Mathematical Cryptography
(Math 404)

An introduction to mathematical cryptography.
Fall 2017

Instructor: Paul Aspinwall

Credits: 1.00, Hours: 03.0

Time: Tuesday and Thursday 10:05AM - 11:20AM.

Location: Physics 235

Exams:

Office Hours: see Sakai.

Math 221 or 216, and some programming experience, preferably Python. Math 401 or 501 would be useful.

A rough outline (not necessarily in order) is as follows

Introductory ideas
- Substitution ciphers
- Modular arithmetic
- Symmetric and asymmetric ciphers
Discrete Logarithms
- Diffie-Hellman key exchange
- El Gamal public key encryption
- A collision algorithm
Integer Factorizations
- RSA public key encryption
- Pollard's factorization algorithm
- Smooth numbers and sieves
- The Quadratic sieve.
Information Theory
- Pollard's ρ method
- P vs NP
Elliptic Curve Cryptography
- The elliptic curve discrete logarithm
- Lenstra's algorithm
- Elliptic curves over F₂ and F_2^k
Applications
- Digital Signatures
- Hash algorithms
- DES and AES

The course will be based on the text:

J. Hoffstein, J. Pipher and J. Silverman, An Introduction to Mathematical Cryptography Springer 2008, ISBN 978-0-387-77993-5

It may also be useful to refer to

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer 2005.
B. Schneier, Applied Cryptography, John Wiley & Sons 1996, ISBN 0-471-11709-9

(Courtesy xkcd.com)

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Duke University, Box 90318
Durham, NC 27708-0318

Mathematical Cryptography(Math 404)