Tilborg Fundamentals of Cryptology

A Professional Reference and Interactive Tutorial
1. Auflage 2006
ISBN: 978-0-306-47053-0
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 528, 507 Seiten

Reihe: The Springer International Series in Engineering and Computer Science

The protection of sensitive information against unauthorized access or fraudulent changes has been of prime concern throughout the centuries. Modern communication techniques, using computers connected through networks, make all data even more vulnerable to these threats. In addition, new issues have surfaced that did not exist previously, for example, adding a signature to an electronic document. Cryptology addresses the above issues - it is at the foundation of all information security.

The techniques employed to this end have become increasingly mathematical in nature. This work serves as an introduction to modern cryptographic methods. After a brief survey of classical cryptosystems, it concentrates on three main areas. First, stream ciphers and block ciphers are discussed. These systems have extremely fast implementations, but sender and receiver must share a secret key. Second, the book presents public key cryptosystems, which make it possible to protect data without a prearranged key. Their security is based on intractable mathematical problems, such as the factorization of large numbers.

The remaining chapters cover a variety of topics, including zero-knowledge proofs, secret sharing schemes and authentication codes. Two appendices explain all mathematical prerequisites in detail: one presents elementary number theory (Euclid's Algorithm, the Chinese Remainder Theorem, quadratic residues, inversion formulas, and continued fractions) and the other introduces finite fields and their algebraic structure. The text is an updated and improved version of "An Introduction to Cryptology," originally published in 1988.

Apart from a revision of the existing material, there are many new sections, and two new chapters on elliptic curves and authentication codes, respectively. In addition, the book is accompanied by a full text electronic version on CD-ROM as an interactive Mathematica manuscript. "Basic Concepts in Cryptology" should be of interest to computer scientists, mathematicians, and researchers, students, and practitioners in the area of cryptography.

Autoren/Hrsg.

Tilborg, Henk C. A. van

Inhaltsverzeichnis

1;Contents;6
2;Preface;14
3;1 Introduction;16
3.1;1.1 Introduction and Terminology;16
3.2;1.2 Shannon's Description of a Conventional Cryptosystem;17
3.3;1.3 Statistical Description of a Plaintext Source;19
3.4;1.4 Problems;22
4;2 Classical Cryptosystems;24
4.1;2.1 Caesar, Simple Substitution, Vigenère;24
4.2;2.2 The Incidence of Coincidences, Kasiski's Method;31
4.3;2.3 Vernam, Playfair, Transpositions, Hagelin, Enigma;35
4.4;2.4 Problems;40
5;3 Shift Register Sequences;42
5.1;3.1 Pseudo-Random Sequences;42
5.2;3.2 Linear Feedback Shift Registers;46
5.3;3.3 Non- Linear Algorithms;64
5.4;3.4 Problems;75
6;4 Block Ciphers;78
6.1;4.1 Some General Principles;78
6.2;4.2 DES;82
6.3;4.3 IDEA;85
6.4;4.4 Further Remarks;87
6.5;4.5 Problems;88
7;5 Shannon Theory;90
7.1;5.1 Entropy, Redundancy, and Unicity Distance;90
7.2;5.2 Mutual Information and Unconditionally Secure Systems;95
7.3;5.3 Problems;100
8;6 Data Compression Techniques;102
8.1;6.1 Basic Concepts of Source Coding for Stationary Sources;102
8.2;6.2 Huffman Codes;108
8.3;6.3 Universal Data Compression - The Lempel-Ziv Algorithms;112
8.4;6.4 Problems;118
9;7 Public-Key Cryptography;120
9.1;7.1 The Theoretical Model;120
9.2;7.2 Problems;124
10;8 Discrete Logarithm Based Systems;126
10.1;8.1 The Discrete Logarithm System;126
10.2;8.2 Other Discrete Logarithm Based Systems;131
10.3;8.3 How to Take Discrete Logarithms;136
10.4;8.4 Problems;160
11;9 RSA Based Systems;162
11.1;9.1 The RSA System;162
11.2;9.2 The Security of RSA: Some Factorization Algorithms;171
11.3;9.3 Some Unsafe Modes for RSA;184
11.4;9.4 How to Generate Large Prime Numbers; Some Primality Tests;197
11.5;9.5 The Rabin Variant;212
11.6;9.6 Problems;224
11.7;9.5 The Rabin Variant;212
12;10 Elliptic Curves Based Systems;228
12.1;10.1 Some Basic Facts of Elliptic Curves;228
12.2;10.2 The Geometry of Elliptic Curves;231
12.3;10.3 Addition of Points on Elliptic Curves;239
12.4;10.4 Cryptosystems Defined over Elliptic Curves;245
12.5;10.5 Problems;251
13;11 Coding Theory Based Systems;252
13.1;11.1 Introduction to Goppa codes;252
13.2;11.2 The McEliece Cryptosystem;256
13.3;11.3 Another Technique to Decode Linear Codes;270
13.4;11.4 The Niederreiter Scheme;275
13.5;11.5 Problems;276
14;12 Knapsack Based Systems;278
14.1;12.1 The Knapsack System;278
14.2;12.2 The L3- Attack;285
14.3;12.3 The Chor-Rivest Variant;294
14.4;12.4 Problems;301
15;13 Hash Codes & Authentication Techniques;302
15.1;13.1 Introduction;302
15.2;13.2 Hash Functions and MAC's;303
15.3;13.3 Unconditionally Secure Authentication Codes;305
15.4;13.4 Problems;329
16;14 Zero Knowledge Protocols;330
16.1;14.1 The Fiat-Shamir Protocol;330
16.2;14.2 Schnorr's Identification Protocol;332
16.3;14.3 Problems;335
17;15 Secret Sharing Systems;336
17.1;15.1 Introduction;336
17.2;15.2 Threshold Schemes;338
17.3;15.3 Threshold Schemes with Liars;341
17.4;15.4 Secret Sharing Schemes;343
17.5;15.5 Visual Secret Sharing Schemes;348
17.6;15.6 Problems;356
18;Appendix A Elementary Number Theory;358
18.1;A.1 Introduction;358
18.2;A.2 Euclid's Algorithm;363
18.3;A.3 Congruences, Fermat, Euler, Chinese Remainder Theorem;367
18.4;A.4 Quadratic Residues;379
18.5;A.5 Continued Fractions;384
18.6;A.6 Möbius Inversion Formula, the Principle of Inclusion and Exclusion;393
18.7;A.7 Problems;397
19;Appendix B Finite Fields;398
19.1;B.1 Algebra;398
19.2;B.2 Constructions;410
19.3;B.3 The Number of Irreducible Polynomials over GF(q);416
19.4;B.4 The Structure of Finite Fields;420
19.5;B.5 Problems;438
20;Appendix C Relevant Famous Mathematicians;440
20.1;Euclid of Alexandria;440
20.2;Leonhard Euler;441
20.3;Pierre de Fermat;443
20.4;Evariste Galois;449
20.5;Johann Carl Friedrich Gauss;454
20.6;Karl Gustav Jacob Jacobi;460
20.7;Adrien-Marie Legendre;461
20.8;August Ferdinand Möbius;462
20.9;Joseph Henry Maclagen Wedderburn;466
21;Appendix D New Functions;468
22;References;476
23;Symbols and Notations;484
24;Index;486
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