Je tiens tout d'abord à remercier mon directeur de thèse Benoît Libert, qui m'a accompagné durant toute la durée de ma thèse et m'a gratifié de sa présence et de sa disponibilité tout au long de cette aventure. Je le remercie aussi de son support lors des phases de soumissions, des possibles \textit{rebuttals} qui s'en suivaient et lors des présentations en conférences.
Ses enseignements et ses conseils m'ont aidé à avoir une vision plus claire de la recherche et me permettront désormais de prendre mon envol.
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I would also like to thank Dario Catalano and David Pointcheval, who accepted to review this thesis during the summer and granted me with their useful remarks. I also thank the rest of the committee: Shweta Agrawal, who also invited me for a visit in the nice city of Chennai and taught me to be cautious with monkeys; Pierre-Alain Fouque, who also accepted to be part of my half-way thesis committee; Philippe Gaborit and our discussions at \textit{La-Londe-lès-Maures}; and Carla Ràfols, who I met in several conferences and for the organization of the insightful \textsc{Cost-Iacr} School on Randomness in Cryptography.
I also want to thank my coauthors for their ideas and our useful discussions: Benoît Libert, San Ling, Khoa Nguyen, Thomas Peters, Huaxiong Wang and Moti Yung. Without you, my research would have be less productive!
For inviting me and their warm reception, I would like to express my gratitude to Shweta Agrawal from IIT Madras; Adeline Langlois and Pierre-Alain Fouque from Rennes; Satya Lokam from Microsoft Bangalore; Abderrahmane Nitaj and Brigitte Vallée from Caen; and Ali El Kaafarani from Oxford.
It was the opportunity for me to discover other research environments and our interesting discussions.
Without having to move so far, I also want to thank the AriC team in Lyon and especially the crypto part with its dynamic that is very supportive to research:
I especially want to thank to Damien Stehlé, who introduced me to cryptography with his course in master, and helped me going further in this topic by introducing me to Fré Vercauteren from KU Leuven who was my first contact with research in cryptography.
Where the boundaries are blurry, I would like to thank Guillaume Hanrot, who was there to guide me in solving the administrative conundrum and also for showing his interest for my research.
From the rest of the permanent members of AriC team, I want to thank
I also want to thanks the young researchers I met during conferences and gdr-im meetings, who help me understanding the social aspect of research, especially during the ``journées C2'', but not only:
Thomas Prest, Pierre Karpman, Thomas Peters, Pierrick Méaux, Yann Rotella, Alain Passelègue, Ilaria Chillotti,
Dahmun Goudarzi,
Geoffroy Couteau, Fabrice Ben Hammouda-{}-Guichoux, Florian Bourse,
