Introduction to cryptography:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Undergraduate texts in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 335 S. graph. Darst. |
| ISBN: | 038721156X 9780387211565 0387207562 9780387207568 |
Staff View
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| 650 | 4 | |a Cryptography | |
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Record in the Search Index
| _version_ | 1804130446455341057 |
|---|---|
| adam_text | Preface for the Second Edition xiii
Preface xv
1 Integers 1
1.1 Basics .... ... .... . .... ... ........... 1
1.2 Divisibility .... ... ... .... ... .... . . 3
1.3 Representation of Integers . . ............ 4
1.4 O-and £2-Notation . . . ........ ..... ... 6
1.5 Cost of Addition, Multiplication, and Division with
Remainder . . . ......... ... V . . .... . 7
1.6 Polynomial Time . . . . . . . . . . . . . • • • . . . 9
1.7 Greatest Common Divisor . . . . . . . . . . . i 9
1.8 Euclidean Algorithm ................. 12
1.9 Extended Euclidean Algorithm . . .... ...... 16
1.10 Analysis of the Extended Euclidean Algorithm . . .18
1.11 Factoring into Primes . . . . . . . . ... . . , . . . 22
1.12 Exercises ..... ................... 24
2 Congruences and Residue Class Rings 29
2.1 Congruences . . . . . .......... . . . .... 29
VÜ
yj|j Con
2.2 Semigroups . . . .... . . . . . . . . . ...
2.3 Groups ... . ... .... . . ... ...........
2.4 Residue Class Ring . . . . . . . . . . . .... . .
2.5 Fields ... . ..... . . . . . . . . . . ..
2.6 Division in the Residue Class Ring ..........
2.7 Analysis of the Operations in the Residue Class Ring
2.8 Multiplicative Group of Residues mod m ......
2.9 Order of Group Elements . . . . . . ... . ... . .
2.10 Subgroups ... ...... ... .... . ... . .
2.11 Fermat s Little Theorem . . . . ...........
2.12 Fast Exponentiation . . . . . . . . . . ... . . . . .
2.13 Fast Evaluation of Power Products ..........
2.14 Computation of Element Orders . . .........
2.15 The Chinese Remainder Theorem ...................
2.16 Decomposition of the Residue Class Ring . . . . . .
2.17 A Formula for the Euler yi-Function....... .
2.18 Polynomials ........ . ..........................
2.19 Polynomials over Fields ... .............
2.20 Construction of Finite Fields .... .........
2.21 The Structure of the Unit Group of Finite Fields . .
2.22 Structure of the Multiplicative Group of Residues
Modulo a Prime Number . • • • • ........ . .
