*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.