Cryptography

Credits
6
Types
Elective
Requirements
This subject has not requirements
Department
MAT
The course aims to introduce modern techniques related to confidenciability, integrity, authenticity and non-repudiation of information.

Teachers

Person in charge

  • Fernando Martínez Sáez ( )

Others

  • Anna Rio Doval ( )
  • Jose Luis Ruiz Muñoz ( )

Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0.4
Autonomous learning
6

Competences

Technical Competences

Common technical competencies

  • CT1 - To demonstrate knowledge and comprehension of essential facts, concepts, principles and theories related to informatics and their disciplines of reference.
    • CT1.2A - To interpret, select and value concepts, theories, uses and technological developments related to computer science and its application derived from the needed fundamentals of mathematics, statistics and physics. Capacity to solve the mathematical problems presented in engineering. Talent to apply the knowledge about: algebra, differential and integral calculus and numeric methods; statistics and optimization.
    • CT1.2C - To use properly theories, procedures and tools in the professional development of the informatics engineering in all its fields (specification, design, implementation, deployment and products evaluation) demonstrating the comprehension of the adopted compromises in the design decisions.

Technical Competences of each Specialization

Information technology specialization

  • CTI2 - To guarantee that the ICT systems of an organization operate adequately, are secure and adequately installed, documented, personalized, maintained, updated and substituted, and the people of the organization receive a correct ICT support.
    • CTI2.3 - To demonstrate comprehension, apply and manage the reliability and security of the computer systems (CEI C6).
  • CTI3 - To design solutions which integrate hardware, software and communication technologies (and capacity to develop specific solutions of systems software) for distributed systems and ubiquitous computation devices.
    • CTI3.1 - To conceive systems, applications and services based on network technologies, taking into account Internet, web, electronic commerce, multimedia, interactive services and ubiquitous computation.

Computer engineering specialization

  • CEC4 - To design, deploy, administrate and manage computer networks, and manage the guarantee and security of computer systems.
    • CEC4.2 - To demonstrate comprehension, to apply and manage the guarantee and security of computer systems.

Transversal Competences

Reasoning

  • G9 - Capacity of critical, logical and mathematical reasoning. Capacity to solve problems in her study area. Abstraction capacity: capacity to create and use models that reflect real situations. Capacity to design and perform simple experiments and analyse and interpret its results. Analysis, synthesis and evaluation capacity.
    • G9.1 - Critical, logical and mathematical reasoning capacity. Capacity to understand abstraction and use it properly.

Objectives

  1. Distinguish between cryptosystems that can be safe and those that are snake oil.
    Related competences: CTI3.1, G9.1, CT1.2A, CT1.2C, G3.1, CEC4.2, CTI2.3,
  2. Distinguish between public-key and secret-key cryptosystems
    Related competences: CTI3.1, G9.1, CT1.2A, CT1.2C, G3.1, CEC4.2, CTI2.3,
  3. To understand the main ideas of secret-key cryptosystems.
    Related competences: CTI3.1, G9.1, CT1.2A, CT1.2C, G3.1, CEC4.2, CTI2.3,
  4. To understand the main ideas of public-key cryptosystems
    Related competences: CTI3.1, G9.1, CT1.2A, CT1.2C, G3.1, CEC4.2, CTI2.3,
    Subcompetences:
    • Integer factorization problem.
    • Discrete logarithm problem in elliptic curves.
    • Discrete logarithm problem in a finite field.

  5. To understand the idea of digital signature and their role nowadays in internet.
    Related competences: CTI3.1, G9.1, CT1.2A, CT1.2C, G3.1, CEC4.2, CTI2.3,

Contents

  1. Basic concepts
    Cryptology, Cryptography, and Cryptanalysis.
    Classic cryptography and modern cryptography.
    Basic techniques: encryption-decryption and signature.
    Private key cryptography and public key cryptography.
    The mathematical bases of cryptography.
  2. Modern secret key techniques
    Block encryption, Stream ciphers.
    Data Encryption Standard: Description, History, Standardisation, Cryptanalysis.
    Advanced Encryption Standard: Description, Standardisation.
    Operation modes for block-encrypted systems.
  3. Public key encryption
    Multi-precision arithmetic operations. Euclidean algorithms.
    Congruences, multiplication group, modular arithmetic, modular exponential, Chinese Remainder Theorem.
    Calculation of square roots.
    Prime numbers, probabilistic criteria of primeness, random generation of prime numbers.
    Factorising integers, current state of the problem.
    The discrete algorithm problem: variants over Finite Fields and elliptic curves.
    RSA cryptosystem (Rivest, Shamir, Adleman).
    ElGamal cryptosystem.
    Diffie-Hellman key exchange.
  4. Digital signatures
    Cryptographic hash functions. Secure Hash Standard.
    Digital signatures: RSA, DSA and ECDSA
    PKI: digital certificates X509, CRL and OCSP.
  5. Cryptographic protocols and standars
    Encryption and decryption transformations. Mixed private key - public key techniques.
    Identification schemes and protocols.
    SSL.
    Micro-payments.
    Shared secrets.
    Electronic voting.
    Watermarks.
    SMIME.
    PKCS...
  6. New trens in Cryptography
    Lattice-Based Public-Key Cryptography. Hyperelliptic curve cryptography. Quantum Cryptography

Activities

Activity Evaluation act


Introduction


Objectives: 2 1
Theory
2h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
2h

secrect-key cryptography


Objectives: 2 1 3
Contents:
Theory
6h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
12h

Secrect-cryptography test


Objectives: 2 1 3
Week: 7
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

public-key cryptography


Objectives: 2 1 4
Contents:
Theory
12h
Problems
0h
Laboratory
8h
Guided learning
0h
Autonomous learning
30h

Digital signature


Objectives: 5
Theory
4h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

Protocols and cryptographic standars


Objectives: 1
Contents:
Theory
3h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
16h

public-key test


Objectives: 2 1 4 5
Week: 14
Type: theory exam
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

New trends in cryptography


Objectives: 2 1
Contents:
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
4h

eDNI

Sol.licitar els certificats digitals del eDNI. http://www.dnielectronico.es/
Objectives: 2 5
Contents:
Theory
0h
Problems
0h
Laboratory
1h
Guided learning
2h
Autonomous learning
1h

secure email

Xifrar/desxifrar, signar/verificar signatures missatges de correu electrònic.
Objectives: 2 1 3 4 5
Contents:
Theory
0h
Problems
0h
Laboratory
2h
Guided learning
2h
Autonomous learning
1h

Cryptographic hash functions


Objectives: 5
Contents:
Theory
0h
Problems
0h
Laboratory
1h
Guided learning
0h
Autonomous learning
2h

AES


Objectives: 2 1 3
Contents:
Theory
0h
Problems
0h
Laboratory
5h
Guided learning
0h
Autonomous learning
6h

Theory
0h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
6h

Theory
0h
Problems
0h
Laboratory
1h
Guided learning
0h
Autonomous learning
0h

Theory
0h
Problems
0h
Laboratory
2h
Guided learning
2h
Autonomous learning
6h

Teaching methodology

Lectures in which the contents of the subject will be exposed. Lab classes where students solve real situations that can be found in practice.

Evaluation methodology

There will be two tests in which the total content corresponding to Secret Key Cryptography has a weight of 20% of the final grade and the total content corresponding to Public Key Cryptography has a weight of 40% of the final grade. These two tests may be replaced by a final examination.

The other 40% of the grade will correspond to the laboratory.

Bibliography

Basic:

Complementary: