We all use cryptography in our daily lives. The security of the most popular Public-Key Cryptosystems are based either on the hardness of factoring or the presumed intractability of the discrete logarithm problem. Advances on these problems or the construction of large quantum computers would dramatically change the landscape: Code-Based Cryptography is a powerful and promising alternative.
The objective of this course is to present the state of the art of these cryptosystems. This course covers the essentials that you should know about this hot topic in Cryptography and Coding Theory: the security-reduction proofs, the possible attacks, several proposals to reduce the key-size, etc.
Note that this is a subject close to research, and the field has evolved since the course's creation (2016). This evolution will continue. Everything that is said remains accurate and provides a good basis for anyone interested in the subject, but the gap with the state of the art is increasing over time.
The course offers video lectures and exercises.
This course is intended for undergraduate and Master’s degree students in mathematics or computer science.
Postgraduate students and researchers from the disciplines of computer algebra, coding theory and cryptography can also benefit from this course.
More widely, mathematicians, physicists or engineers interested in information and communication technologies and every person who wants to know more about cryptography, coding theory or code-based cryptography can be interested in this course.
Knowledge about linear algebra, finite field and complexity theory is required.
Evaluation et Certification
Plan de cours
Week 2: McEliece Cryptosystem
Week 3: Message Attacks (ISD)
Week 4: Key Attacks
Week 5: Other cryptographic constructions relying on coding theory