MATH 408 Page

Introduction to Cryptology

This course is an introduction to the mathematical theory of secure communication. Topics to be developed will include:

• Classical cryptographic systems: substitution, transposition, polyalphabetic systems.
• Brief introduction to Shannon's information theory.
• Introduction to modern (public key) cryptology.
• Intoduction to complexity theory.
• One-way and trapdoor functions.
• Knapsacks (an example of an NP problem).
• RSA
• Diffie-Helman: discrete logarithms
• Attack methods.
• Some ideas from probability theory.
• Elliptic curves and ECC
• Other topics as time permits (e.g., lattice cryptosystems).
  
  

Course requirements include: weekly homework assignments; a midterm exam; and a project to be done by each student or group of two students. Course will involve some computer use, particularly of Mathematica. (Alternatively, download pari.gp)

Useful Links:

Home page for Introduction to Mathematical Cryptography, by Hoffstein, Pipher, and Silverman.

General cryptology links

Certicom's White Papers on Cryptography (useful for elliptic curve info). See also their on-line tutorial on elliptic curve cryptology.

Counterpane's bibliography of cryptology papers available online

Handbook of Applied Cryptology

Number theory links

Big Number Calculator applet