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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

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