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Master Mathťmatiques et Applications, Cryptographie

The Master Mathťmatiques et Applications, Cryptographie is delivered by the UFR Mathťmatiques of the Universitť de Rennes.

Program Details

• ECTS: 120
• Duration: 2 years, full-time, starting from Bac +3
• Program Director: Sylvain Duquesne
• Location: Rennes

Presentation

This master's program trains mathematical engineer-experts to become experts in protecting digital information. It is aimed at students who have validated a license in mathematics and those who wish to develop skills related to the rapid evolution of information domains (cryptography, error correction) involving a growing share of mathematics.

Competences Acquired

• Knowledge in symmetric, asymmetric, post-quantum cryptography, cryptanalysis, and hidden channel attacks
• Mastery of complex mathematics for implementation in various fields (mobile phones, wireless networks, internet transactions, generalized use of smart cards for securing commercial transactions, biometric identification techniques, remote identification)
• Double competence in mathematics and computer science to enable students to work in the fields of information security, computer security, and development of secure software
• Ability to adapt to new problems or attacks, as well as to new environments

Target Audience

This program is designed for students who hold a license (or equivalent) in mathematics. When applying, students should provide details of their relevant experiences in the field, in their letter of motivation and CV.

Internships

Students in the Master Mathťmatiques et Applications, Cryptographie program must complete two internships during their course:

• An optional internship of 2 to 3 months in the first year, starting from mid-May
• A mandatory internship of 6 months in the second year, starting from early March These internships can be carried out in a company or research laboratory.

Course Program

The course program includes the following courses:

Master 1

Semester 1

• Algebra basics 5 ECTS
• Basic algorithmics 5 ECTS
• English 3 ECTS
• Low-level programming 5 ECTS
• Software formal analysis and design 5 ECTS
• Probability and statistics tools for mathematical engineering and artificial intelligence 5 ECTS
• Information theory 2 ECTS

Semester 2

• Error-correcting codes 5 ECTS
• Complements in cryptography 2 ECTS
• Complexity 3 ECTS
• Cryptography 5 ECTS
• Network security 5 ECTS
• R&D project 5 ECTS
  • Choose one of the following three courses:
    • Commutative algebra and algebraic geometry 5 ECTS
    • Statistical learning 5 ECTS
    • Number theory 5 ECTS

Master 2

Semester 3

• Elliptic curves for cryptography 5 ECTS
• Cryptanalysis 3 ECTS
• Java 3 ECTS
• Secured implementations for cryptography 3 ECTS
• Advanced network security 3 ECTS
• Euclidean networks in cryptography 4 ECTS
• Security proofs 3 ECTS
  • Choose two of the following six courses:
    • Blockchain 3 ECTS
    • C++, complements 3 ECTS
    • C++, basics 3 ECTS
    • Law and cybersecurity 3 ECTS
    • Parallel programming, GPU 3 ECTS
    • Protocol security 3 ECTS

Semester 4

• Error-correcting codes in cryptography 3 ECTS
• Quantum cryptography 3 ECTS
• English 3 ECTS
• Internship 18 ECTS
• Algorithmic number theory for cryptography 3 ECTS

Career Opportunities

Due to the importance of digital exchanges, cryptography is a rapidly growing field. The Master's program provides a double competence in mathematics and computer science, which is rare in the current job market. Graduates can apply for positions such as:

• Research and Development Engineer in information security
• Specialist Engineer in computer security
• Developer of secure software

The CyberSchool also has strong links with research, facilitating further studies towards a doctorate.

Partnerships

This Master's program is part of a partnership between the Institut de Mathťmatiques de Rennes (IRMAR) and the Laboratoire de Cryptographie de la Direction Gťnťrale de l'Armement (DGA), which is responsible for designing government cryptographic algorithms. There are also links with the IRISA (Institut de Recherche en Informatique et SystŤmes Alťatoires) teams involved in cryptography research.

Label SecNumedu

The program benefits from the SecNumedu label awarded by the ANSSI. This label guarantees the relevance of the training in relation to its objectives.