MATH 408 Page

Introduction to Cryptology

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

• Mathematical preliminaries - number theory. (EGCD algorithm is here.)
• Classical cryptographic systems: substitution, transposition, polyalphabetic systems.
• Introduction to modern (public key) cryptology.
• Diffie-Helman: discrete logarithms
• RSA and Integer Factorization
• Brief introduction to Shannon's information theory. (His original paper is here)
• Brief Introduction to complexity theory.
• One-way and trapdoor functions..
• Some ideas from probability theory.
• Elliptic curves and ECC
• Lattices and Lattice Cryptosystems
• Other topics as time permits (e.g., Post-Quantum Crypto).
  
  

Detailed Syllabus

HW2 notebook

Digital Signatures

Course requirements include: weekly homework assignment (25%)s; two exams (50%); and a project to be done by each student or group of two students (25%). Course will involve some computer use. Mathematica is one possibility. (Alternatively, download pari.gp)

Useful Links as of December 2024 (these tend to go out of date!):

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

arXiV cryptology papers

IACR eprint archive and IACR

Centre for Applied Cryptographic Research

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

Cryptography Research, Inc. (Now Rambus)

Oded Goldreich Homepage Bruce Schneier Homepage Paul Kocher research links

NIST - National Institute of Standards and Technology

NSA - National Security Agency Cryptologic Heritage

Handbook of Applied Cryptology

Number theory links

General cryptology links (way out of date but there might be something there)

Big Number Calculator applet

RecordNations Encryption Learning Center

Basic Cryptanalysis -- 1990 U.S. Army Field Manual