7 citations · 11 across the 6 of their papers we have counts for
8 papers
The special case of cyclotomic fields in quantum algorithms for unit groups
Razvan Barbulescu, Adrien Poulalion
Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is . In this work we propose a mo…
ECM And The Elliott-Halberstam Conjecture For Quadratic Fields
Razvan Barbulescu, Florent Jouve
The complexity of the elliptic curve method of factorization (ECM) is proven under the celebrated conjecture of existence of smooth numbers in short intervals. In this work we tack…
Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg's -rationality conjecture
Razvan Barbulescu, Jishnu Ray
In this paper we make a series of numerical experiments to support Greenberg's -rationality conjecture, we present a family of -rational biquadratic fields and we find new ex…
Improvements to the number field sieve for non-prime finite fields
Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic +1
We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes…
Some mathematical remarks on the polynomial selection in NFS
Razvan Barbulescu, Armand Lachand
In this work, we consider the proportion of smooth (free of large prime factors) values of a binary form . In a particular case, we give an asymptotic equ…
A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic
Razvan Barbulescu, Pierrick Gaudry, Antoine Joux +1
In the present work, we present a new discrete logarithm algorithm, in the same vein as in recent works by Joux, using an asymptotically more efficient descent approach. The main r…
Selecting polynomials for the Function Field Sieve
Razvan Barbulescu
The Function Field Sieve algorithm is dedicated to computing discrete logarithms in a finite field GF(q^n), where q is small an prime power. The scope of this article is to select…
Finding ECM-friendly curves through a study of Galois properties
Razvan Barbulescu, Joppe W. Bos, Cyril Bouvier +2
In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Mon…