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Theory of cryptography

Degree course Information and Communication Technologies (ICT) Engineering
Curriculum Curriculum unico
Learnings Orientamento unico
Academic Year 2016/2017
ECTS 6
Scientific Disciplinary Sector MAT/03
Year Third year
Time unit Second semester
Class hours 48
Educational activity Educational activities chosen by the student (art.10, paragraph 5, letter a)

Single group

Supplying course 1000275 Teoria della crittografia in Ingegneria Elettronica LM-29 BONANZINGA VITTORIA
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 1.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

Further information

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