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A world wide number field sieve factoring record: on to 512 bits

Publications associées (32)

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Data and scripts for the RaFSIP scheme

Athanasios Nenes, Paraskevi Georgakaki

This repository contains microphysics routines, scripts, and processed data from the Weather Research and Forecasting (WRF) model simulations presented in the paper "RaFSIP: Parameterizing ice multiplication in models using a machine learning approach", by ...

Zenodo2024

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

Computation of a 768-Bit Prime Field Discrete Logarithm

Arjen Lenstra, Thorsten Kleinjung

This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly disc ...

Springer International Publishing Ag2017

Quadratic Sieving

Thorsten Kleinjung

We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we ...

American Mathematical Society2016

On the Analysis of Public-Key Cryptologic Algorithms

Andrea Miele

The RSA cryptosystem introduced in 1977 by Ron Rivest, Adi Shamir and Len Adleman is the most commonly deployed public-key cryptosystem. Elliptic curve cryptography (ECC) introduced in the mid 80's by Neal Koblitz and Victor Miller is becoming an increasin ...

EPFL2015

Producing absorption mode Fourier transform ion cyclotron resonance mass spectra with non-quadratic phase correction functions

Yury Tsybin, Anton Kozhinov, Konstantin Nagornov, Konstantin Zhurov

RATIONALE: Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some ins ...

Wiley-Blackwell2015

Runtime Prediction for Scale-Out Data Analytics

Adrian Daniel Popescu

Many analytics applications generate mixed workloads, i.e., workloads comprised of analytical tasks with different processing characteristics including data pre-processing, SQL, and iterative machine learning algorithms. Examples of such mixed workloads ca ...

EPFL2015

Combine and Conquer

Vincent Etter

In this thesis, we explore the application of data mining and machine learning techniques to several practical problems. These problems have roots in various fields such as social science, economics, and political science. We show that computer science tec ...

EPFL2015

Cofactorization on Graphics Processing Units

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Andrea Miele

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-a ...

Springer-Verlag Berlin2014

Towards the ultimate SM fit to close in on Higgs physics

Francesco Riva

With the discovery of the Higgs at the LHC, experiments have finally addressed all aspects of the Standard Model (SM). At this stage, it is important to understand which windows for beyond the SM (BSM) physics are still open, and which are instead tightly ...

Springer2014