Introduction to algebraic number theory and cryptography (2018 spring)

Lectures: Wednesdays 13–15 Kerékjártó classroom

Topics

Algebraic number fields: the ring of algebraic integers, Dedekind domains, unique factorization, the group of units, ideals, class number. Quadratic fields, quadratic reciprocity. Public-key cryptography: RSA, Diffie–Hellman key exchange, discrete logarithm, ElGamal, elliptic curve methods. Primality tests and factorization methods.

Links:

1. Pick's theorem (Wikipedia)
2. lattice points on a circle (cdf)
3. Gaussian Primes (Wolfram Demonstrations)
4. A Stroll through the Gaussian Primes (American Mathematical Monthly)
5. Primes of the Form x² + ny² and the Geometry of (Convenient) Numbers
6. lattices (pdf)
7. ideals in imaginary quadratic fields (cdf)

Bibliography

• Neal Koblitz: A course in number theory and cryptography
• Richard A. Mollin: Algebraic number theory
• M. Ram Murty, Jody Esmonde: Problems in algebraic number theory