These are my (unofficial) lecture notes for the lecture Computer Algebra held by Prof. G. Kemper at the Technical University Munich in the winter semester 2021/22.
Topics covered include:
- primality testing, e.g. the Fermat test, Miller-Rabin test and AKS-test
- the basics of cryptography, including RSA encryption and the Diffie-Hellman key exchange
- fast factorization using Pollard’s rho method and \(p-1\) algorithm
- fast matrix multiplication, in particular the Strassen multiplication
- Gröbner bases and their applications