1. Pseudorandom Number Generators from Elliptic Curves
Several constructions of PRNG's from elliptic curves will be described. In particular, elliptic curve analogues of the linear congruential generator and the Naor-Reingold generator will be considered. We will also outline some underlying tools such as bounds of exponential sums along elliptic curves, some properties of division points and the group structure of elliptic curves. Some open questions will be outlined as well.

2. Smooth Numbers and Their Applications to Cryptography
It is common knowledge that smooth numbers play an essential role in design an analysis of most of the algorithms for primality testing, integer factorisation and finding discrete logarithms. There are, however, several recently emerged applications of a very different spirit, which unfortunately are now so widely known as they deserve. In the first part I will give a necessary background on smooth numbers and present several classical and more recent results on smooth numbers as well as a brief introduction of underlying methods. In the second part, I will survey the aforementioned applications of smooth numbers to several cryptographic problems and also discuss some open questions.