Maths for Security

Course description

In this course, several notions of mathematics are required to understand encryption algorithms and primitive cryptographic attacks.

The first part of this course is a reminder of linear algebra based on linear equations system resolution.

The second and major part reports on probabilities and statistics, with a reminder of elementary notions on probabilities (independent event, conditional probabilities, expectation) and statistics (variance, standard deviation) as well as Markov chains and the law of large numbers.

The last part of the course will be devoted to modular arithmetic basis (elementary operation, modular inversion) to enable RSA algorithm.

Course content

Matrix inversion, modular arithmetic, conditional probability, expectancy, law of large numbers.


Linear Algebra, Probabilities, Statistics, Arithmetic, Proof.


  • Mathematics for Computer Science, by Eric Lehman, F Thomson Leighton, Albert R Meyer, 2010


Patrick Derbez is an Associate Professor at the University of Rennes 1. He is a recognised authority in the field of symmetrical cryptography. He is notably the author of several famous attacks on AES, the standard for symmetrical encryption. He has been a member of the ToSC programme committee since 2016 and has participated in numerous conferences and workshops. He was recently named to the GSMA Hall of Fame for his work on GEA-1 and GEA-2 encryption algorithms used to secure non-verbal communications in 2G/2G+. He also received a Best Paper Award for his article on boomerang attacks published in ToSC 2020-4.

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