UCL - Cryptography

[MAT2450]

[30h] 5 credits

This course is taught in the 2d semester.

Teacher(s): Jean-Jacques Quisquater

Language: French

Level: Second

Aims
Main themes
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Aims

To introduce the student to the basic techniques of mathematical cryptography.

Main themes

The course will be devoted to the study of cryptography, this corresponding algorithms, various examples and possible protocols, with each time a mathematically oriented approach. Historical aspects will also be considered.1. Information theory ; public and secret keys.2. Probabilistic algorithms and proofs in cryptography.3. Some cryptographic algorithms, like DES, RSA, El-Gamal, Diffle-Hellman, complexity analysis.4. Active and passive attitudes, false signatures.5. The zero-knowledge theory.6. Elliptic curves in cryptography.7. Norms, standards, precautions.8. Examples of cryptographic protocols.9. A detailed example of a formal proof in cryptography.10. Theoretical aspects.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

Precursorycourses Basic linear algebra, modular arithmetics.

Evaluation Oral exam.
Support A classical book on this subject : for example A. Menezes, P. Van Oorschot, S. Vanstone : Handbook of appled cryptography, CRC press, 1996 (disponible librement sur le WEB à http://www.cacr.math.uwaterloo.ca/hac/)S. Stinson, Cryptography, theory and practice, CRC Press, 2005 (3e édition).N. Koblitz, A course in number theory and cryptography, Springer-Verlag, Graduate Texts in Mathematics, 1994 (2e édition).