Math 1580 Cryptography, Fall 2011

Course Information

A printable pdf version of the syllabus is here.

Basic Information

Instructor: Chris Kottke

Office: 303 Kassar-Gould House


Office hours: WF 2-3pm, or by appointment.

Text: An Introduction to Mathematical Cryptography, by Hoffstein, Pipher, and Silverman. Springer. ISBN: 978-0-387-77993-5.


Grading: Your final grade will depend on weekly homework scores and exams (1 midterm and 1 final), weighted as below. Your lowest homework score will be dropped. The final will be about 1/3 cumulative material and 2/3 new material.


This class will be an introduction to the theory of mathematical cryptography. While we will discuss symmetric key cryptography, the main focus is on the difficult mathematical problems which underlie asymmetric (public key) cryptography.

These problems include the discrete logarithm problem (ElGamal and Elliptic Curve Cryptography), integer factorization (RSA) and the Shortest Vector Problem (NTRU).

In the course of studying these problems, we will consider what it means for a mathematical problem to be considered difficult, what are some of the best known algorithms for solving such problems, and how they may be exploited for cryptographic purposes.

Topics will include modular arithmetic, finite fields, discrete logarithms, Diffie-Hellman key exchange, ElGamal, integer factorization, RSA, an introduction to probability and information theory, elliptic curves, lattices, and digital signatures.

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