This course provides an introduction to modern cryptography. 
It starts with a refresh of basic number theory and algebra such as groups and finite fields and then treats symmetric cryptography and public key cryptography. It explains the most common attacker models, the concept of security strength and the basis for cryptographic security: public scrutiny.
In symmetric cryptography it discusses the design principles and cryptanalysis of primitives such as stream ciphers, block ciphers and hash functions and their modes of use. 
For the latter, we show how easily reductionist security proofs can be given.
In public key cryptography the course treats discuss key establishment and signature schemes and identification protocols. 
It covers both the RSA cryptosystem and discrete-log based crypto on the other, with the emphasis on elliptic curve groups. 
It treats different attack methods for solving the discrete log problem and the consequence for the size parameters of the group used in discrete-log cryptography. Schemes and protocols are built on top of groups where the discrete log is hard and they include the Schnorr identification protocol, Schnorr and Elgamal signatures and Diffie-Hellman key exchange.