Complexity of Lattice Problems: A Cryptographic Perspective
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...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2002
|
| Schriftenreihe: | The Springer International Series in Engineering and Computer Science
671 |
| Schlagworte: | |
| Online-Zugang: | FHI01 BTU01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | 1 Online-Ressource (X, 220 p) |
| ISBN: | 9781461508977 |
| DOI: | 10.1007/978-1-4615-0897-7 |
Internformat
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| 520 | |a 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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Datensatz im Suchindex
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| author | Micciancio, Daniele Goldwasser, Shafi |
| author_facet | Micciancio, Daniele Goldwasser, Shafi |
| author_role | aut aut |
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| bvnumber | BV045148873 |
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| dewey-full | 005.74 |
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| discipline | Informatik |
| doi_str_mv | 10.1007/978-1-4615-0897-7 |
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| id | DE-604.BV045148873 |
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| indexdate | 2024-07-10T08:10:02Z |
| institution | BVB |
| isbn | 9781461508977 |
| language | English |
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| publisher | Springer US |
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| series2 | The Springer International Series in Engineering and Computer Science |
| spelling | Micciancio, Daniele Verfasser aut Complexity of Lattice Problems A Cryptographic Perspective by Daniele Micciancio, Shafi Goldwasser Boston, MA Springer US 2002 1 Online-Ressource (X, 220 p) txt rdacontent c rdamedia cr rdacarrier The Springer International Series in Engineering and Computer Science 671 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 Computer Science Data Structures, Cryptology and Information Theory Theory of Computation Electrical Engineering Discrete Mathematics in Computer Science Computer science Data structures (Computer science) Computers Computer science / Mathematics Electrical engineering Algorithmus (DE-588)4001183-5 gnd rswk-swf Gitterpunktproblem (DE-588)4157387-0 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Gitterpunktproblem (DE-588)4157387-0 s Algorithmus (DE-588)4001183-5 s Kryptologie (DE-588)4033329-2 s 1\p DE-604 Goldwasser, Shafi aut Erscheint auch als Druck-Ausgabe 9781461352938 https://doi.org/10.1007/978-1-4615-0897-7 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Micciancio, Daniele Goldwasser, Shafi Complexity of Lattice Problems A Cryptographic Perspective Computer Science Data Structures, Cryptology and Information Theory Theory of Computation Electrical Engineering Discrete Mathematics in Computer Science Computer science Data structures (Computer science) Computers Computer science / Mathematics Electrical engineering Algorithmus (DE-588)4001183-5 gnd Gitterpunktproblem (DE-588)4157387-0 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4157387-0 (DE-588)4033329-2 |
| title | Complexity of Lattice Problems A Cryptographic Perspective |
| title_auth | Complexity of Lattice Problems A Cryptographic Perspective |
| title_exact_search | Complexity of Lattice Problems A Cryptographic Perspective |
| title_full | Complexity of Lattice Problems A Cryptographic Perspective by Daniele Micciancio, Shafi Goldwasser |
| title_fullStr | Complexity of Lattice Problems A Cryptographic Perspective by Daniele Micciancio, Shafi Goldwasser |
| title_full_unstemmed | Complexity of Lattice Problems A Cryptographic Perspective by Daniele Micciancio, Shafi Goldwasser |
| title_short | Complexity of Lattice Problems |
| title_sort | complexity of lattice problems a cryptographic perspective |
| title_sub | A Cryptographic Perspective |
| topic | Computer Science Data Structures, Cryptology and Information Theory Theory of Computation Electrical Engineering Discrete Mathematics in Computer Science Computer science Data structures (Computer science) Computers Computer science / Mathematics Electrical engineering Algorithmus (DE-588)4001183-5 gnd Gitterpunktproblem (DE-588)4157387-0 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Computer Science Data Structures, Cryptology and Information Theory Theory of Computation Electrical Engineering Discrete Mathematics in Computer Science Computer science Data structures (Computer science) Computers Computer science / Mathematics Electrical engineering Algorithmus Gitterpunktproblem Kryptologie |
| url | https://doi.org/10.1007/978-1-4615-0897-7 |
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