Complexity and cryptography: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XII, 292 S. graph. Darst. |
| ISBN: | 0521617715 9780521617710 0521852315 9780521852319 |
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| 245 | 1 | 0 | |a Complexity and cryptography |b an introduction |c John Talbot ; Dominic Welsh |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface page ix
Notation xi
1 Basics of cryptography 1
1.1 Cryptographic models 2
1.2 A basic scenario: cryptosystems 3
1.3 Classical cryptography 7
1.4 Modern cryptography 8
2 Complexity theory 10
2.1 What is complexity theory? 10
2.2 Deterministic Turing machines 16
2.3 Decision problems and languages 22
2.4 Complexity of functions 30
2.5 Space complexity 33
3 Non deterministic computation 39
3.1 Non deterministic polynomial time NP 39
3.2 Polynomial time reductions 43
3.3 NP completeness 45
3.4 Turing reductions and NP hardness 54
3.5 Complements of languages in NP 56
3.6 Containments between complexity classes 60
3.7 NP revisited non deterministic Turing machines 62
4 Probabilistic computation 67
4.1 Can tossing coins help? 67
4.2 Probabilistic Turing machines and RP 71
v
vi Contents
4.3 Primality testing 74
4.4 Zero error probabilistic polynomial time 80
4.5 Bounded error probabilistic polynomial time 81
4.6 Non uniform polynomial time 83
4.7 Circuits 86
4.8 Probabilistic circuits 92
4.9 The circuit complexity of most functions 93
4.10 Hardness results 94
5 Symmetric cryptosystems 99
5.1 Introduction 99
5.2 The one time pad: Vernam s cryptosystem 101
5.3 Perfect secrecy 102
5.4 Linear shift register sequences 106
5.5 Linear complexity 111
5.6 Non linear combination generators 113
5.7 Block ciphers and DES 115
5.8 Rijndael and the AES 118
5.9 The Pohlig Hellman cryptosystem 119
6 One way functions 125
6.1 In search of a definition 125
6.2 Strong one way functions 129
6.3 One way functions and complexity theory 132
6.4 Weak one way functions 135
7 Public key cryptography 141
7.1 Non secret encryption 141
7.2 The Cocks Ellis non secret cryptosystem 142
7.3 The RSA cryptosystem 145
7.4 The Elgamal public key cryptosystem 147
7.5 Public key cryptosystems as trapdoor functions 150
7.6 Insecurities in RSA 153
7.7 Finding the RSA private key and factoring 155
7.8 Rabin s public key cryptosystem 158
7.9 Public key systems based on NP hard problems 161
7.10 Problems with trapdoor systems 164
8 Digital signatures 170
8.1 Introduction 170
8.2 Public key based signature schemes 171
Contents vii
8.3 Attacks and security of signature
schemes 172
8.4 Signatures with privacy 176
8.5 The importance of hashing 178
8.6 The birthday attack 180
9 Key establishment protocols 187
9.1 The basic problems 187
9.2 Key distribution with secure channels 188
9.3 Diffie Hellman key establishment 190
9.4 Authenticated key distribution 193
9.5 Secret sharing 196
9.6 Shamir s secret sharing scheme 197
10 Secure encryption 203
10.1 Introduction 203
10.2 Pseudorandom generators 204
10.3 Hard and easy bits of one way functions 207
10.4 Pseudorandom generators from hard core
predicates 211
10.5 Probabilistic encryption 216
10.6 Efficient probabilistic encryption 221
11 Identification schemes 229
11.1 Introduction 229
11.2 Interactive proofs 231
11.3 Zero knowledge 235
11.4 Perfect zero knowledge proofs 236
11.5 Computational zero knowledge 240
11.6 The Fiat Shamir identification scheme 246
Appendix 1 Basic mathematical background 250
A 1.1 Order notation 250
A 1.2 Inequalities 250
Appendix 2 Graph theory definitions 252
Appendix 3 Algebra and number theory 253
A3.1 Polynomials 253
A3.2 Groups 253
A3.3 Number theory 254
viii Contents
Appendix 4 Probability theory 257
Appendix 5 Hints to selected exercises and problems 261
Appendix 6 Answers to selected exercises and problems 268
Bibliography 278
Index 287
|
| adam_txt |
Contents
Preface page ix
Notation xi
1 Basics of cryptography 1
1.1 Cryptographic models 2
1.2 A basic scenario: cryptosystems 3
1.3 Classical cryptography 7
1.4 Modern cryptography 8
2 Complexity theory 10
2.1 What is complexity theory? 10
2.2 Deterministic Turing machines 16
2.3 Decision problems and languages 22
2.4 Complexity of functions 30
2.5 Space complexity 33
3 Non deterministic computation 39
3.1 Non deterministic polynomial time NP 39
3.2 Polynomial time reductions 43
3.3 NP completeness 45
3.4 Turing reductions and NP hardness 54
3.5 Complements of languages in NP 56
3.6 Containments between complexity classes 60
3.7 NP revisited non deterministic Turing machines 62
4 Probabilistic computation 67
4.1 Can tossing coins help? 67
4.2 Probabilistic Turing machines and RP 71
v
vi Contents
