Complexity of Lattice Problems

Shafi Goldwasser

Editore: Springer Mrz 2002, 2002
ISBN 10: 0792376889 / ISBN 13: 9780792376880
Usato / Buch / Quantità: 0
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Neuware - 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. 234 pp. Englisch. Codice inventario libreria

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Riassunto: 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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Titolo: Complexity of Lattice Problems
Casa editrice: Springer Mrz 2002
Data di pubblicazione: 2002
Legatura: Buch
Condizione libro: Neu

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Descrizione libro Kluwer Academic Publishers, United States, 2002. Hardback. Condizione libro: New. 2002 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Codice libro della libreria LIE9780792376880

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Descrizione libro Springer, 2002. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780792376880

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Descrizione libro Kluwer Academic Publishers, United States, 2002. Hardback. Condizione libro: New. 2002 ed.. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice libro della libreria APC9780792376880

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Descrizione libro Springer, Netherlands, 2002. Hardback. Condizione libro: New. 2002 ed.. Language: English . Brand New Book ***** Print on Demand *****.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. Codice libro della libreria APC9780792376880

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