Fundamentals of cryptology: a professional reference and interactive tutorial
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer
2001
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | The Kluwer international series in engineering and computer science
528 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Frühere Ausg. u.d.T.: Tilborg, Henk C. van: An introduction to cryptology |
| Beschreibung: | XIV, 491 S. Ill., graph. Darst. CD-ROM (12 cm) |
| ISBN: | 0792386752 |
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| 245 | 1 | 0 | |a Fundamentals of cryptology |b a professional reference and interactive tutorial |c by Henk C. A. van Tilborg |
| 250 | |a 2. print. | ||
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| 500 | |a Frühere Ausg. u.d.T.: Tilborg, Henk C. van: An introduction to cryptology | ||
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Datensatz im Suchindex
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| adam_text | Titel: Fundamentals of cryptology
Autor: Tilborg, Henk C. A. van
Jahr: 2001
FUNDAMENTALS OF
CRYPTOLOGY
A Professional Reference
and Interactive Tutorial
by
Henk C.A. van Tilborg
Eindhoven University of Technology
The Netherlands
w
KLUWER ACADEMIC PUBLISHERS
Boston / Dordrecht / London
Contents
Preface xiii
1 Introduction 1
1.1 Introduction and Terminology 1
1.2 Shannon s Description of a Conventional Cryptosystem 2
1.3 Statistical Description of a Plaintext Source 4
1.4 Problems 7
2 Classical Cryptosystems 9
2.1 Caesar, Simple Substitution, Vigenere 9
2.1.1 Caesar Cipher 9
2.1.2 Simple Substitution 10
The System and its Main Weakness 10
Cryptanalysis by The Method of a Probable Word 11
2.1.3 Vigenere Cryptosystem 13
2.2 The Incidence of Coincidences, Kasiski s Method 16
2.2.1 The Incidence of Coincidences 16
2.2.2 Kasiski s Method 19
2.3 Vernam, Playfair, Transpositions, Hagelin, Enigma 20
2.3.1 The One-Time Pad 20
2.3.2 The Playfair Cipher 20
2.3.3 Transposition Ciphers 21
2.3.4 Hagelin 22
2.3.5 Enigma 24
2.4 Problems 25
3 Shift Register Sequences 27
3.1 Pseudo-Random Sequences 27
3.2 Linear Feedback Shift Registers 31
3.2.1 (Linear) Feedback Shift Registers 31
3.2.2 PN-Sequences 34
3.2.3 Which Characteristic Polynomials give PN-Sequences? 38
3.2.4 An Alternative Description of fl(/) for Irreducible / 44
3.2.5 Cryptographic Properties of PN Sequences 46
3.3 Non-Linear Algorithms 49
3.3.1 Minimal Characteristic Polynomial 49
3.3.2 The Berlekamp-Massey Algorithm 52
3.3.3 A Few Observations about Non-Linear Algorithms 58
vi
3.4 Problems 60
4 Block Ciphers 63
4.1 Some General Principles 63
4.1.1 Some Block Cipher Modes 63
Codebook Mode 63
Cipher Block Chaining 64
Cipher Feedback Mode 65
4.1.2 An Identity Verification Protocol 66
4.2 DES 67
DES 67
Triple DES 69
4.3 IDEA 70
4.4 Further Remarks 72
4.5 Problems 73
5 Shannon Theory 75
5.1 Entropy, Redundancy, and Unicity Distance 75
5.2 Mutual Information and Unconditionally Secure Systems 80
5.3 Problems 85
6 Data Compression Techniques 87
6.1 Basic Concepts of Source Coding for Stationary Sources 87
6.2 Huffman Codes 93
6.3 Universal Data Compression - The Lempel-Ziv Algorithms 97
Initialization 98
Encoding 99
Decoding 101
6.4 Problems 103
7 Public-Key Cryptography 105
7.1 The Theoretical Model 105
7.1.1 Motivation and Set-up 105
7.1.2 Confidentiality 106
7.1.3 Digital Signature 107
7.1.4 Confidentiality and Digital Signature 108
7.2 Problems 109
8 Discrete Logarithm Based Systems 111
8.1 The Discrete Logarithm System 111
8.1.1 The Discrete Logarithm Problem 111
8.1.2 The Diffie-Hellman Key Exchange System 114
8.2 Other Discrete Logarithm Based Systems 116
8.2.1 ElGamal s Public-Key Cryptosystems 116
Setting It Up 116
ElGamal s Secrecy System 116
ElGamal s Signature Scheme 118
