Cryptography

Credits
6
Types
  • GRAU: Elective
  • GCED: Elective
Requirements
This subject has not requirements , but it has got previous capacities
Department
MAT
The course aims to introduce modern techniques related to confidenciability, integrity, authenticity and non-repudiation of information.

The subject is suitable for students of all majors and is focused on 4th year students, with the minimum requirement having passed all the compulsory subjects or having passed 150 ECTS.

Teachers

Person in charge

Others

Weekly hours

Theory
2
Problems
0
Laboratory
2
Guided learning
0
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 [Avaluable] - 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
    Theory
    0h
    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
    Theory
    0h
    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
    0h
    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
    0h
    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

    Key distribution and digital signatures


    Objectives: 2 3 4 5
    Contents:
    Theory
    0h
    Problems
    0h
    Laboratory
    4h
    Guided learning
    0h
    Autonomous learning
    6h

    Cryptographic system


    Objectives: 2 3 4 5
    Contents:
    Theory
    0h
    Problems
    0h
    Laboratory
    1h
    Guided learning
    0h
    Autonomous learning
    0h

    Openssl/TLS


    Objectives: 3 4 5
    Contents:
    Theory
    0h
    Problems
    0h
    Laboratory
    2h
    Guided learning
    0h
    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