
CRYPTOGRAPHY
Second cycle degree in MATHEMATICS
Campus:
PADOVA
Language:
English
Teaching period:
First Semester
Lecturer:
ALESSANDRO LANGUASCO
Number of ECTS credits allocated:
6
Prerequisites:

The topics of the following courses: Algebra, Calculus. 
Examination methods:

Written exam 
Course unit contents:

First Part: Basic theoretical facts: Modular arithmetic. Prime numbers. Little Fermat theorem. Chinese remainder theorem. Finite fields: order of an element and primitive roots. Pseudoprimality tests. AgrawalKayalSaxena's test. RSA method: first description, attacks. Rabin's method and its connection with the integer factorization. Discrete logarithm methods. How to compute the discrete log in a finite field. Elementary factorization methods. Some remarks on Pomerance's quadratic sieve.
Second Part: Protocols and algorithms. Fundamental crypto algorithms. Symmetric methods (historical ones, DES, AES) . Asymmetric methods. Attacks. Digital signature. Pseudorandom generators (remarks). Key exchange, Key exchange in three steps, secret splitting, secret sharing, secret broadcasting, timestamping. Signatures with RSA and discrete log. 