8.2.2 Further Variations 119
Digital Signature Standard 119
Schnorr s Signature Scheme 120
The Nyberg-Rueppel Signature Scheme 120
8.3 How to Take Discrete Logarithms 121
8.3.1 The Pohlig-Hellman Algorithm 121
Special Case: q - 1 = 2 121
General Case: q - 1 has only small prime factors 123
An Example of the Pohlig-Hellman Algorithm 124
8.3.2 The Baby-Step Giant-Step Method 128
8.3.3 The Pollard-p Method 131
8.3.4 The Index-Calculus Method / . 135
General Discussion 135
Z*, i.e. the Multiplicative Group of GF(p) 136
GF(2n
) 141
8.4 Problems 145
9 RSA Based Systems 147
9.1 The RSA System 147
9.1.1 Some Mathematics 147
9.1.2 Setting Up the System 148
Step 1 Computing the Modulus 148
Step 2 Computing the Exponents ey and dy 149
Step 3 Making Public: ey and ny 150
9.1.3 RSA for Privacy 150
9.1.4 RSA for Signatures 153
9.1.5 RSA for Privacy and Signing 154
9.2 The Security of RSA: Some Factorization Algorithms 156
9.2.1 What the Cryptanalist Can Do 156
9.2.2 A Factorization Algorithm for a Special Class of Integers 158
Pollard s p - 1 Method 158
9.2.3 General Factorization Algorithms 161
The Pollard-£ Method 161
Random Square Factoring Methods 162
Quadratic Sieve 167
9.3 Some Unsafe Modes for RSA 169
9.3.1 A Small Public Exponent 169
Sending the Same Message to More Receivers ... 169
Sending Related Messages to a Receiver with Small Public Exponent 171
9.3.2 A Small Secret Exponent; Wiener s Attack
9.3.3 Some Physical Attacks
Timing Attack
The Microwave Attack
9.4 How to Generate Large Prime Numbers; Some Primality Tests
9.4.1 Trying Random Numbers
9.4.2 Probabilistic Primality Tests
The Solovay and Strassen Primality Test
Miller-Rabin Test
9.4.3 A Deterministic Primality Test
9.5 The Rabin Variant
9.5.1 The Encryption Function
9.5.2 Decryption
Precomputation
Finding a Square Root Modulo a Prime Number
The Four Solutions
9.5.3 How to Distinguish Between the Solutions
9.5.4 The Equivalence of Breaking Rabin s Scheme and Factoring
9.6 Problems
10 Elliptic Curves Based Systems
10.1 Some Basic Facts of Elliptic Curves
10.2 The Geometry of Elliptic Curves
A Line Through Two Distinct Points
A Tangent Line
10.3 Addition of Points on Elliptic Curves
10.4 Cryptosystems Defined over Elliptic Curves
10.4.1 The Discrete Logarithm Problem over Elliptic Curves
10.4.2 The Discrete Logarithm System over Elliptic Curves
10.4.3 The Security of Discrete Logarithm Based EC Systems
10.5 Problems
11 Coding Theory Based Systems
11.1 Introduction to Goppa codes
11.2 The McEliece Cryptosystem
11.2.1 The System
Setting Up the System
Encryption
Decryption
11.2.2 Discussion
Summary and Proposed Parameters
Heuristics of the Scheme
Not a Signature Scheme
11.2.3 Security Aspects 244
Guessing SB and PB 244
Exhaustive Codewords Comparison 245
Syndrome Decoding 246
Guessing Correct and Independent Coordinates 248
Multiple Encryptions of the Same Message 251
11.2.4 A Small Example of the McEliece System 252
11.3 Another Technique to Decode Linear Codes 255
11.4 The Niederreiter Scheme 260
11.5 Problems 261
12 Knapsack Based Systems 263
12.1 The Knapsack System 263
12.1.1 The Knapsack Problem 263
12.1.2 The Knapsack System 265
Setting Up the Knapsack System 265
Encryption 267
Decryption 267
A Further Discussion 268
12.2 The L3
-Attack 270
12.2.1 Introduction 270
12.2.2 Lattices 271
12.2.3 A Reduced Basis 274
12.2.4 The L3
-Attack 275
12.2.5 The L3
-Lattice Basis Reduction Algorithm 277
12.3 The Chor-Rivest Variant 279
Setting Up the System 279
Encryption 282
Decryption 284
12.4 Problems 286
13 Hash Codes Authentication Techniques 287
13.1 Introduction 287
13.2 Hash Functions and MACs 288
13.3 Unconditionally Secure Authentication Codes 290
13.3.1 Notions and Bounds 290
13.3.2 The Projective Plane Construction 295
