Complexity of lattice problems: a cryptographic perspective
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston
Kluwer Academic
2002
|
| Schriftenreihe: | The Kluwer international series in engineering and computer science
671 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. [211]-216) and index |
| Beschreibung: | X, 220 S. graph. Darst. |
| ISBN: | 0792376889 9780792376880 |
Internformat
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| 245 | 1 | 0 | |a Complexity of lattice problems |b a cryptographic perspective |c Daniele Micciancio, Shafi Goldwasser |
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| 490 | 1 | |a The Kluwer international series in engineering and computer science |v 671 | |
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| 650 | 4 | |a Codage | |
| 650 | 4 | |a Complexité de calcul (Informatique) | |
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| 650 | 4 | |a Coding theory | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Lattice theory | |
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Datensatz im Suchindex
| _version_ | 1804129244817653760 |
|---|---|
| adam_text | Contents
i
i
Preface ix
1. BASICS 1
1 Lattices 1
1.1 Determinant 6
1.2 Successive minima 7
1.3 Minkowski s theorems 11
2 Computational problems 14
2.1 Complexity Theory 15
2.2 Some lattice problems 17
2.3 Hardness of approximation 19
3 Notes 21
2. APPROXIMATION ALGORITHMS 23
1 Solving SVP in dimension 2 24
1.1 Reduced basis 24
1.2 Gauss algorithm 27
1.3 Running time analysis 30
2 Approximating SVP in dimension n 32
2.1 Reduced basis 32
2.2 The LLL basis reduction algorithm 34
2.3 Running time analysis 36
3 Approximating CVP in dimension n 40
4 Notes 42
3. CLOSEST VECTOR PROBLEM 45
1 Decision versus Search 46
2 NP completeness 48
vi COMPLEXITY OF LATTICE PROBLEMS
3 SVP is not harder than CVP 52
3.1 Deterministic reduction 53
3.2 Randomized Reduction 56
4 Inapproximability of CVP 58
4.1 Polylogarithmic factor 58
4.2 Larger factors 61
5 CVP with preprocessing 64
6 Notes 67
4. SHORTEST VECTOR PROBLEM 69
1 Kannan s homogenization technique 70
2 The Ajtai Micciancio embedding 77
3 NP hardnessofSVP 83
3.1 Hardness under randomized reductions 83
3.2 Hardness under nonuniform reductions 85
3.3 Hardness under deterministic reductions 86
4 Notes 87
5. SPHERE PACKINGS 91
1 Packing Points in Small Spheres 94
2 The Exponential Sphere Packing 96
2.1 The Schnorr Adleman prime number lattice 97
2.2 Finding clusters 99
2.3 Some additional properties 104
3 Integer Lattices 105
4 Deterministic construction 108
5 Notes 110
6. LOW DEGREE HYPERGRAPHS 111
1 Sauer s Lemma 112
2 Weak probabilistic construction 114
2.1 The exponential bound 115
2.2 Well spread hypergraphs 118
2.3 Proof of the weak theorem 121
3 Strong probabilistic construction 122
4 Notes 124
7. BASIS REDUCTION PROBLEMS 125
1 Successive minima and Minkowski s reduction 125
Contents vii
2 Orthogonality defect and KZ reduction 131
3 Small rectangles and the covering radius 136
4 Notes 141
8. CRYPTOGRAPHIC FUNCTIONS 143
1 General techniques 146
1.1 Lattices, sublattices and groups 147
1.2 Discrepancy 153
1.3 Statistical distance 157
2 Collision resistant hash functions 161
2.1 The construction 162
2.2 Collision resistance 164
2.3 The iterative step 168
2.4 Almost perfect lattices 182
3 Encryption Functions 184
3.1 The GGH scheme 185
3.2 The HNF technique 187
3.3 The Ajtai Dwork cryptosystem 189
3.4 NTRU 191
4 Notes 194
9. INTERACTIVE PROOF SYSTEMS 195
1 Closest vector problem 198
1.1 Proof of the soundness claim 201
1.2 Conclusion 204
2 Shortest vector problem 204
3 Treating other norms 206
4 What does it mean? 208
5 Notes 210
References 211
Index
219
|
| any_adam_object | 1 |
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| dewey-full | 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 |
| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV014359267 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:04Z |
| institution | BVB |
| isbn | 0792376889 9780792376880 |
| language | English |
| lccn | 2002016053 |
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| series | The Kluwer international series in engineering and computer science |
| series2 | The Kluwer international series in engineering and computer science |
| spelling | Micciancio, Daniele Verfasser aut Complexity of lattice problems a cryptographic perspective Daniele Micciancio, Shafi Goldwasser Boston Kluwer Academic 2002 X, 220 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Kluwer international series in engineering and computer science 671 Includes bibliographical references (p. [211]-216) and index Codage Complexité de calcul (Informatique) Treillis, Théorie des Coding theory Computational complexity Lattice theory Gitterpunktproblem (DE-588)4157387-0 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Gitterpunktproblem (DE-588)4157387-0 s Algorithmus (DE-588)4001183-5 s Kryptologie (DE-588)4033329-2 s DE-604 Goldwasser, Shafi Sonstige oth The Kluwer international series in engineering and computer science 671 (DE-604)BV023545171 671 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Micciancio, Daniele Complexity of lattice problems a cryptographic perspective The Kluwer international series in engineering and computer science Codage Complexité de calcul (Informatique) Treillis, Théorie des Coding theory Computational complexity Lattice theory Gitterpunktproblem (DE-588)4157387-0 gnd Kryptologie (DE-588)4033329-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4157387-0 (DE-588)4033329-2 (DE-588)4001183-5 |
| 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 Daniele Micciancio, Shafi Goldwasser |
| title_fullStr | Complexity of lattice problems a cryptographic perspective Daniele Micciancio, Shafi Goldwasser |
| title_full_unstemmed | Complexity of lattice problems a cryptographic perspective 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 | Codage Complexité de calcul (Informatique) Treillis, Théorie des Coding theory Computational complexity Lattice theory Gitterpunktproblem (DE-588)4157387-0 gnd Kryptologie (DE-588)4033329-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Codage Complexité de calcul (Informatique) Treillis, Théorie des Coding theory Computational complexity Lattice theory Gitterpunktproblem Kryptologie Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023545171 |
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