Cryptography

Introduction to Cryptography
MAT 6973-01F
Summer I, 2005
Instructor: J. Iovino

Brief Description

The course in a basic introduction to modern cryptographic techniques. Some of the better known cryptosystems will be discussed as examples; the emphasis, however, will be on the mathematical foundations.

Intended Audience

Graduate and upper division students in mathematics, as well as computer science and statistics students who are comfortable with mathematical rigor.

Prerequisites

Real Analysis I (MAT 4213) or consent of instructor.

Content

Elementary number theory: congruences and residue class rings, Wilson's Theorem, Fermat's Little Theorem, The Euler phi-funtion, the Chinese Reminder Theorem.

Symmetric-key cryptosystems: block ciphers, DES and AES, stream ciphers.

Public-key cryptosystems: exponentiation, discrete logarithms, RSA, ElGamal, Knapsack.

Digital signatures

Textbook

Mollin, Richard A. An Introduction to Cryptography. Chapman-Hall, 2001.

Additional references

Kenneth H. Rosen. Elementary Number Theory and its Applications. Fourth Edition. Addison-Wesley, 2000.

Buchmann, Johannes A. Introduction to Cryptography. Undergraduate Texts in Mathematics. Springer-Verlag, 2001.

Evaluation

There will be five problem sets; each of them will be worth 20% of the grade.

How to contact the instructor

Office: SB 4.01.34

Telephone: (210) 458-5531

Email: iovino@math.utsa.edu

Office hours: M, W, 4-5 pm, or by appointment.