A Finite Projective Plane 295
A General Construction of a Projective Plane 299
The Projective Plane Authentication Code 303
13.3.3 A-Codes From Orthogonal Arrays 305
13.3.4 A-Codes From Error-Correcting Codes
13.4 Problems
309
314
14 Zero Knowledge Protocols 315
14.1 The Fiat-Shamir Protocol 315
14.2 Schnorr s Identification Protocol 317
14.3 Problems 320
15 Secret Sharing Systems 321
15.1 Introduction 321
15.2 Threshold Schemes 323
15.3 Threshold Schemes with Liars 326
15.4 Secret Sharing Schemes 328
15.5 Visual Secret Sharing Schemes 333
15.6 Problems 341
A Elementary Number Theory 343
A.l Introduction 343
A.2 Euclid s Algorithm 348
A.3 Congruences, Fermat, Euler, Chinese Remainder Theorem 352
A.3.1 Congruences 352
A.3.2 Euler and Fermat 354
A.3.3 Solving Linear Congruence Relations 358
A.3.4 The Chinese Remainder Theorem 361
A.4 Quadratic Residues 364
A.5 Continued Fractions 369
A.6 Möbius Inversion Formula, the Principle of Inclusion and Exclusion 378
A.6.1 Möbius Inversion Formula 378
A.6.2 The Principle of Inclusion and Exclusion 380
A.7 Problems 382
Finite Fields 383
B.l Algebra 383
B.l.l Abstract Algebra 383
Set operations 383
Group 384
Ring 386
Ideal 386
Field 387
Equivalence Relations 387
Cyclic Groups 389
B.1.2 Linear Algebra 391
Vector Spaces and Subspaces 391
Linear Independence, Basis and Dimension 392
B.2
.
.4
.4.1
.4.2
.4.4
.4.5
.4.6
.5
Inner Product, Orthogonality
Constructions
The Number of Irreducible Polynomials over
The Structure of Finite Fields
The Cyclic Structure of a Finite Field
The Cardinality of a Finite Field
Some Calculus Rules over Finite Fields
GF(q)
; Conjugates
Minimal Polynomials, Primitive Polynomials
Further Properties
Cyclotomic Polynomials
Problems
Relevant Famous Mathematicians
Euclid of Alexandria
Leonhard Euler
Pierre de Fermat
Evariste Galois
Johann Carl Friedrich Gauss
Karl Gustav Jacob Jacobi
Adrien-Marie Legendre
August Ferdinand Möbius
Joseph Henry Maclagen Wedderburn
D New Functions
References
Symbols and Notations
393
395
401
405
405
409
411
413
418
420
423
425
425
426
428
434
439
445
446
447
451
453
461
469
Index
|
| any_adam_object | 1 |
| author | Tilborg, Henk C. van |
| author_facet | Tilborg, Henk C. van |
| author_role | aut |
| author_sort | Tilborg, Henk C. van |
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| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.9.A25 |
| callnumber-search | QA76.9.A25 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 ST 276 |
| ctrlnum | (OCoLC)248958986 (DE-599)BVBBV014888482 |
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| dewey-ones | 005 - Computer programming, programs, data, security |
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| dewey-search | 005.8 |
| dewey-sort | 15.8 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 2. print. |
| format | Book |
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| spelling | Tilborg, Henk C. van Verfasser aut Fundamentals of cryptology a professional reference and interactive tutorial by Henk C. A. van Tilborg 2. print. Boston [u.a.] Kluwer 2001 XIV, 491 S. Ill., graph. Darst. CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier The Kluwer international series in engineering and computer science 528 Frühere Ausg. u.d.T.: Tilborg, Henk C. van: An introduction to cryptology Kryptologie (DE-588)4033329-2 gnd rswk-swf Kryptologie (DE-588)4033329-2 s DE-604 The Kluwer international series in engineering and computer science 528 (DE-604)BV023545171 528 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010068321&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Fundamentals of cryptology a professional reference and interactive tutorial |
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