Algebraic Methods in Cryptography

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/02 Algebra.

Examination method

Oral exam.

Learning
objectives

The course aims to present some of the main cryptographic systems that are historically important or currently in use, with particular regard to the role played in the construction of such systems by algebraic tools such as modular arithmetic, the theory of finite fields and the algebraic aspects of the theory of elliptic curves.

Syllabus

The Euclidean algorithm (successive divisions), time estimates. Time estimates for operations in the set of integers modulo m. Symmetric cryptosystems. Finite fields and their order. Public-key ciphers. Use of finite fields in cryptography. The RSA system. Elliptic curve cryptosystems. Solovay-Strassen and Miller-Rabin primality tests and pseudoprimality; the ECPP primality test.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

know and understand the algebraic methods and cryptographic systems covered;
are able to apply the knowledge acquired to solving concrete examples;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, clarity of presentation, rigour in the use of language, confidence in using the notions acquired.

Algebraic Methods in Cryptography