Concept

General number field sieve

Related publications (39)

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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Fluorescence lifetime imaging with a single-photon SPAD array using long overlapping gates: an experimental and theoretical study

Edoardo Charbon, Claudio Bruschini, Andrei Ardelean, Arin Can Ülkü

Developing large arrays of single-photon avalanche diodes (SPADs) with on-chip time-correlated single-photon counting (TCSPC) capabilities continues to be a difficult task due to stringent silicon real estate constraints, high data rates and system complex ...

2019

Design Tools for Small Implantable antennas

Anja Skrivervik, Zvonimir Sipus, Ismael Vico Triviño

Implantable applications have been increasing in number in an exponential manner since the turn of the millennium. This is largely due to the increasing availability of ultra low power consumption electronics, enabling the emergence of healthcare services ...

The European Association on Antennas and Propagation (EurAAP)2018

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

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

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

Shimura Curves and Special Values of p-adic L-functions

Ernest Hunter Brooks

We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...

Oxford University Press2015

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

A sieve algorithm based on overlattices

Anja Annemone Becker

In this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie ...

Cambridge Univ Press2014