CRC Seminar Series - Maria Corte-Real Santos

Isogeny-based schemes often come with special requirements on the field of definition of the involved elliptic curves. For instance, the efficiency of SQIsign requires a large power of two and a large smooth integer T to divide p^2 − 1 for its prime parameter p.

In this talk, we present joint work with Jonathan Komada Eriksen, Michael Meyer and Francisco Rodríguez-Henríquez, which proposes two new methods for finding suitable primes. We use these methods to obtain new parameters for the Round 1 NIST submission of SQIsign, AprèsSQI, and POKE. For these schemes, the parameters we present offer the best performance among all parameters proposed in the literature. If time permits, we will also see how this prime-finding problem appears for new constructions based on the signature scheme PRISM.

Maria is currently a post-doctoral researcher at ENS de Lyon, in the Unité de Mathématiques pures et appliquées (UMPA), working with Benjamin Wesolowski. Her main research interests are post-quantum cryptography, specifically isogeny-based cryptography, and computational number theory. Previously, Maria completed her PhD at University College London, as part of the CDT for Cybersecurity and the Information Security group, under the supervision of Philipp Jovanovic and Sarah Meiklejohn.

Before starting my PhD, Maria completed her Undergraduate and Master’s degree in Mathematics at the University of Cambridge, specialising in Algebraic Number Theory and Elliptic Curves. Maria is also a co-organiser of The Isogeny Club, together with Jonathan Komada Eriksen.

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