Enrica Barrilli
Nationality: Italian
Host: Inria Université Côte d’Azur
| Background: Enrica recently completed a Master’s degree in Mathematics with a specialization in Cryptography at the University of Trento. Her studies primarily focused on the theoretical aspects of cryptographic protocols, with an emphasis on post-quantum cryptography. Her thesis explored computational and theoretical advancements in isogeny-based cryptography. During her MSc, she was selected to participate in the Blended Intensive Programme “Secure Communication in the Digital Age: Exploring the Synergy between Cryptography, Algebra, and Industrial Mathematics” at Adam Mickiewicz University in Poznan. This program provided her with the opportunity to attend various courses on elliptic curves, tensors, and quantum computing. She also presented a final project on isogeny-based cryptography, specifically focusing on the CSIDH protocol. Additionally, she participated in the Cyprus Tech Odyssey 2024: XRPL Hackathon, where her team won first prize for our project, “The Whistler”. This project involved developing a secure communication system for whistleblowing using distributed ledger technology. She is a member of De Componendis Cifris and has attended several courses and conferences on cryptography and mathematics, which have helped her stay updated on the latest advancements in the field. Throughout her academic career, she has also been involved in tutoring bachelor students, helping them strengthen their understanding of mathematical concepts. |
| Master thesis: Complexity of isogeny-based cryptography assuming GRH Abstract: This thesis investigates the complexity of isogeny-based post-quantum cryptography, focusing on the intricate landscape of isogeny graphs associated with supersingular elliptic curves over finite fields. The assumption of the Generalized Riemann Hypothesis (GRH) plays a crucial role in the analysis, providing the foundation for the polynomial expected time reductions that are essential for understanding the complexity of these problems. Beyond the structural analysis and algorithmic development, this thesis explores the equivalence between the path-finding problem in isogeny graphs and the endomorphism ring problem for supersingular elliptic curves. This equivalence provides a deeper insight into the security assumptions and potential vulnerabilities of isogeny-based cryptographic protocols. Furthermore, we discuss recent advancements in computing the endomorphism ring of supersingular elliptic curves, particularly those with non-scalar endomorphisms. |
| Research interests: Her research interests are centered on several cutting-edge areas in mathematics and cryptography: Post-Quantum Cryptography, Elliptic Curve Cryptography, Commutative Algebra, Computational Algebra, Number Theory, Algebraic Geometry |
| PhD Goals: As a PhD candidate in the TENORS project, she will focus on developing cutting-edge solutions to the tensor decomposition problem by crafting innovative and advanced techniques and efficient algorithms. Her aim is to contribute to the understanding and advancement of this field through incremental improvements. Additionally, she is eager to collaborate with researchers across the international network. By engaging with colleagues from various backgrounds, she hopes to explore related topics, learn from diverse perspectives, and foster a collaborative research environment that supports shared learning and innovation. |
| Hobby: Beyond her research, she enjoys engaging in challenging activities and exploring new experiences. Among her passions, she has achieved the rank of black belt in karate, a martial art that requires constant discipline and dedication. Additionally, she plays the saxophone, performing in orchestral concerts and for personal enjoyment. These activities allow her to develop skills such as concentration, creativity, and resilience, which she considers essential in her academic journey as well. |
