A course in mathematical cryptography:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin/Boston
De Gruyter
2015
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIII, 376 S. Diagramme 24 cm |
| ISBN: | 9783110372762 3110372762 |
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| 245 | 1 | 0 | |a A course in mathematical cryptography |c Gilbert Baumslag ... |
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| 300 | |a XIII, 376 S. |b Diagramme |c 24 cm | ||
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Record in the Search Index
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| adam_text |
CONTENTS
PREFACE V
1 BASIC IDEAS OF CRYPTOGRAPHY 1
1.1 MATHEMATICAL CRYPTOGRAPHY 1
1.2 CRYPTOGRAPHY, CRYPTANALYSIS AND CRYPTOSYSTEMS 3
1.3 A VERY BRIEF HISTORY OF CRYPTOGRAPHY 7
1.4 ENCRYPTION AND NUMBER THEORY 9
1.5 PUBLIC KEY CRYPTOGRAPHY 12
1.6 CRYPTOSYSTEMS AND THE KEY SPACE 14
1.7 CRYPTOGRAPHIC PROTOCOLS 15
1.8 EXERCISES 16
2 SYMMETRIC KEY CRYPTOSYSTEMS 19
2.1 MIXED ENCRYPTION 19
2.2 BLOCK CIPHERS 20
2.3 STREAM CIPHERS 22
2.4 FEISTEL NETWORKS, DES AND AES 27
2.5 ONE-WAY FUNCTIONS AND TRAPDOORS 29
2.6 EXERCISES 29
3 CRYPTANALYSIS AND COMPLEXITY 31
3.1 CRYPTANALYSIS AND CRYPTANALYTIC ATTACKS 31
3.2 STATISTICAL METHODS 32
3.3 CRYPTOGRAPHIC SECURITY 33
3.3.1 SECURITY PROOFS 34
3.4 PERFECT SECURITY AND THE ONE-TIME PAD 35
3.4.1 VIGENERE ENCRYPTION AND POLYALPHABETIC CIPHERS 37
3.4.2 BREAKING A PROTOCOL 40
3.5 COMPLEXITY OF ALGORITHMS 40
3.6 EXERCISES 43
4 CRYPTOGRAPHIC PROTOCOLS 47
4.1 CRYPTOGRAPHIC PROTOCOLS 47
4.2 CRYPTOGRAPHIC HASH FUNCTIONS 48
4.3 AUTHENTICATION PROTOCOLS 51
4.4 DIGITAL SIGNATURES 53
4.5 SECRET SHARING SCHEMES 56
4.5.1 THE SHAMIR SECRET SHARING SCHEME 57
HTTP://D-NB.INFO/1066332215
X
* CONTENTS
4.5.2 ALTERNATIVES FOR SECRET SHARING PROTOCOLS 60
4.5.3 VERIFYING SECRET SHARING PROTOCOLS (VSS) 62
4.6 ZERO-KNOWLEDGE PROOFS 64
4.7 EXERCISES 68
5 ELEMENTARY NUMBER THEORETIC TECHNIQUES *
5.1 CRYPTOGRAPHY AND NUMBER THEORY 71
5.2 MODULAR ARITHMETIC 71
5.3 UNITS AND THE MULTIPLICATIVE GROUP Z* *
5.4 THE FIELD Z
P
AND FINITE FIELDS 78
5.5 FINITE ABELIAN GROUPS 81
5.6 CYCLIC GROUPS AND PRIMITIVE ELEMENTS
5.7 THE CHINESE REMAINDER THEOREM 86
5.8 EXERCISES 88
6 SOME NUMBER THEORETIC ALGORITHMS 91
6.1 ALGORITHMS FOR PUBLIC KEY CRYPTOGRAPHY 91
6.2 QUADRATIC RESIDUES AND SQUARE ROOTS 91
6.3 MODULAR SQUARE ROOTS 94
6.4 PRODUCTS OF TWO PRIMES 97
6.5 THE DISCRETE LOG PROBLEM 102
6.5.1 SHANK'S BABY STEP GIANT STEP ALGORITHM (BSGS) 103
6.5.2 POLLARD'S P-ALGORITHM 104
6.5.3 THE INDEX CALCULUS METHOD 108
6.6 PRIMALITY TESTING 110
6.6.1 SIEVING METHODS 111
6.6.2 FERMAT'S PRIMALITY TESTING 112
6.6.3 PSEUDOPRIMES AND PROBABILISTIC PRIMALITY TESTING 115
6.6.4 MILLER-RABIN PRIMALITY TESTING 119
6.6.5 MERSENNE PRIMES AND THE LUCAS-LEHMER TEST 121
6.7 EXERCISES 121
7 PUBLIC KEY CRYPTOGRAPHY 125
7.1 PUBLIC KEY CRYPTOGRAPHY 125
7.2 STANDARD MODEL FOR PUBLIC KEY ENCRYPTION 127
7.3 THE DIFFIE-HELLMAN KEY EXCHANGE AND PROTOCOL 128
7.4 ELGAMAL ENCRYPTION 130
7.4.1 GENERALIZATIONS OF ELGAMAL 133
7.5 THE RSA ALGORITHM AND PROTOCOL 133
7.5.1 THE RSA CRYPTOSYSTEM 135
7.5.2 RSA AS A BLOCK CIPHER 137
