Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

We describe how to compute the ideal class group and the unit group of an order in a
number field in subexponential time. Our method relies on the generalized Riemann …

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime
field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever …

In this paper, we compute $\ell $-isogenies between abelian varieties over a field of
characteristic different from $2 $ in polynomial time in $\ell $, when $\ell $ is an odd prime …

Efficient algorithms for abelian varieties and their moduli spaces Page 1 HAL Id: tel-03498268
https://hal.science/tel-03498268 Submitted on 20 Dec 2021 HAL is a multi-disciplinary open …

The first practical public key cryptosystem ever published, the Diffie–Hellman key exchange
algorithm, relies for its security on the assumption that discrete logarithms are hard to …

Diffie–Hellman key exchange is at the foundations of public-key cryptography, but
conventional group-based Diffie–Hellman is vulnerable to Shor's quantum algorithm. A …

Hafner and McCurley described a subexponential time algorithm to compute the ideal class
group of a quadratic field, which was generalized to families of fixed degree number fields …

Depuis le milieu des années 1980, les variétés abéliennes ont été abondamment utilisées
en cryptographie à clé publique: le problème du logarithme discret et les protocoles qui s' …

Le logarithme discret sur les courbes elliptiques fournit la panoplie standard de la
cryptographie à clé publique: chiffrement asymétrique, signature, authentification. Son …