Publication

Efficient SIMD arithmetic modulo a Mersenne number

Publications associées (24)

Toroidal families and averages of L-functions, I

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

Polish Acad Sciences Inst Mathematics-Impan2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Revisiting Offline Compression: Going Beyond Factorization-based Methods for Transformer Language Models

Karl Aberer, Rémi Philippe Lebret, Mohammadreza Banaei

Recent transformer language models achieve outstanding results in many natural language processing (NLP) tasks. However, their enormous size often makes them impractical on memory-constrained devices, requiring practitioners to compress them to smaller net ...

Assoc Computational Linguistics-Acl2023

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

The Lang-Trotter conjecture for products of non-CM elliptic curves

Vlad Serban

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

SPRINGER2022

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

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 ...

EPFL2022

Recoloring subgraphs of K-2n for sports scheduling

Dominique de Werra

The exploration of one-factorizations of complete graphs is the foundation of some classical sports scheduling problems. One has to traverse the landscape of such one-factorizations by moving from one of those to a so-called neighbor one-factorization. Thi ...

ELSEVIER2021

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2022

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Timothée Ewart, Fabien Jonathan Delalondre, Francesco Cremonesi

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

Computing Cyclic Isogenies between Principally Polarized Abelian Varieties over Finite Fields

Marius Lorenz Vuille

Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's ...

EPFL2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

Kinetic Euclidean Distance Matrices

Martin Vetterli, Ivan Dokmanic, Puoya Tabaghi

Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize point ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Role of higher order plasmonic modes in one-dimensional nanogratings

Foziyeh Sohrabi, Ershad Mohammadi

By theoretically investigating the optical behavior of one-dimensional gold nanogratings using Fourier Modal Method, we have shown that both integer and non-integer multiples of surface plasmon polariton wavelengths should be taken into consideration in sp ...

SPRINGER2019

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for ...

OXFORD UNIV PRESS2019

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

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 ...

EPFL2018

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Lonely Runner Polyhedra

Matthias Schymura

We study the Lonely Runner Conjecture, conceived by Jörg M. Wills in the 1960's: Given positive integers n_1, n_2, ... , n_k, there exists a positive real number t such that for all 1 \le j \le k the distance of t n_j to the nearest integer is at least 1 / ...

2019

Isogeny graphs of ordinary abelian varieties

Benjamin Pierre Charles Wesolowski, Dimitar Petkov Jetchev, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Some consequences of Masser's counting theorem on elliptic curves

Valéry Aurélien Mahé

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

Publications associées (24)

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020