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Theory of cryptography

Degree course Electronic Engineering
Curriculum Curriculum unico
Learnings Orientamento unico
Academic Year 2018/2019
ECTS 6
Scientific Disciplinary Sector MAT/03
Year First year
Time unit Second semester
Class hours 48
Educational activity Related and integrative training activities

Single group

Professor VITTORIA BONANZINGA
Objectives
Knowledge of the basic notions of Algebra, Number Theory and Geometry which are essential in the development of cryptographic protocols. Knowledge of the tools and techniques of Algebra, number theory and geometry for the study of cryptographic protocols. Ability to understand and use appropriate mathematical tools for solving problems of cryptography. Ability to communicate the knowledge gained through scientific-technical language appropriate.
Programme - Integers and finite fields, modular arithmetic, Euler function, Chinese remainder theorem. Structu.re of Z/pZ. Gauss' theorem: the existence of primitive roots.

- Primality and factorization: Consequences of Fermat's little theorem, pseudoprimes numbers, some primality test (Fermat, Miller-Rabin), method (p-1) for the factorization of Pollard. Complexity of the algorithms.

- Symmetric cryptographic systems and public key cryptography: RSA. Diffie and Hellman cryptosystem. The discrete logarithm problem.

- Elliptic curves: Weierstrass equation, the group of points of an elliptic curve, elliptic curves over finite fields. Cryptosystems based on elliptic curves: exchange of key Diffie-Hellman, ElGamal protocol.

- -Factoring with elliptic curves, primality test with elliptic curves.
Books N. Koblitz. A Course in Number Theory and Cryptography, Second Edition, Springer, 1994.
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation Yes
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation No
Internship evaluation No
Evaluation in itinere No
Practice Test No
Professor GIOIA FAILLA
Objectives
Knowledge of the basic notions of Algebra, Number Theory and Geometry which are essential in the development of cryptographic protocols. Knowledge of the tools and techniques of Algebra, number theory and geometry for the study of cryptographic protocols. Ability to understand and use appropriate mathematical tools for solving problems of cryptography. Ability to communicate the knowledge gained through scientific-technical language appropriate.
Programme Recall on integers and finite fields, modular arithmetic, Euler function, Chinese theorem of the rest. Structure of Z / pZ. Gauss's theorem: existence of primitive roots.
- Primality and factorization: consequences of Fermat's Small Theorem, pseudoprime numbers, some primality tests (Fermat, Miller-Rabin), Pollard's (p-1) method for factorization. Overview of the complexity of the algorithms.
- Symmetric cryptographic systems and public key cryptography: RSA. Diffie and Hellman Cryptosystem. The problem of discrete logarithm.
- Elliptic curves: Weierstrass equation, group of points of an elliptic curve, elliptic curves on finite fields. Crittosystems based on elliptic curves: exchange of
keys of Diffie-Hellmann, protocol of ElGamal.
- Fitting with elliptic curves, primality test with elliptic curves.
Books 1.N. Koblitz. A Course in Number Theory and Cryptography, Second Edition, Springer, 1994.
2. A. Languasco, A. Zaccagnini. Introduzione alla Crittografia, Ulrico Hoepli Editore, Milano, 2004.
3. A. Languasco, A Zaccagnini, Manuale di Crittografia, 2015, Hoepli Informatica.
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation Yes
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation No
Internship evaluation No
Evaluation in itinere No
Practice Test No

Further information


Office hours list:

Description News
Office hours by: Vittoria Bonanzinga
Si avvisano gli studenti che per l'anno accademico 2018/2019 durante il I semestre il ricevimento per i corsi di Geometria, Teoria dei grafi e Teoria della Crittografia è fissato il giovedì mattina alle 10:00, si invitano gli studenti a contattare il docente per e-mail almeno il giorno prima per la conferma.
Office hours by: Gioia Failla
Il ricevimento è fissato il Venerdì dalle 9.30 alle 11 nello studio della docente (Blocco biennio, III piano). Per altri giorni contattare il docente per email
No news posted
No class timetable posted
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