An introduction to Mathematical Cryptography — MCR

 

Instructor: Dr. Péter MAGA

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

Prerequisite: Basic enumeration techniques (the necessary number theory, algebra and probability theory will be covered in the class).

Course description: The course provides an introduction to the mathematical approach to addressing the main problems of cryptography.

Topics:
Introduction. Simple substitution ciphers. Cryptanalysis. Mathematical formulation of ciphers. Interlude on algebra and number theory,
Discrete logarithms and Diffie-Hellman. Public key cryptography. The discrete logarithm problem. The Diffie-Hellman key exchange. The ElGamal cryptosystem.
Integer factorization and RSA. The RSA cryptosystem. Primality testing. Factorization algorithms.
Combinatorics, probability, and information theory. The Vigenere cipher. Statistical tools. Probability and information theory.
Elliptic curves and cryptography. Elliptic curves over finite fields. Elliptic curve cryptography.
Additional topics (if time permits). Digital signatures. Zero-knowledge proofs. Secret sharing.