Cryptography [ LMAT2450 ]
5.0 crédits ECTS
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Pereira Olivier ;
of the course
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.
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.
Prerequisites: Basic notions in linear algebra and modular arithmetic (bachelor level).
Lectures in French, with all written materials in English
Evaluation: Oral examination.
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)
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