Brigitte Vallée
Encyclopedia
Brigitte Vallée is a French
mathematician
and computer scientist
. She entered the École Normale Supérieure
de Jeunes Filles in 1970, and received her PhD in 1986 at the University of Caen (Lattice reduction algorithms in small dimensions). She is Directrice de Recherche
at the French CNRS, at Université de Caenhttp://www.unicaen.fr/ufr/sciences/visualise.php?id=306, since 2001 and specialized in computational number theory
http://www.numbertheory.org/ntw/number_theorists.html and analysis of algorithms
. Amongst the algorithms she had studied, are the celebrated LLL
algorithm
used for basis reductions in Euclidean lattice
and the different Euclidean algorithm
s to determine GCD
. The main tool used to achieve her results is the so called dynamical analysis. Loosely speaking, it is a mix between analysis of algorithms and dynamical systems. Brigitte Vallée greatly contributed to develop
this method.
In the early 90s, Brigitte Vallée's work on small modular squares allowed her to hold the fastest factorisation algorithm with a proved probabilistic complexity bound. Nowadays, other factorisation algorithms are faster.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
. She entered the École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
de Jeunes Filles in 1970, and received her PhD in 1986 at the University of Caen (Lattice reduction algorithms in small dimensions). She is Directrice de Recherche
at the French CNRS, at Université de Caenhttp://www.unicaen.fr/ufr/sciences/visualise.php?id=306, since 2001 and specialized in computational number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
http://www.numbertheory.org/ntw/number_theorists.html and analysis of algorithms
Analysis of algorithms
To analyze an algorithm is to determine the amount of resources necessary to execute it. Most algorithms are designed to work with inputs of arbitrary length...
. Amongst the algorithms she had studied, are the celebrated LLL
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
The LLL-reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982, see...
algorithm
used for basis reductions in Euclidean lattice
Lattice (group)
In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn can be generated from a basis for the vector space by forming all linear combinations with integer coefficients...
and the different Euclidean algorithm
Euclidean algorithm
In mathematics, the Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, also known as the greatest common factor or highest common factor...
s to determine GCD
Greatest common divisor
In mathematics, the greatest common divisor , also known as the greatest common factor , or highest common factor , of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.For example, the GCD of 8 and 12 is 4.This notion can be extended to...
. The main tool used to achieve her results is the so called dynamical analysis. Loosely speaking, it is a mix between analysis of algorithms and dynamical systems. Brigitte Vallée greatly contributed to develop
this method.
In the early 90s, Brigitte Vallée's work on small modular squares allowed her to hold the fastest factorisation algorithm with a proved probabilistic complexity bound. Nowadays, other factorisation algorithms are faster.