Concept

Sieve theory

Related publications (22)

Mass transport of water vapor and ions from Å-scale graphene nanopores

Hydrodynamics at the nanoscale involves both fundamental study and application of fluid and mass transport phenomena in nanometer-sized confinements. Nanopores in single-layer graphene can be highly attractive for exploring the molecular transport of gas a ...

EPFL2022

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 Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

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

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

We prove that the Kloosterman sum changes sign infinitely often as runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomaki, replacing 10 by 23, 18 and 15, respectively ...

Springer Verlag2015

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

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013

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

SUPERSYMMETRY PHENOMENOLOGY BEYOND THE MSSM AFTER 5/fb OF LHC DATA

Paolo Lodone

We briefly review the status of motivated beyond-the-MSSM phenomenology in the light of the LHC searches to date. In particular, we discuss the conceptual consequences of the exclusion bounds, of the hint for a Higgs boson at about 125 GeV, and of interpre ...

2012

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

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013