7.5.3 PRACTICAL IMPLEMENTATION OF RSA 141
*71
*74
82
CONTENTS *
XI
7.5.4 FEASIBILITY OF THE RSA ALGORITHM 143
7.5.5 SECURITY OF RSA 143
7.5.6 CRYPTANALYSIS OF RSA 144
7.6 RABIN ENCRYPTION 145
7.6.1 QUADRATIC RESIDUES AND RABIN ENCRYPTION 145
7.6.2 THE RABIN CRYPTOSYSTEM 147
7.6.3 SECURITY EQUIVALENCE OF THE RABIN CRYPTOSYSTEM 148
7.7 SESSION KEYS AND MIXED ENCRYPTION 149
7.8 THE RSA SIGNATURE METHOD 150
7.9 EXERCISES 151
8 ELLIPTIC CURVE CRYPTOGRAPHY 155
8.1 THE ELGAMAL AND ELLIPTIC CURVE ENCRYPTION SYSTEM 155
8.2 ELLIPTIC CURVES 156
8.2.1 FIELDS AND FIELD EXTENSIONS 156
8.2.2 ELLIPTIC CURVES 160
8.2.3 ELLIPTIC CURVE GROUPS 162
8.2.4 THE ORDER OF AN ELLIPTIC CURVE GROUP 165
8.2.5 CALCULATING POINTS IN ELLIPTIC CURVE GROUPS 167
8.3 ELLIPTIC CURVE CRYPTOGRAPHY 172
8.4 CRYPTOANALYSIS OF ELLIPTIC CURVE CRYPTOSYSTEMS 173
8.5 THE MOV-ALGORITHM 174
8.6 THE ELLIPTIC CURVE DIGITAL SIGNATURE 178
8.7 EXERCISES 180
9 BASIC CONCEPTS FROM GROUP THEORY 183
9.1 GROUPS AND GROUP THEORY 183
9.2 COSETS AND NORMAL SUBGROUPS 185
9.3 EXAMPLES OF GROUPS 187
9.4 GENERATORS AND GROUP PRESENTATIONS 191
9.5 FREE GROUPS AND GROUP PRESENTATIONS 193
9.6 GROUP PRESENTATIONS 198
9.6.1 THE MODULAR GROUP 200
9.7 PRESENTATIONS OF SUBGROUPS 204
9.8 GROUP DECISION PROBLEMS 206
9.9 GROUP AMALGAMS 208
9.10 EXERCISES 213
10 GROUP BASED CRYPTOGRAPHY 217
10.1 GROUP BASED METHODS 217
10.2 THE MAGNUS METHOD 218
10.2.1 THE WAGNER-MAGYARIK METHOD 219
XII
* CONTENTS
10.3 FREE GROUP CRYPTOSYSTEMS 220
10.3.1 AN IMPLEMENTATION WITHIN THE CLASSICAL MODULAR GROUP 223
10.3.2 A VARIATION USING THE MAGNUS REPRESENTATION 224
10.4 CRYPTOGRAPHIC PROTOCOLS USING GROUPS 229
10.5 NON-ABELIAN DIGITAL SIGNATURES 230
10.6 PASSWORD SECURITY 231
10.6.1 THE STRONG GENERIC FREE GROUP PROPERTY 235
10.6.2 SECURITY ANALYSIS OF THE GROUP RANDOMIZER PROTOCOLS 239
10.6.3 ACTUAL IMPLEMENTATION OF A GROUP RANDOMIZER SYSTEM PROTOCOL 240
10.7 A SECRET SHARING SCHEME 241
10.8 EXERCISES 242
11
BRAID GROUP CRYPTOGRAPHY 245
11 1
CRYPTOGRAPHIC PLATFORMS AND PLATFORM GROUPS 245
11 2 THE KO-LEE AND AAG PROTOCOLS 246
11 2.1
THE KO-LEE PROTOCOL 247
11 2.2
THE ANSHEL-ANSHEL-GOLDFELD PROTOCOL 250
11
3
SOME OTHER GROUP BASED CRYPTOSYSTEMS 253
11
4
THE SHAMIR THREE-PASS 255
11
5
HARD GROUP THEORETIC PROPERTIES 257
11 6
BRAID GROUP CRYPTOGRAPHY 258
11
7
THE BRAID GROUPS 259
11 7.1
THE ARTIN PRESENTATION 262
11 7.2 NORMAL FORMS WITHIN B
N
263
11
7.3
THE PURE BRAID GROUP FOR B
N
267
11
7.4
LINEAR REPRESENTATIONS OF B
N
267
11
8
CRYPTANALYSIS OF BRAID GROUP CRYPTOSYSTEMS 269
11 8.1
ATTACKS ON THE CONJUGACY SEARCH PROBLEM 270
11
8.2
LENGTH BASED ATTACKS 270
11 8.3
REPRESENTATION THEORETIC ATTACKS 271
11
8.4
BRAID GROUP SECURITY SUMMARY 272
11
9
SOME OTHER BRAID GROUP BASED PROTOCOLS 273
11 10 EXERCISES 273
12 FURTHER APPLICATIONS 275
12.1 FINITELY PRESENTED GROUPS AND CRYPTOGRAPHY 275
12.2 GROUP THEORY FOR ACCESS CONTROL 276
12.3 PUBLIC KEY CONTROL GROUPS 279
12.4 DIOPHANTINE CONTROL SECURITY GROUPS 281
12.5 THE SOCIAL SECURITY CONTROL GROUPS 286
12.6 FURTHER EXTENSIONS OF DIFFIE-HELLMAN AND RSA 292
12.7 EXERCISES 293
CONTENTS *
XIII
13 COMMUTATIVE GRBBNER BASIS METHODS 297
13.1 COMMUTATIVE GROBNER BASES 297
13.2 COMMUTATIVE GROBNER BASIS CRYPTOSYSTEMS 301
13.3 ALGEBRAIC ATTACKS USING GROBNER BASES 306
13.3.1 THE GROBNER BASIS ATTACK 309
13.3.2 THE INTEGER PROGRAMMING ATTACK 311
13.3.3 THE SAT ATTACK 312
13.4 EXERCISES 314
14 NON-COMMUTATIVE GRSBNER BASIS METHODS 317
14.1 NON-COMMUTATIVE GROBNER BASES 317
14.2 ELIMINATION AND ITS APPLICATIONS 324
14.3 GROBNER BASES OF MODULES 328
14.4 NON-COMMUTATIVE GB CRYPTOSYSTEMS 335
14.5 EXERCISES 342
15 LATTICE-BASED CRYPTOGRAPHY 345
15.1 LATTICE-BASED CRYPTOGRAPHY 345
15.2 GENERAL CRYPTOPRIMITIVES 346
15.3 LATTICES AND THEIR PROPERTIES 348
15.3.1 THE GEOMETRY OF NUMBERS 351
15.4 HARD LATTICE PROBLEMS 353
15.5 LATTICE REDUCTION AND BABAI'S ALGORITHM 355
15.6 MAIN LATTICE BASED CRYPTOSYSTEMS 357
15.6.1 AJTAI'S HASH FUNCTION AND CRYPTOSYSTEM 358
15.6.2 THE AJTAI-DWORK CRYPTOSYSTEM 358
15.6.3 THE GGH CRYPTOSYSTEM 360
15.6.4 NTRU CRYPTOSYSTEM 361
15.7 SECURITY PROOFS 361
15.8 EXERCISES 362
BIBLIOGRAPHY 365
INDEX 371 |
| any_adam_object | 1 |
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| dewey-search | 005.82 |
| dewey-sort | 15.82 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-08-03T02:32:16Z |
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| isbn | 9783110372762 3110372762 |
| language | English |
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| physical | XIII, 376 S. Diagramme 24 cm |
| publishDate | 2015 |
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| spelling | A course in mathematical cryptography Gilbert Baumslag ... Berlin/Boston De Gruyter 2015 XIII, 376 S. Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Literaturangaben Kryptologie (DE-588)4033329-2 gnd rswk-swf Fachhochschul-/Hochschulausbildung (DE-588)4123623-3 Lehrbuch gnd-content Kryptologie (DE-588)4033329-2 s 1\p DE-604 Baumslag, Gilbert 1933-2014 Sonstige (DE-588)1065372957 oth Erscheint auch als Online-Ausgabe, PDF 978-3-11-037277-9 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-038616-5 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5145785&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028124142&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | A course in mathematical cryptography Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4033329-2 (DE-588)4123623-3 |
| title | A course in mathematical cryptography |
| title_auth | A course in mathematical cryptography |
| title_exact_search | A course in mathematical cryptography |
| title_full | A course in mathematical cryptography Gilbert Baumslag ... |
| title_fullStr | A course in mathematical cryptography Gilbert Baumslag ... |
| title_full_unstemmed | A course in mathematical cryptography Gilbert Baumslag ... |
| title_short | A course in mathematical cryptography |
| title_sort | a course in mathematical cryptography |
| topic | Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Kryptologie Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=5145785&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028124142&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT baumslaggilbert acourseinmathematicalcryptography |