Cryptography and secure communication:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2014
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 587 S. Ill., graph. Darst. |
| ISBN: | 9781107014275 1107014271 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804152157846372352 |
|---|---|
| adam_text | Titel: Cryptography and secure communication
Autor: Blahut, Richard E
Jahr: 2014
Contents
Preface
Acknowledgments
Introduction
1.1 Classical cryptography
1.2 Notions of cryptographic secrecy
1.3 Block ciphers
1.4 Stream ciphers
1.5 Public-key cryptography
1.6 Iterated and cascade ciphers
1.7 Cryptanalysis
1.8 Implementation attacks
1.9 Complexity theory
1.10 Authentication and identification
1.11 Ownership protection
1.12 Covert communications
1.13 History of information protection
2 The integers
2.1 Basic number theory
2.2 The euclidean algorithm
2.3 Prime fields
2.4 Quadratic residues
2.5 Quadratic reciprocity
2.6 The Jacobi symbol
2.7 Primality testing
page XV
xix
1
2
5
7
11
13
14
15
18
19
21
23
24
25
32
32
38
41
42
47
51
55
viii Contents
2.8 The Fermât algorithm 56
2.9 The Solovay-Strassen algorithm 59
2.10 The Miller-Rabin algorithm 61
2.11 Factoring of integers 65
2.12 The Pollard algorithm for factoring 67
2.13 Square roots in a prime field 69
3 Cryptography based on the integer ring 82
3.1 Biprime cryptography 83
3.2 Implementing biprime cryptography 85
3.3 Protocol attacks on biprime cryptography 87
3.4 Direct attacks on biprime encryption 89
3.5 Factoring biprimes 90
3.6 The quadratic sieve 91
3.7 The number-field sieve 95
3.8 The Rabin cryptosystem 99
3.9 The rise and fall of knapsack cryptosystems 102
4 Cryptography based on the discrete logarithm 107
4.1 Diffie-Hellman key exchange 107
4.2 Discrete logarithms 109
4.3 The Elgamal cryptosystem 110
4.4 Trapdoor one-way functions 112
4.5 The Massey-Omura cryptosystem 113
4.6 The Pohlig-Hellman algorithm 114
4.7 The Shanks algorithm 121
4.8 The Pollard algorithm for discrete logarithms 123
4.9 The method of index calculus 127
4.10 Complexity of the discrete-log problem 129
5 Information-theoretic methods in cryptography 135
5.1 Probability space 136
5.2 Entropy 137
5.3 Perfect secrecy 139
Contents
5.4 The Shannon-McMillan theorem
5.5 Unicity distance
5.6 Entropy of natural language
5.7 Entropy expansion
5.8 Data compaction
5.9 The wiretap channel
Block ciphers
6.1 Block substitution
6.2 The Feistel network
6.3 The Data Encryption Standard
6.4 Using the Data Encryption Standard
6.5 Double and triple DES encryption
6.6 The Advanced Encryption Standard
6.7 Differential cryptanalysis
6.8 Linear cryptanalysis
Stream ciphers
7.1 State-dependent encryption
7.2 Additive stream ciphers
7.3 Linear shift-register sequences
7.4 The linear-complexity attack
7.5 Analysis of linear complexity
7.6 Keystreams from nonlinear feedback
7.7 Keystreams from nonlinear combining
7.8 Keystreams from nonlinear functions
7.9 The correlation attack
7.10 Pseudorandom sequences
7.11 Nonlinear sets of sequences
Authentication and ownership protection
8.1 Authentication
8.2 Identification
8.3 Authentication signatures
141
144
147
149
150
152
160
160
162
164
168
170
171
176
177
181
182
183
185
189
190
194
196
199
207
210
212
218
219
219
220
X Contents
8.4 Hash functions 223
8.5 The birthday attack 225
8.6 Iterated hash constructions 227
8.7 Formal hash functions 228
8.8 Practical hash functions 230
9 Groups, rings, and fields 238
9.1 Groups 239
9.2 Rings 242
9.3 Fields 243
9.4 Prime fields 245
9.5 Binary fields and ternary fields 246
9.6 Univariate polynomials 247
9.7 Extension fields 255
