Mathematical Cryptology

Code:

M4004

Acronym:

M4004

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - 1S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ENM	6	Official Study Plan since 2013-2014	1	-	6	56	162
			2

Teaching language

Portuguese and english

Objectives

Upon completion of this curricular unit, the student should:

— master the concepts, methods and results presented, on cryptography and on cryptanalysis, and some of its applications;
— be able to analyze and solve problems of Cryptology, using the methods and results that best apply to the problem under study;
— have adequate preparation to conduct studies and research in areas of mathematics that integrate or use Cryptology;
— be able to communicate, in an efficient manner, his or hers own solutions to problems, and the various topics lectured.

Learning outcomes and competences

Described in the objectives.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

To have had introductory courses on both Algebra and on Number Theory at the undergraduate level.

Program

Some classic ciphers and their cryptanalysis.

Detailed description of DES and AES. Differential cryptanalysis.

Public Key Encryption: Diffie-Hellman protocol, RSA, ElGamal.

Some attacks on the RSA cipher, namely the Wiener attack. Factoring algorithms: Fermat, Kraitchik, continuous fractions.

A brief introduction to elliptic curves and their cryptographic uses.

Mandatory literature

Menezes Alfred J.; Handbook of applied cryptography. ISBN: 0-8493-8523-7

Complementary Bibliography

Kahn David 1930-; The codebreakers. ISBN: 0-684-83130-9
Shemanske Thomas R. 1952-; Modern cryptography and elliptic curves. ISBN: 978-1-4704-3582-0
Martin Keith M.; Everyday cryptography. ISBN: 978-0-19-969559-1

Comments from the literature

Articles and other documents available on this page, in the "Documents" folder.

Teaching methods and learning activities

Lectures, problem sessions; student presentations.

keywords

Physical sciences > Mathematics > Algorithms

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	60,00
Trabalho prático ou de projeto	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	96,00
Frequência das aulas	56,00
Trabalho escrito	10,00
Total:	162,00

Eligibility for exams

Timely delivery of written assignments.

Calculation formula of final grade

The final classification is the weighted average of the practical work (40%) and the two tests (30% each).