Faster ECC over $\mathbb{F}_{2^{521}-1}$

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Driven by the demand for real-time processing and the need to minimize latency in AI algorithms, edge computing has experienced remarkable progress. Decision-making AI applications stand out for their heavy reliance on data-centric operations, predominantl ...

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Vision systems built around conventional image sensors have to read, encode and transmit large quantities of pixel information, a majority of which is redundant. As a result, new computational imaging sensor architectures were developed to preprocess the r ...

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

This contribution focuses on the fabrication and characterization of microchannel plates made of hydrogenated amorphous silicon (AMCPs). Flexible fabrication processes and the semi-conducting nature of amorphous silicon could give these detectors the advan ...

We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed fro ...

Microchannel plates (MCPs) fabricated out of hydrogenated amorphous silicon offer a promising alternative to conventional lead glass ones. Progress in the fabrication process has allowed for detectors with higher aspect ratios, which significantly increase ...

Reducing the number of AND gates plays a central role in many cryptography and security applications. We propose a logic synthesis algorithm and tool to minimize the number of AND gates in a logic network composed of AND, XOR, and inverter gates. Our appro ...

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture for Distributed Storage Systems (DSS) that achieves a small repair bandwidth while guaranteeing a high availability. Specifically, we partition the set of servers in a DSS into s c ...

PurposeMagnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as ir ...

We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

We construct liftings of reduction maps from complex multiplication (CM) points to supersingular points for general quaternion algebras and use these liftings to establish a precise correspondence between CM points on indefinite quaternion algebras with a ...

This paper presents a low-latency algorithm designed for parallel computer architectures to compute the scalar multiplication of elliptic curve points based on approaches from cryptographic side-channel analysis. A graphics processing unit implementation u ...

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Chattez avec Graph Search

EdgeAI-Aware Design of In-Memory Computing Architectures

Non-planarity of Markoff graphs mod p

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

Computational Imaging SPAD Cameras

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

Fabrication and Characterization of High Aspect Ratio Amorphous Silicon Based Microchannel Plates

Experiments with the Markoff Surface

Characterization of Amorphous Silicon Based Microchannel Plates with High Aspect Ratio

Reducing the Multiplicative Complexity in Logic Networks for Cryptography and Security Applications

Arithmetic and geometric structures in cryptography

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Increasing Availability in Distributed Storage Systems via Clustering

MRI artifact correction using sparse plus low-rank decomposition of annihilating filter-based hankel matrix

Fast Computation Of Spectral Projectors Of Banded Matrices

Bilinear forms with Kloosterman sums and applications

Computational Aspects of Jacobians of Hyperelliptic Curves

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Liftings of reduction maps for quaternion algebras

Low-Latency Elliptic Curve Scalar Multiplication

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication