Articles liés à Complexity of Lattice Problems: A Cryptographic Perspective

9780792376880: Complexity of Lattice Problems: A Cryptographic Perspective
Couverture rigide
ISBN 10 : 0792376889 ISBN 13 : 9780792376880
Editeur : Kluwer Academic Publishers, 2002

Synopsis

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De- spite their apparent simplicity, lattices hide a rich combinatorial struc- ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap- plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de la quatrième de couverture

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De­ spite their apparent simplicity, lattices hide a rich combinatorial struc­ ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap­ plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Kluwer Academic Publishers
Date d'édition
2002
Langue
anglais
ISBN 10 
0792376889
ISBN 13 
9780792376880
Reliure
Relié
Nombre de pages
220
Coordonnées du fabricant
non disponible
Personne responsable
non disponible