2.23 Exercises .......... . . . ... ........
32
34
35
36
36
38
39
41
42
44
45
48
49
51
53
55
56
58
61
65
66
67
3 Encryption 71
3.1 Encryption Schemes . V . . . . . . . . . ............. 71
3.2 Symmetric and Asymmetric Cryptosystems . ... 73
3.3 Cryptanalysis ........ ..... . .... ... 74
3.4 Alphabets and Words . . . . . . . . . . ...... 77
3.5 Permutations . . . ....... ... ......... 80
3.6 Block Ciphers . . . .. ..... . .... . . . . . . . 81
3.7 Multiple Encryption . .... . . . . . . . ...... 82
3.8 The Use of Block Ciphers . . . .... . . ...... 83
3.9 Stream Ciphers .... . . . . ... ...................... 93
3.10 The Affine Cipher .... .............................. 95
3.11 Matrices and Linear Maps . . . . . . . ............... 97
3.12 Affine Linear Block Ciphers . ...................... 102
3.13 Vigenere, Hill, and Permutation Ciphers.... 103
Contents
3.14 Cryptanalysis of Affine Linear Block Ciphers . . . 104
3.15 Secure Cryptosystems . . . ..... • • • • • • • • • 105
3.16 Exercises . . . ........ ........ . . ... Ill
4 Probability and Perfect Secrecy 115
4.1 Probability . ... . . . . 9 4 ♦ *. * . • « 4 4 . 4 » • 9 9- 9 115
4.2 Conditional Probability . • • » • * « ♦ 9 9 .4 • • . 4 4 „ 9 9 117
4.3 Birthday Paradox . . . . . 4 4 • 4 8 • - » 4 4.4.4 4, 4. 4 4 118
4.4 Perfect Secrecy . ... . . 119
4.5 Vemam One-Time Pad . • 4 • • 4 4 • 4 4- 4 . 4 4 4 4 -4 123
4.6 Random Numbers . . . . -4 -4. * 4 4 .4 4 4 124
4.7 Pseudorandom Numbers • * ♦ « « • • 4 .4 . 4 4 .4 4 4 4 124
4.8 Exercises . ...... . . m • * • • • 9 * « • 4’ 4 4- 9 4 . 4 4 125
DES 127
5.1 Feistel Ciphers ...... • • • • 4 4 * . • ‘ •- 4 -4 . 4 4 4 9 4 127
5.2 DES Algorithm . . . . . . • 4 4 4 4 » « • 4 4 4- . 4 4- 4 - 4 4. 128
5.3 An Example- ... . . • « « 4 • V ♦. * .4 4 4 4 . 4 - • 4 .4 134
5.4 Security of DES . . . . . m ♦ 4.« • * 4 9 4 4 4 4 . ‘ 4 4 . 136
5.5 Exercises......... . . . . 137
AES 139
6.1 Notation ......... 139
6.2 Cipher . . . . . . .... • « ■ ♦ .4 4 • - • 4‘ 4* 4 » 4 • 4 • 4 ♦ 140
6.3 KeyExpansion . . 4 9 4 : 4 4 4 4 . 9 • - 4 145
6.4 An Example . . . . . . . 146
6.5 InvCipher . ... . . . ... .♦ • ’’ ♦ . ♦ . • - .4 4 4 4 4 « 4 4 4’ 148
6.6 Exercises . . . . . ... . • .. 148
Prime Number Generation 151
7.1 THal Division . . .... . • 4.-9 9 9 .4 • 4 - - 4 4 . 4.4 4 . - 4 • 4 • 151
7.2 Fermât Ttest. . . . ... . • * 4 4.4 444 4 9 4 4 4 . . 4 . 9 . 4 153
7.3 Carmichael Numbers . . 154
7.4 Miller-Rabin Ibst . . . . . 156
7.5 Random Primes ... . 159
7.6 Exercises ......... 160
Contents
8 Public-Key Encryption 163
8.1 Idea........................... ..... . . . 163
8.2 Security ....... .... ... .......... . 165
8.3 RSA Cryptosystem . . ..... .... . . ...... 167
8.4 Rabin Encryption ............... . . . . 181
8.5 Diffie-Hellman Key Exchange . .... . . .... ... 186
8.6 ElGamal Encryption ........... . . . ... . 191
8.7 Exercises ........... ....... ...... 196
9 Factoring 199
9.1 Trial Division...... . ........... .... 199
9.2 p - 1 Method.... ... ... ... 200
9.3 Quadratic sieve ......... ..... . . . . . . 201
9.4 Analysis of the Quadratic Sieve . . . . .... . . . 206
9.5 Efficiency of Other Factoring Algorithms ...... 210
9.6 Exercises ..... ........ ... .................... . 211
10 Discrete Logarithms 213
10.1 The DL Problem....................... . . . ..... 213
10.2 Enumeration.................... ... .... . 214
10.3 Shanks Baby-Step Giant-Step Algorithm . .... . . 214
10.4 The Pollard p-Algorithm . .... .......... 217
10.5 The Pohlig-Hellman Algorithm . . .......... 221
10.6 Index Calculus ... . .... . . . ... . . . . . ... 226
10.7 Other Algorithms ... . ... . . . . . . . . . . . . 230
10.8 Generalization of the Index Calculus Algorithm . . 231
10.9 Exercises ... .......... ...... ... . . 232
