Concept

Prime k-tuple

Publications associées (11)

A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

We investigate how spectral properties of a measure-preserving system (X, B, mu, T) are reflected in the multiple ergodic averages arising from that system. For certain sequences a :N -> N, we provide natural conditions on the spectrum sigma (T) such that, ...

2019

A PRACTICAL ANALYTIC METHOD FOR CALCULATING pi(x)

Thorsten Kleinjung

In this paper we give a description of a practical analytic method for the computation of pi(x), the number of prime numbers

American Mathematical Society2017

Primeless Factoring-Based Cryptography

Serge Vaudenay, Sonia Mihaela Bogos

Factoring-based public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off process ...

2013

Primeless Modular Cryptography (Extended Abstract)

Serge Vaudenay, Sonia Mihaela Bogos

Most of the known public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off proce ...

2012

On the Reduction of Points on Abelian Varieties and Tori

Antonella Perucca

Let G be the product of an abelian variety and a torus defined over a number field K. Let R-1, ..., R-n be points in G(K). Let l be a rational prime, and let a(1), ..., a(n) be nonnegative integers. Consider the set of primes p of K satisfying the followin ...

2011

Primality Testing

Kamal Tahiri Jouti

Since the discovery of the utility of the numbers, the human being tried to differentiate them. We decide between them according to whether they are even or odd. Or, according to the fact that they are prime or composite. A natural number n >1 is called a ...

2006

Digital Signature Schemes with Domain Parameters

Serge Vaudenay

Digital signature schemes often use domain parameters such as prime numbers or elliptic curves. They can be subject to security threats when they are not treated like public keys. In this paper we formalize the notion of "signature scheme with domain param ...

2004

Stabilization for SLn in bounded cohomology

Nicolas Monod

We prove that for all local fields SLn is stable over n in terms of continuous bounded cohomology. We complement this by various computations in low degree, showing notably the vanishing of the third bounded cohomology of SLn(R) for all n. We link the corr ...

2004

Efficient generation of prime numbers

Serge Vaudenay

The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of in ...

2000

Stickelberger Codes

Mohammad Amin Shokrollahi

Let

p

be an odd prime and

zeta_p

be a primitive pth root of unity over

smallBbbQ

. The Galois group

G

K:=smallBbbQ(zeta_p)

over

smallBbbQ

is a cyclic group of order

p-1

. The integral group ring

smallBbbZ[G]

contains the Stickelberger idea ...

1996

Graph Chatbot

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

Connectez-vous pour utiliser Chat avec Graph Search