Elements of Cryptography

Code: MAT14348M

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Presentation

Cryptography is a fundamental element of data security. In this CU we study the most commonly used encryption algorithms to transform data into ciphertext.

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

Knowledge: having contact with the main objects in cryptography and experiencing problems in this context, applying general algebraic techniques and creating strategies that are specific to each problem; exploring applications of cryptography in other fields.
Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems.

Integers.
Congruence and residue rings.
Little Fermat theorem. Chinese remainder theorem. Encryption function.
Probabilities.
DES.
Public-key encryption.
Discrete logarithms.
Hash functions.
Digital signatures.
Finite fields.
Elliptic curves.

Teaching Methods

Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through two or three oral presentations, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final mark.