Politecnico di Torino
Politecnico di Torino
Politecnico di Torino
Anno Accademico 2007/08
Curve ellittiche e crittografia
Dottorato di ricerca in Ingegneria Elettronica E Delle Comunicazioni - Torino
Docente Qualifica Settore Lez Es Lab Tut Anni incarico
Elia Michele ORARIO RICEVIMENTO     20 0 0 0 2
SSD CFU Attivita' formative Ambiti disciplinari
*** N/A ***    
Obiettivi dell'insegnamento
This course is an introduction to elliptic curves over finite fields and their arithmetic properties that relevant in their cryptographic applications. The aspects of computational complexity are analyzed in some details as they are the main choice criterion of encryption schemes.
The presentation is set in the historical perspective of the development of elliptic functions which were discovered by an Italian mathematician and brilliantly extended by Euler.
1. Elliptic Function, Abelian integrals, and Elliptic curves.
2. Elliptic curves over Q and Diophantine Equations.
3. Structure and properties of the additive point group of an elliptic curve.
4. Elliptic curves over finite fields.
5. Structure of the additive point group of an elliptic curve over finite fields.
6. Iterated sums and duplications over elliptic curves in both affine and homogeneous co-ordinates, and related complexity.
7. Discrete logarithm over elliptic curves.
8. Diffie-Hellman and El Gamal public-key cryptographic schemes via elliptic curves
9. Computational complexity
10. Arithmetical complexity of sums, multiplications, and powers of elements in finite fields.
11. Arithmetical complexity of point sums, duplications, and 'powers' on elliptic curves over finite fields.
12. Good choices of elliptic curves for cryptographic applications.
13. Public and secret parameters. Comparison with classic public-key systems.
14. Elliptic curves and factoring.
Orario delle lezioni
Statistiche superamento esami

Programma definitivo per l'A.A.2007/08

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