4.3 Primality testing 74
4.4 Zero error probabilistic polynomial time 80
4.5 Bounded error probabilistic polynomial time 81
4.6 Non uniform polynomial time 83
4.7 Circuits 86
4.8 Probabilistic circuits 92
4.9 The circuit complexity of most functions 93
4.10 Hardness results 94
5 Symmetric cryptosystems 99
5.1 Introduction 99
5.2 The one time pad: Vernam's cryptosystem 101
5.3 Perfect secrecy 102
5.4 Linear shift register sequences 106
5.5 Linear complexity 111
5.6 Non linear combination generators 113
5.7 Block ciphers and DES 115
5.8 Rijndael and the AES 118
5.9 The Pohlig Hellman cryptosystem 119
6 One way functions 125
6.1 In search of a definition 125
6.2 Strong one way functions 129
6.3 One way functions and complexity theory 132
6.4 Weak one way functions 135
7 Public key cryptography 141
7.1 Non secret encryption 141
7.2 The Cocks Ellis non secret cryptosystem 142
7.3 The RSA cryptosystem 145
7.4 The Elgamal public key cryptosystem 147
7.5 Public key cryptosystems as trapdoor functions 150
7.6 Insecurities in RSA 153
7.7 Finding the RSA private key and factoring 155
7.8 Rabin's public key cryptosystem 158
7.9 Public key systems based on NP hard problems 161
7.10 Problems with trapdoor systems 164
8 Digital signatures 170
8.1 Introduction 170
8.2 Public key based signature schemes 171
Contents vii
8.3 Attacks and security of signature
schemes 172
8.4 Signatures with privacy 176
8.5 The importance of hashing 178
8.6 The birthday attack 180
9 Key establishment protocols 187
9.1 The basic problems 187
9.2 Key distribution with secure channels 188
9.3 Diffie Hellman key establishment 190
9.4 Authenticated key distribution 193
9.5 Secret sharing 196
9.6 Shamir's secret sharing scheme 197
10 Secure encryption 203
10.1 Introduction 203
10.2 Pseudorandom generators 204
10.3 Hard and easy bits of one way functions 207
10.4 Pseudorandom generators from hard core
predicates 211
10.5 Probabilistic encryption 216
10.6 Efficient probabilistic encryption 221
11 Identification schemes 229
11.1 Introduction 229
11.2 Interactive proofs 231
11.3 Zero knowledge 235
11.4 Perfect zero knowledge proofs 236
11.5 Computational zero knowledge 240
11.6 The Fiat Shamir identification scheme 246
Appendix 1 Basic mathematical background 250
A 1.1 Order notation 250
A 1.2 Inequalities 250
Appendix 2 Graph theory definitions 252
Appendix 3 Algebra and number theory 253
A3.1 Polynomials 253
A3.2 Groups 253
A3.3 Number theory 254
viii Contents
Appendix 4 Probability theory 257
Appendix 5 Hints to selected exercises and problems 261
Appendix 6 Answers to selected exercises and problems 268
Bibliography 278
Index 287 |
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| spelling | Talbot, John Verfasser aut Complexity and cryptography an introduction John Talbot ; Dominic Welsh 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XII, 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Complexité de calcul (Informatique) Cryptographie Computational complexity Cryptography Komplexität (DE-588)4135369-9 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Kryptologie (DE-588)4033329-2 s Komplexität (DE-588)4135369-9 s DE-604 Welsh, Dominic J. A. Verfasser aut http://www3.ub.tu-berlin.de/ihv/001718567.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014743805&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Talbot, John Welsh, Dominic J. A. Complexity and cryptography an introduction Complexité de calcul (Informatique) Cryptographie Computational complexity Cryptography Komplexität (DE-588)4135369-9 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4135369-9 (DE-588)4033329-2 |
| title | Complexity and cryptography an introduction |
| title_auth | Complexity and cryptography an introduction |
| title_exact_search | Complexity and cryptography an introduction |
| title_exact_search_txtP | Complexity and cryptography an introduction |
| title_full | Complexity and cryptography an introduction John Talbot ; Dominic Welsh |
| title_fullStr | Complexity and cryptography an introduction John Talbot ; Dominic Welsh |
| title_full_unstemmed | Complexity and cryptography an introduction John Talbot ; Dominic Welsh |
| title_short | Complexity and cryptography |
| title_sort | complexity and cryptography an introduction |
| title_sub | an introduction |
| topic | Complexité de calcul (Informatique) Cryptographie Computational complexity Cryptography Komplexität (DE-588)4135369-9 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Complexité de calcul (Informatique) Cryptographie Computational complexity Cryptography Komplexität Kryptologie |
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