Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in $\mathbb{F}_{2^{4 \cdot 1223}}$ and $\mathbb{F}_{2^{12 \cdot 367}}$)
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 ...
This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...
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 ...
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 ...
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 ...
This paper considers the problem of second-degree price discrimination when the type distribution is unknown or imperfectly specified by means of an ambiguity set. As robustness measure we use a performance index, equivalent to relative regret, which quant ...
With the looming threat of large-scale quantum computers, a fair portion of recent cryptographic research has focused on examining cryptographic primitives from the perspective of a quantum adversary. Shor's 1994 result revealed that quantum computers can ...
Factored form is a powerful multi-level representation of a Boolean function that readily translates into an implementation of the function in CMOS technology. In particular, the number of literals in a factored form correlates strongly with the number of ...
Description (through texts, images, models or samples) played a central role in the patent regimes that emerged in the eighteenth century, first in England, later in the United States and in France. Description ensured that the contract—protection in excha ...
We consider the problem of compressing an information source when a correlated one is available as side information only at the decoder side, which is a special case of the distributed source coding problem in information theory. In particular, we consider ...
Cyclopentadienyl (Cp) metal complexes and their chiral counterparts (CpX) have enabled the development of challenging C-H activation transformations. While major progresses were made in developing new chiral CpX complexes and exploring their reactivity, th ...
In the framework of Impagliazzo's five worlds, a distinction is often made between two worlds, one where public-key encryption exists (Cryptomania), and one in which only one-way functions exist (MiniCrypt). However, the boundaries between these worlds can ...
Four recent trends have emerged in the evolution of authenticated encryption schemes: (1) Regarding simplicity, the adoption of public permutations as primitives allows for sparing a key schedule and the need for storing round keys; (2) using the sums of p ...
We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our mod ...
The Supersingular Isogeny Diffie-Hellman (SIDH) protocol has been the main and most efficient isogeny-based encryption protocol, until a series of breakthroughs led to a polynomial-time key-recovery attack. While some countermeasures have been proposed, th ...
Current machine learning models for vision are often highly specialized and limited to a single modality and task. In contrast, recent large language models exhibit a wide range of capabilities, hinting at a possibility for similarly versatile models in co ...
Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms.
This ...
This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...
