, as well as a proof of Shannon's noiseless coding theorem

There are two streams in this paper: the Mathematics Steam and the Computer Science Stream.

The Mathematics Stream do more theoretical work in the first half of the semester, but will not need to do the final group project.

The Computer Science Stream will do less from the Number Theory half but will have a final group programming project to undertake, which will be assessed at the end of the course.