M343L Syllabus

APPLIED NUMBER THEORY

Prerequisite and degree relevance:  Mathematics 328K or 343K with a grade of at least C-.

Text: An Introduction to Mathematical Cryptography by Jill Pipher, Jeffrey Hoffstein, Joseph H. Silverman.

Topics: Basic properties of integers. Prime numbers and unique factorization. Congruences, Theorems of Fermat and Euler, primi- tive roots. Primality testing and factorization methods. Cryptogra- phy, basic notions. Public key cryptosystems. RSA. Implementa- tion and attacks. Discrete log cryptosystems. Diffie-Hellman and the Digital Signature Standard. Elliptic curve cryptosystems. Symmetric cryptosystems, such as DES and AES.

Responsible party: Kathy Davis and Felipe Voloch, Spring 2010