9.8 The multiplication cycle in a finite field 261
9.9 Cyclotomic polynomials 263
9.10 Vector spaces 267
9.11 Linear algebra 269
9.12 The Fourier transform 272
9.13 Existence of finite fields 276
9.14 Bivariate polynomials 281
9.15 Modular reduction and quotient groups 285
9.16 Factoring of univariate polynomials 287
10 Cryptography based on elliptic curves 294
10.1 Elliptic curves 295
10.2 Elliptic curves over finite fields 300
10.3 The operation of point addition 303
10.4 The order of an elliptic curve 308
10.5 The group of an elliptic curve 310
10.6 Supersingular elliptic curves 312
10.7 Elliptic curves over binary fields 315
10.8 Computation of point multiples 319
10.9 Elliptic curve cryptography 320
10.10 The projective plane 323
10.11 Point counting in an extension field 325
xi Contents
10.12 Morphisms of elliptic curves over the rationals 333
10.13 Morphisms of elliptic curves over finite fields 337
10.14 Point counting in a ground field 343
10.15 The method of xedni calculus 347
10.16 Elliptic curves and the complex field 351
10.17 Curves constructed using complex multiplication 355
11 Cryptography based on hyperelliptic curves 369
11.1 Hyperelliptic curves 369
11.2 Coordinate rings and function fields 374
11.3 Poles and zeros 376
11.4 Divisors 379
11.5 Principal divisors 383
11.6 Principal divisors on elliptic curves 385
11.7 Jacobians as quotient groups 390
11.8 The group of a hyperelliptic curve 392
11.9 Semireduced divisors and jacobians 394
11.10 The Mumford transform 396
11.11 The Cantor reduction algorithm 402
11.12 Reduced divisors and jacobians 405
11.13 The Cantor-Koblitz algorithm 406
11.14 Hyperelliptic-curve cryptography 411
11.15 Order of the hyperelliptic jacobians 412
11.16 Some examples of the jacobian group 414
12 Cryptography based on bilinear pairings 422
12.1 Bilinear pairings 423
12.2 Pairing-based cryptography 425
12.3 Pairing-based key exchange 426
12.4 Identity-based encryption 428
12.5 Pairing-based signatures 431
12.6 Attacks on the bilinear Diffie-Hellman protocol 432
12.7 Torsion points and embedding degree 433
12.8 The torsion structure theorem 438
12.9 The structure of a pairing 446
12.10 Attacks using bilinear pairings 448
xii Contents
12.11 The Tate pairing 451
12.12 The Miller algorithm 457
12.13 The Weil pairing 460
12.14 Pairing-friendly curves 464
12.15 Barreto-Naehrig elliptic curves 465
12.16 More pairing-friendly curves 468
13 Implementation 475
13.1 Pairing enhancements 476
13.2 Accelerated pairings 478
13.3 Doubling and tripling 482
13.4 Point representations 484
13.5 Algorithms for elliptic-curve arithmetic 486
13.6 Modular addition in an integer ring 487
13.7 Modular multiplication in an integer ring 488
13.8 Representations of binary fields 491
13.9 Multiplication and squaring in a binary field 495
13.10 Complementary bases 500
13.11 Division in a finite field 503
14 Cryptographic protocols for security and identification 508
14.1 Protocols for cryptographic security 509
14.2 Identification protocols 510
14.3 Zero-knowledge protocols 512
14.4 Methods of secure identification 513
14.5 Signature protocols 519
14.6 Protocols for secret sharing 524
15 More public-key cryptography 527
15.1 Introduction to lattices 528
15.2 Elementary problems in lattice theory 535
15.3 Reduction of a lattice basis 536
15.4 Lattice-based cryptography 543
15.5 Attacks on lattice cryptosystems 547
xiii Contents
15.6 Introduction to codes 548
15.7 Subspace projection 552
15.8 Code-based cryptography 553
Bibliography
Index
558
576
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