# Abstract
In the realm of fully homomorphic encryption on the torus, we investigate the algebraic framework and manipulations essential for handling polynomials within cyclotomic rings characterized by prime power indices. This includes operations such as modulo reduction, scalar product and duality structures, computation of the trace operator, extraction, and the blind rotation integral to the bootstrapping procedure, all of which we reformulate within this mathematical framework.
# About the speakers
Mohammed Lemou is currently a Senior Researcher (Directeur de Recherche) at the French National Center for Scientific Research (CNRS). His research focuses on two main areas:
1/ Homomorphic Cryptography, with a particular emphasis on Fully Homomorphic Encryption (FHE) techniques and their applications.
2/ Mathematical Analysis, Modeling, and Numerical Approximation of PDEs, particularly in the study of particle interactions and stellar dynamics. This includes stability issues in kinetic models, asymptotic analysis, and numerical approximations of multiscale PDEs.
He is also interested in the interplay between machine learning and numerical methods for PDEs, as well as investigating the feasibility of leveraging FHE techniques for secure and privacy-preserving machine learning.
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