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Useful Links as of January 2012 (these tend to go out of date!):

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

General cryptology links

arXiV cryptology papers

IACR eprint archive and IACR

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

Centre for Applied Cryptographic Research

Cipher - IEEE Electronic Newsletter of the Technical Commitee on Security & Privacy

Cryptography Research, Inc. resources

Oded Goldreich Homepage Bruce Schneier Homepage Paul Kocher research links

NIST - National Institute of Standards and Technology NSA - National Security Agency

RSA - RSA Laboratories

Handbook of Applied Cryptology

Number theory links

Big Number Calculator applet