# Cryptography (C)

Credits Dept.
7.5 (6.0 ECTS) MAT

## Instructors

 Person in charge: (-) Others: (-)

## General goals

Upon finishing this subject, students should:
-  Be familiar with the basic principles (especially those related to public key cryptography) underlying the most important techniques in cryptography: symmetrical and asymmetrical coding-decoding and the digital signature.
-  Understand the most important algorithms behind each of the relevant techniques, especially those used in the most commonly-accepted standards.
-  Be familiar with some of the applications of cryptography.

## Specific goals

### Knowledges

1. Secret key cryptography. Flow and block encryption. DES and AES.
2. Public key cryptography. The integer factorising problem.

The discrete logarithm problem.
3. Digital signatures.
4. Cryptography protocols.

### Abilities

1. Characteristics of secret key algorithms. Extracting the general characteristics of a given secret key algorithm. Understand and programme a given public key algorithm.
2. Characteristics of public key algorithms. Knowing how to classify a digital signature algorithm depending on the problem it is based on. Understanding and programming a given public key algorithm.
3. Knowing how to classify a digital signature algorithm depending on the problem it is based on. Understanding and programming a given public key algorithm.
4. Understanding the workings of a given cryptographic protocol and finding its strengths and weaknesses.
5. Telling the difference between sound cryptography and "snake-oil".

### Competences

1. Critical, logical-mathematical reasoning.
2. Ability to create and use models of reality.
3. Ability to design and carry out experiments and analyse the results.
4. Ability to design a test to check the validity of the response after being given the answer.

## Contents

Estimated time (hours):

 T P L Alt Ext. L Stu A. time Theory Problems Laboratory Other activities External Laboratory Study Additional time

1. Basic concepts
T      P      L      Alt    Ext. L Stu    A. time Total
3,0 0 0 0 0 3,0 0 6,0
- 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
T      P      L      Alt    Ext. L Stu    A. time Total
9,0 0 12,0 0 12,0 9,0 0 42,0

- Block encryption, flow encryption.

- The Data Encryption Standard: Description, History, Standardisation, Cryptanalysis.

- The Advanced Encryption Standard: Description, Standardisation.

- Operation modes for block-encrypted systems.

3. Public key encryption systems
T      P      L      Alt    Ext. L Stu    A. time Total
18,0 0 12,0 0 12,0 18,0 0 60,0
- 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 and the outlook in this field.

- Concepts behind the unidirectional trap-door function.

- Power function trap-door.

- Discrete exponential function and the discrete algorithm problem. Finite body variants.

- The knapsack problem.

- RSA cryptosystem (Rivest, Shamir, Adleman).

- ElGamal cryptosystem.

- Diffie-Hellman system for distributing keys.

- Knapsack cryptosystem. Shamir"s cryptanalysis.

4. Digital signatures
T      P      L      Alt    Ext. L Stu    A. time Total
3,0 0 4,0 0 4,0 3,0 0 14,0

- Cryptographic hash functions. Secure Hash Standard.

- Digital signatures: RSA and DSA

- Public key certificates.

- Certifying authorities.

- PKI

5. Cryptographic protocols
T      P      L      Alt    Ext. L Stu    A. time Total
12,0 0 2,0 0 2,0 12,0 0 28,0

- Encryption and decryption transformations. Mixed private key - public key techniques.

- Identification schemes and protocols.

- SSL.

- SET.

- Micro-payments.

- Shared secrets.

- Electronic voting.

- Watermarks.

Others aspects of cryptography:

- Standardisations. Bodies involved.

- Patents.

- Policy aspects. Government control.

- The Telecommunications Act.

- The Digital Signature Act.

- International Laws.

 Total per kind T P L Alt Ext. L Stu A. time Total 45,0 0 30,0 0 30,0 45,0 0 150,0 Avaluation additional hours 0 Total work hours for student 150,0

## Docent Methodolgy

Theory classes and exercises.

The nature of the theme under consideration will determine the scheduling of problems and theory.

Lab classes will consolidate students" knowledge.

## Evaluation Methodgy

* Lab exercise (4 points).

* Final exam (6 points).

## Basic Bibliography

• José Pastor Franco, Miguel Ángel Sarasa López, José Luis Salazar Riaño Criptografía digital: fundamentos y aplicaciones, Publicaciones Universitarias Universidad de Zaragoza, 2001.
• Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone Handbook of applied cryptography, CRC Press,, 1997.
• Mollin, Richard A. RSA and public-key cryptography, Chapman & Hall/CRC , 2003.
• William Stallings Cryptography and network security: principles and practice, Prentice Hall, 2010.
• PAAR, Christof , PRENEEL, Bart Understanding Cryptography, Springer, 2010.

## Complementary Bibliography

• Ross Anderson Security Engineering, Wiley (http://www.cl.cam.ac.uk/~rja14/book.html), .
• Gustavus J. Simmons, [editors] Contemporary cryptology : the science of information integrity, IEEE Press, 1992.
• Douglas R. Stinson Cryptography : theory and practice, Chapman & Hall / CRC, 2002.
• Katzenbeisser, S., Petitcolas, F.A.P. Information hiding techniques for steganography and digital watermaking, Artech House, 2000.
• Rolf Oppliger Security technologies for the World Wide Web, Artech House, 2003.
• Ingemar J. Cox, Matthew L. Miller, Jeffrey A. Bloom Digital watermarking, Morgan Kaufmann, 2002.
• O'Mahony, D., Peirce, M., Tewari, H. Electronic Payment Systems for E-commerce, Artech House, 2001.
• Salomaa, A. Public-key Cryptography, Springer-Verlag, 1990.
• Neal Koblitz Algebraic aspects of cryptography, Springer,, 1998.
• Koblitz, N. A A course in Number Theory and Cryptography , Springer-Verlag, 1994.
• Ian Blake, Gadiel Seroussi & Nigel Smart Elliptic curves in cryptography, Cambridge University Press, 1999.
• Manuel José Lucena López Criptografía y seguridad en computadores, , 2003.
• Jorge Ramió Aguirre Aplicaciones criptográficas : libro guía de la asignatura de Seguridad Informática, Escuela Universitaria de Informática. Universidad Politécnica de Madrid, 1998.
• Song Y. Yan Number theory for computing, Springer, 2002.
• BALDONI, M.W., CILIBERTO, C., PIACENTINI CATTANEO, G.M. Elementary Number Theory, Cryptography and Codes, Springer, 2009.
• VAUDENAY, Serge A classical Introduction to Cryptography, Springer, 2006.
• DELFS, Hans; KNEBL, Helmut Introduction to Cryptography, Springer, 2007.
• Bruce Schneier Applied cryptography : protocols, algorithms, and source code in C, John Wiley & Sons, 1996.

1. http://www-ma2.upc.es/~cripto

## Previous capacities

Students are recommended to take this course a few terms before completing the Selection Stage.

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