This course provides an introduction to modern cryptography. 

It includes 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 security definitions for block ciphers, stream ciphers, MAC functions, hash functions.. It provides an introduction to cryptanalysis and generic attacks including exhaustive key search. It defines the concept of security strength and the basis for cryptographic security: public scrutiny.
In symmetric cryptography it discusses the design principles and cryptanalysis of stream ciphers and treats block ciphers and hash functions and their modes of use. 
For the latter, it is shows how reductionist security proofs can be given.
In public key cryptography the course treats key establishment protocols, public key encryption, authentication protocols and signature schemes and treats their security definitions. It covers RSA and discrete-log based crypto over cyclic subgroups of multiplicative groups modulo a prime and 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.
They include Diffie-Hellman key exchange.  ElGamal encryption, Schnorr authentication protocol, the Fiat-Shamir transform, Schnorr signatures and (EC)DSA. 

Instructional Modes