Publications related to Arithmetic and geometric structures in cryptography

Side-channel analysis of isogeny-based key encapsulation mechanisms and hash-based digital signatures

Current cryptographic solutions will become obsolete with the arrival of large-scale universal quantum computers. As a result, the National Institute of Standards and Technology supervises a post-quantum standardization process which involves evaluating ca ...

EPFL2024

On the Theory and Practice of Modern Secure Messaging

Daniel Patrick Collins

Billions of people now have conversations daily over the Internet. A large portion of this communication takes place via secure messaging protocols that offer "end-to-end encryption'" guarantees and resilience to compromise like the widely-used Double Ratc ...

EPFL2024

Isogeny Problems with Level Structure

Tako Boris Fouotsa

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the beh ...

2024

Secure and Efficient Cryptographic Algorithms in a Quantum World

Loïs Evan Huguenin-Dumittan

Since the advent of internet and mass communication, two public-key cryptographic algorithms have shared the monopoly of data encryption and authentication: Diffie-Hellman and RSA. However, in the last few years, progress made in quantum physics -- and mo ...

EPFL2024

Some Mordell-Weil lattices and applications to sphere packings

Gauthier Leterrier

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

EPFL2024

Exploring SIDH-Based Signature Parameters

Laurane Chloé Angélina Marco, Andrea Basso, Tako Boris Fouotsa

Isogeny-based cryptography is an instance of post-quantum cryptography whose fundamental problem consists of finding an isogeny between two (isogenous) elliptic curves E and E′. This problem is closely related to that of computing the endomorphism ring of ...

Springer2024

Multiplicity-free Representations of Algebraic Groups

Donna Testerman, Martin W. Liebeck

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Scalable Quantum Algorithms for Noisy Quantum Computers

Julien Sebastian Gacon

Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition ...

EPFL2024

A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

Silvestro Micera, Simone Romeni

A method for optimizing at least one of a geometry, an implantation procedure, and/or stimulation protocol of one or more electrodes for an electrical stimulation of a target structure in a nervous system of a living being by a computer device, the method ...

2024

Electron-beam based nanoscale quantum controls

Hoda Shirzad

Advancing quantum technologies depends on the precise control of individual quantum systems, the so-called qubits, and the exploitation of their quantum properties. Nowadays, expanding the number of qubits to be entangled is at the core of the developments ...

EPFL2024

Strain-based analysis on the influence of local undercut geometry on fatigue crack initiation life

Alain Nussbaumer, Heikki Tapani Remes, Abinab Niraula

The local undercut defects at the weld toe provide a potential initiation site for fatigue cracks and significantly impact the structure's fatigue strength. The influence of continuous undercut depth on fatigue performance is widely studied, but the resear ...

2024

Rational Points in the Noether-Lefschetz Locus of Moduli Spaces of K3 Surfaces

Domenico Valloni

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture impli ...

Oxford Univ Press2024

Stress tolerance of lightweight glass-free PV modules for vehicle integration

Christophe Ballif, Aïcha Hessler-Wyser, Antonin Faes, Jacques Levrat, Matthieu Despeisse, Gianluca Cattaneo, Fahradin Mujovi, Umang Bhupatrai Desai

Electric vehicles (EVs) currently dominate the sales in the automotive market. A big leap in this market can be made by developing a photovoltaic product that can be integrated to an EV, as it can boost the driving range of the EV while reducing the chargi ...

Edp Sciences S A2024

Quantum Error Correction and Simulation in Open Bosonic Systems

David Schlegel

Quantum computers have the potential to surpass conventional computing, but they are hindered by noise which induces errors that ultimately lead to the loss of quantum information. This necessitates the development of quantum error correction strategies fo ...

EPFL2024

Mean value theorems for collections of lattices with a prescribed group of symmetries

Nihar Prakash Gargava

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Josephine Anna Eleanor Hughes, Max Mirko Polzin

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

Wiley2024

Cochains are all you need

Kelly Spry Maggs

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

K3 surfaces, cyclotomic polynomials and orthogonal groups

Eva Bayer Fluckiger

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

Matthias Ruf, Matthias Benjamin Ruf

Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...

Ecole Polytechnique2024

Investigation of room-temperature single-photon emitters in GaN-based materials and GaN/AlN quantum dots

Johann Nicolaï Stachurski

Over the past decade, quantum photonics platforms aiming at harnessing the fundamental properties of single particles, such as quantum superposition and quantum entanglement, have flourished. In this context, single-photon emitters capable of operating at ...

EPFL2024