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Cryptography [ LMAT2450 ]

5.0 crédits ECTS  30.0 h   1q 

Teacher(s) Pereira Olivier ;
Language English
of the course
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.
Aims We introduce the fundamental concepts of modern cryptography, with a special attention given to the mathematical and algorithmic aspects. Historical problems and constructions are discussed, and will serve as a basis for the construction and discussion of today's most widely used algorithms. The following aspects are discussed: 1. Elements of information theory, perfect encryption 2. Probabilistic algorithms, computational security, attacker models, construction and use of proofs in cryptography 3. Symmetric encryption: security notions, basic constructions, DES, AES, cryptanalysis, operation modes 4. Authentication codes, hash functions 5. Asymmetric cryptography: Diffie-Hellman protocol, public-key encryption (RSA, El Gamal, ...), signature (RSA, hash-and-sign paradigm, DSS, ...), public key infrastructures 6. Elements of algorithmic number theory (primality testing, factoring, discrete logarithm extraction, ...), elliptic curve cryptography 7. Protocols: challenge-response, identification, authentication, zero-knowledge, GQ protocol 8. Main cryptographic standards, how they are built, and how to use them. The relative importance accorded to these aspects can vary from year to year.
Other information Prerequisites: Basic notions in linear algebra and modular arithmetic (bachelor level). Lectures in French, with all written materials in English Evaluation: Oral examination. References: The book by Jonathan Katz et Yehuda Lindell: Introduction to Modern Cryptography (Chapman & Hall/CRC Press, 2007) can be used as support for most of the topics covered in this class. Other useful references: - N. Koblitz: A course in number theory and cryptography, Springer-Verlag, Graduate Texts in Mathematics, 1994 (2nd edition) - W. Mao: Modern Cryptography - Theory and Practice, Prentice Hall PTR, 2003 - A. Menezes, P. Van Oorschot, S. Vanstone: Handbook of applied cryptography (CRC press, 1996) (freely available from ) - S. Stinson: Cryptography, theory and practice, CRC Press, 2005 (3rd edition)
Cycle et année
> Master [120] in Mathematics
> Master [60] in Mathematics
> Master [120] in Mathematical Engineering
> Master [120] in Computer Science and Engineering
> Master [120] in Computer Science
> Master [120] in Electrical Engineering
> Master [120] in Electro-mechanical Engineering
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