CRYPTOGRAPHY FOUNDATION

Anno accademico
2019/2020 Programmi anni precedenti
Titolo corso in inglese
CRYPTOGRAPHY FOUNDATION
Codice insegnamento
CM0525 (AF:306555 AR:166122)
Modalità
In presenza
Crediti formativi universitari
6
Livello laurea
Laurea magistrale (DM270)
Settore scientifico disciplinare
INF/01
Periodo
II Semestre
Anno corso
1
Sede
VENEZIA
In questo corso si forniranno basi matematiche e relative applicazioni pratiche della crittografia matematica.
Gli studenti alla fine del corso dovrebbero avere acquisito le tecniche matematiche fondamentali della crittografia matematica.
Basi di Matematica Discreta
1. What is a group. Cryptography in a Group. Polynomial and Exponential Time.

2. Arithmetics of Integers: Division and Ideals. GCD. Complexity of Euclidean algorithm. GCD and Matrices. Modular Arithmetics: Fermat, Wilson and Euler. Chinese remainder Theorem.

3. The Fast Powering Algorithm. The Discrete Logarithm Problem (DLP). Shanks's Babystep-Giantstep Algorithm. Pohlig-Hellman Algorithm. The Elgamal Public Key Cryptosystem.

4. Solovay-Strassen Probabilistic Test of Primality. Polynomial Deterministic Test of Primality: The AKS algorithm. Probabilistic encryption and the Goldwasser-Micali cryptosystem.

5. The geometry of cubics. Weierstrass Normal Form of cubic curves. Singular cubics. Elliptic curves. The group operation. Algorithm for the group law in an elliptic curve. Elliptic curves on rational numbers Q, real numbers R, complex numbers C and finite fields.

6. Diffie-Hellman Key Exchange (DHP) and The Elgamal Public Key Cryptosystem over Elliptic Curves. The elliptic curve discrete logarithm problem (ECDLP).

7. Factorisation Algorithms: Pollard Algorithm. Lenstra's elliptic curve factorization algorithm. Factorization via difference of squares (Fermat and beyond). Pomerance Quadratic Sieve. Number Field Sieve.
A. Salibra. Slides del corso. 2018.
M.W. Baldoni, C. Ciliberto, G.M. Piacentini Cattaneo: Elementary Number Theory, Cryptography and Codes, Springer-Verlag, 2009.
J.H. Silverman, J. T. Tate: Rational Points on Elliptic Curves, Springer-Verlag, 2015.
J. Hoffstein, J. Pipher, J. H. Silverman: An Introduction to Mathematical Cryptography, Springer-Verlag, 2008.

Esercizi e compiti in classe
Svolgimento del corso con l'ausilio della lavagna luminosa e tradizionale.
Inglese
orale
Programma definitivo.
Data ultima modifica programma: 27/03/2019