11 Cryptographic Hash Functions 235
11.1 Hash Functions and Compression Functions . . . . 235
11.2 Birthday Attack . . . . ........ . . ... . . . 238
11.3 Compression Functions from Encryption Functions 239
11.4 Hash Functions from Compression Functions ... 239
11.5 SHA-1 ... . ....... . . . . . . . . . . .... . 242
11.6 Other Hash Functions . ... . . . . . ... ..... 244
11.7 An Arithmetic Compression Function . . . . . . . . 245
11.8 Message Authentication Codes . ......... . . 247
11.9 Exercises . . . . .... . . . . . . . . .... .... 248
Contents
12 Digital Signatures
12.1 Idea ........ .... ... . ...... . . . . .
12.2 Security.... . . . . ......... ..........
12.3 RSA Signatures . . . . . . . ... . . . . . . . . . .
12.4 Signatures from Public-Key Systems . . • . . • • • •
12.5 ElGamal Signature . . . .... . . . . . ... . . .
12.6 The Digital Signature Algorithm (DSA) . . . . .
12.7 Undeniable Signatures . . . . . .... .....;.
12.8 Blind Signatures . . . .......... . . . . . . .
12.9 Exercises ...... . . . . . . . . . . .... .
13 Other Systems
13.1 Finite Fields . . ... .... . . . . . . ...... .
13.2 Elliptic Curves . . . . ... . . . . . . . . . . . . .
13.3 Quadratic Forms..... . .. .. . .... ... .... . . .
13.4 Exercises ... . . . . . . ..............
14 Identification
14.1 Passwords . ... ..... . . . . . ........
14.2 One-Time Passwords . . . . . . . ...... . . . .
14.3 Challenge-Response Identification . ..... . . . .
14.4 Exercises . . . . ........ ............
15 Secret Sharing
15.1 The Principle ... . . ........ . . . . . . . .
15.2 The Shamir Secret Sharing Protocol . . . . . . .
15.3 Exercises .... . . .... . ... .......
16 Public-Key Infrastructures
16.1 Personal Security Environments ... . .... . . .
16.2 Certification Authorities . . . . ...........
16.3 Certificate Chains . . . . . . , . ..........
• - ■ . . ; ■ ■ ■ • ■ • • . O ..
Solutions of the exercises
References
Index
XI
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| spelling | Buchmann, Johannes 1953- Verfasser (DE-588)105019178 aut Introduction to cryptography Johannes Buchmann 2. ed. New York [u.a.] Springer 2004 XVI, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Codage Computabilidade e complexidade larpcal Criptologia larpcal Cryptographie Geheimschrift gtt Coding theory Cryptography Kryptologie (DE-588)4033329-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Kryptologie (DE-588)4033329-2 s DE-604 Deutsche Ausg. u.d.T.: Buchmann, Johannes A. Einführung in die Kryptographie Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010652618&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buchmann, Johannes 1953- Introduction to cryptography Codage Computabilidade e complexidade larpcal Criptologia larpcal Cryptographie Geheimschrift gtt Coding theory Cryptography Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4033329-2 (DE-588)4123623-3 |
| title | Introduction to cryptography |
| title_auth | Introduction to cryptography |
| title_exact_search | Introduction to cryptography |
| title_full | Introduction to cryptography Johannes Buchmann |
| title_fullStr | Introduction to cryptography Johannes Buchmann |
| title_full_unstemmed | Introduction to cryptography Johannes Buchmann |
| title_short | Introduction to cryptography |
| title_sort | introduction to cryptography |
| topic | Codage Computabilidade e complexidade larpcal Criptologia larpcal Cryptographie Geheimschrift gtt Coding theory Cryptography Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Codage Computabilidade e complexidade Criptologia Cryptographie Geheimschrift Coding theory Cryptography Kryptologie Lehrbuch |
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