Concept
Algorithme de factorisation par crible sur les corps de nombres spécialisé
Publications associées (18)
On the Analysis of Public-Key Cryptologic Algorithms
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 ...
EPFL2015A sieve algorithm based on overlattices
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 Press2014A 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 Verlag2012Factorization 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 Usa2010A 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