# Elementi di Crittografia

This is an intensive
course to be given in Siena, Italy, January 17-21, 2000.

Introduction; One-way and trapdoor functions; Pseudorandom generators;
Pseudorandom function generators; Private-key encryption; Public-key
encryption; Signatures; Authentication.
### Schedule of Lectures

- [Jan 17] Introduction, definition of one-way and
trapdoor functions. Review of probability and number theory

- [Jan 18] Candidate one way and trapdoor functions:
exponentiation, RSA, Rabin's function.
Hard core bit of a one-way function, quadratic residuosity
Goldreich-Levin theorem

- [Jan 19] Trapdoor predicates. Private-key encryption: definitions
and constructions (Goldwasser-Micali, Blum-Goldwasser,
Bellare-Roghaway)

- [Jan 20] Pseudorandom generators, pseudorandom functions,
pseudorandom permutations, private-key encryption.
- [Jan 21] Authentication and signatures.

## Textbooks and other suggested readings

The main reference for the course are the following
sets of lecture notes.

More advanced treatments are in

Any undergraduate book on algebra will be good as a reference on
modular arithmetic and elementary number theory. A good one for
computer scientists is

- L.N. Childs.
*A Concrete Introduction to Higher Algebra*,
Second Edition, Springer, 1995.

This page has been accessed times
since December 13, 1999.

luca@cs.columbia.edu