# Cryptography and Computer Security

Universidad Carlos III de Madrid

## Course Description

• ### Course Name

Cryptography and Computer Security

• ### Host University

Universidad Carlos III de Madrid

• ### Location

Madrid, Spain

• ### Area of Study

Computer Engineering, Computer Science

• ### Language Level

Taught In English

• ### Prerequisites

STUDENTS ARE EXPECTED TO HAVE COMPLETED:

Programming
Statistics
Discrete Mathematics

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

6
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4
• ### Overview

Cryptography and computer security (218 - 15973)
Study: Bachelor in Informatics Engineering
Semester 2/Spring Semester
2nd Year Course/Lower Division

Students are expected to have completed:

Programming
Statistics
Discrete Mathematics

Compentences and Skills that will be Acquired and Learning Results:

The objectives of this course are to make the student aware of the current importance of computer security and to show the vulnerabilities and threats the technology involved faces. Thus, the student will learn the principles and methods used by security systems. In order to achieve these goals, the student must acquire specific knowledge, capacities and attitudes.

Regarding knowledge, at the end of the course the student will be able to:
- Know mathematical fundaments of cryptography and cryptanalysis, especially those related to number theory.
- Master cryptosystems and main encryption algorithms.
- Master digital signature schemes based on public key cryptography.
- Understand the key management problem and main proposed solutions.
- Understand the principles of security measures, focusing on cryptographic systems and protocols, their methods and means.
- Know main authentication systems; acknowledge their advantages and disadvantages
- Distinguish the different security objectives

The capacities the student will acquire can be divided in specific and generic:

Specific capacities:
- Solve number theory problems related to cryptography (P.O.: a)
- Acknowledge the advantages and disadvantages of secret and public key cryptographic systems. (P.O.: a, c)
- Sign and verify in different environments, identifying possible attacks. (P.O.: a, c)
- Design and implementation of the appropriate security mechanisms (mainly cryptographic) for specific information systems (P.O.: a, c, e)
- Apply appropriate authentication mechanisms to different information systems (P.O.: a, c, e)

General capacities:
- Search relevant information to solve a particular problem (P.O.: a, b)
- Solve particular problems with multidisciplinary knowledge (P.O.: a, c, e, g)
- Analyze specific systems to identify vulnerabilities and threats (P.O.: a, b)

Regarding attitudes, the student will be encouraged to:
- Adopt a critical view of the security provided by a particular system (P.O.: i)
- Distrust the purported security of information systems and cryptographic protocols deployed in them. (P.O.: i)

Regarding basic capacities detailed in the third article of the RD 1393/2007 modified by the RD 861/2010, this subject considers capacity CB1.

Regarding capacities specified in section 5 of Annex II of Resolución del 8 de junio de 2009, by the Secretaría General de Universidades (BOE of August 4th of 2009), this subject considers capacity CGB3.

Description of Contents: Course Description

1. Mathematical background
1.1. Number theory
1.2. Modular arithmetic
1.3. Computation of multiplicative inverses
1.4. Discrete logarithm
1.5. Galois fields
2. Cryptography
2.1. Introduction
2.2. Classic encryption methods and cryptanalysis
2.3. Symmetric cryptosystems.
2.4. Hash functions and MAC
2.5. Asymmetric cryptosystems.
2.6. Key generation and distribution.
2.7. Digital signature.
2.8. Public Key Infrastructure
3. User authentication
4. Introduction to information security
4.1. Threats and vulnerabilities
4.2. Security measures and mechanisms

Learning Activities and Methodology:

The teaching methodology includes:

(1) Lectures (2 ECTS). Teachers will present the theoretic concepts. It is expected that students participate actively in the lectures. Basic documentation (lecture notes, bibliography, and complementary documentation) will be accessible to students through the web-based learning platform. Students have to read and study the basic documentation (student work). (P.O.: a, c, g, i)
(2) Problem solving (2 ECTS). Students, guided by teachers, will solve a set of representative problems during problem sessions in order to apply the theoretic concepts. Students will solve additional problems outside the regular problem sessions (student work). (P.O.: a, c, g, i)
(3) Laboratory assignments (2 ECTS). Students will learn main defensive practical cryptographic tools. Instructions will be published in advance. Students will attend laboratory sessions where teachers will support students in the development of the laboratory assignment. Students will complete the laboratory assignments outside the regular laboratory sessions (student work). (P.O.: a, b, c, e, g, i)

Assessment System:

Assessment will consider:
1) Hand in of laboratory assignment results and tests: 40% (P.O.: a, b, c, e, g, i)

2) Exams regarding theory and problems: 60% (P.O.: a, c, g, i)
2.1) Exam 1 and 2 of continuous assessment: 20%
2.1.a) Exam 1 (continuous assessment). Mathematical background
2.1.b) Exam 2 (continuous assessment). Classical cryptography, cryptanalysis and symmetric encryption
The grade will be calculated as the sum of the grades of all continuous assessment exams.
2.2) Final exam (mandatory). Theory questions and problems: 40%. A minimum grade will be required to pass the course.

Basic Bibliography:

A. MENEZES. HANDBOOK OF APPLIED CRYPTOGRAPHY. CRC PRESS.
A.I. González-Tablas Ferreres y P. Martín González. Problem Book 2010-2015. Final Exam problem collection. Cryptography and Computer Security.. CopyRed. 2016
J. PASTOR; M.A. SARASA; J.L. SALAZAR. CRIPTOGRAFÍA DIGITAL. FUNDAMENTOS Y APLICACIONES. (2 EDICIÓN). PRENSAS UNIVERSITARIAS DE ZARAGOZA.
W. STALLINGS. CRYPTOGRAPHY AND NETWORK SECURITY. (5 EDICIÓN). PRENTICE HALL.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

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