Complexity of Lattice Problems: A Cryptographic Perspective: 671 (The Springer International Series in Engineering and Computer Science, 671) - Tapa dura

Libro 119 de 260: The Springer International Series in Engineering and Computer Science

Micciancio, Daniele; Goldwasser, S.; Goldwasser, Shafi

 
9780792376880: Complexity of Lattice Problems: A Cryptographic Perspective: 671 (The Springer International Series in Engineering and Computer Science, 671)
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ISBN 10: 0792376889 ISBN 13: 9780792376880
Editorial: Springer, 2002

Sinopsis

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.

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Reseña del editor

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.

Reseña del editor

The book presents a self-contained overview of the state of the art in the complexity of lattice problems, with particular emphasis on problems that are related to the construction of cryptographic functions. Specific topics covered are the strongest known inapproximability result for the shortest vector problem; the relations between this and other computational lattice problems; an exposition of how cryptographic functions can be built and prove secure based on worst-case hardness assumptions about lattice problems; and a study of the limits of non-approximability of lattice problems. Some background in complexity theory, but no prior knowledge about lattices, is assumed.

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Editorial
Springer
Año de publicación
2002
Idioma
Inglés
ISBN 10 
0792376889
ISBN 13 
9780792376880
Encuadernación
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Número de páginas
236
Contacto del fabricante
ProductSafety@springernature.com
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Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9781461352938: Complexity of Lattice Problems: A Cryptographic Perspective: 671 (The Springer International Series in Engineering and Computer Science)

Edición Destacada

ISBN 10:  1461352932 ISBN 13:  9781461352938
Editorial: Springer, 2012
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