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Publications associées (33)

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

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

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

Multi-objectives, multi-period optimization of district energy systems: I. Selection of typical operating periods

François Maréchal, Laurent Gabriel Félix Alexandre Stéphane Bungener, Samira Fazlollahi

Abstract The long term optimization of a district energy system is a computationally demanding task due to the large number of data points representing the energy demand profiles. In order to reduce the number of data points and therefore the computational ...

Elsevier2014

A heterogeneous computing environment to solve the 768-bit RSA challenge

Arjen Lenstra, Pénélope Leyland, Pascal Jermini, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Michela Thiémard, Heinz Stockinger

In December 2009 the 768-bit, 232-digit number RSA-768 was factored using the number field sieve. Overall, the computational challenge would take more than 1700 years on a single, standard core. In the article we present the heterogeneous computing approac ...

Springer Verlag2012

Cryptographic Hash Functions in Groups and Provable Properties

Juraj Sarinay

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...

EPFL2011

Faster and Smoother - VSH Revisited

Juraj Sarinay

We reconsider the provably collision resistant Very Smooth Hash and propose a small change in the design aiming to improve both performance and security. While the original proofs of security based on hardness of factoring or discrete logarithms are preser ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011

Factorization of a 768-Bit RSA Modulus

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Patric Zimmermann

This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA. ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

"Compressed" Compressed Sensing

Michael Christoph Gastpar

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller num ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

A kilobit special number field sieve factorization

Arjen Lenstra, Thorsten Kleinjung, Dag Arne Osvik

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 -1. Although this factorization is orders of magnitude ...

2007

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