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Fundamentals of Cryptology: A Professional Reference and Interactive Tutorial Softcover reprint of the original 1st ed. 2002Suurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781475782837.html
Märksõnad:
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, e.g. 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. Fundamentals of Cryptology 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.
Fundamentals of Cryptology 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.
Fundamentals of Cryptology will be of interest to computer scientists, mathematicians, and researchers, students, and practitioners in the area of cryptography.

Arvustused

`This is a thoroughly written wonderful book on cryptography! This excellent book is warmly recommended for mathematicians, computer scientists, for professors and students, and, as a reference book, for researchers in the area of cryptography.' Acta Scientiarum Mathematicarum, 69

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Springer Book Archives
Preface xiii
1 Introduction
1(8)
1.1 Introduction and Terminology
1(1)
1.2 Shannon's Description of a Conventional Cryptosystem
2(2)
1.3 Statistical Description of a Plaintext Source
4(3)
1.4 Problems
7(2)
2 Classical Cryptosystems
9(18)
2.1 Caesar, Simple Substitution, Vigenere
9(7)
2.1.1 Caesar Cipher
9(1)
2.1.2 Simple Substitution
10(1)
The System and its Main Weakness
10(1)
Cryptanalysis by The Method of a Probable Word
11(2)
2.1.3 Vigenere Cryptosystem
13(3)
2.2 The Incidence of Coincidences, Kasiski's Method
16(4)
2.2.1 The Incidence of Coincidences
16(3)
2.2.2 Kasiski's Method
19(1)
2.3 Vernam, Playfair, Transpositions, Hagelin, Enigma
20(5)
2.3.1 The One-Time Pad
20(1)
2.3.2 The Playfair Cipher
20(1)
2.3.3 Transposition Ciphers
21(1)
2.3.4 Hagelin
22(2)
2.3.5 Enigma
24(1)
2.4 Problems
25(2)
3 Shift Register Sequences
27(36)
3.1 Pseudo-Random Sequences
27(4)
3.2 Linear Feedback Shift Registers
31(18)
3.2.1 (Linear) Feedback Shift Registers
31(4)
3.2.2 PN-Sequences
35(3)
3.2.3 Which Characteristic Polynomials give PN-Sequences?
38(6)
3.2.4 An Alternative Description of Ω(f) for Irreducible f
44(2)
3.2.5 Cryptographic Properties of PN Sequences
46(3)
3.3 Non-Linear Algorithms
49(11)
3.3.1 Minimal Characteristic Polynomial
49(3)
3.3.2 The Berlekamp-Massey Algorithm
52(6)
3.3.3 A Few Observations about Non-Linear Algorithms
58(2)
3.4 Problems
60(3)
4 Block Ciphers
63(12)
4.1 Some General Principles
63(4)
4.1.1 Some Block Cipher Modes
63(1)
Codebook Mode
63(1)
Cipher Block Chaining
64(1)
Cipher Feedback Mode
65(1)
4.1.2 An Identity Verification Protocol
66(1)
4.2 DES
67(3)
DES
67(2)
Triple DES
69(1)
4.3 IDEA
70(2)
4.4 Further Remarks
72(1)
4.5 Problems
73(2)
5 Shannon Theory
75(12)
5.1 Entropy, Redundancy, and Unicity Distance
75(5)
5.2 Mutual Information and Unconditionally Secure Systems
80(5)
5.3 Problems
85(2)
6 Data Compression Techniques
87(18)
6.1 Basic Concepts of Source Coding for Stationary Sources
87(5)
6.2 Huffman Codes
92(5)
6.3 Universal Data Compression - The Lempel-Ziv Algorithms
97(6)
Initialization
98(1)
Encoding
99(2)
Decoding
101(2)
6.4 Problems
103(2)
7 Public-Key Cryptography
105(6)
7.1 The Theoretical Model
105(4)
7.1.1 Motivation and Set-up
105(1)
7.1.2 Confidentiality
106(1)
7.1.3 Digital Signature
107(1)
7.1.4 Confidentiality and Digital Signature
108(1)
7.2 Problems
109(2)
8 Discrete Logarithm Based Systems
111(36)
8.1 The Discrete Logarithm System
111(5)
8.1.1 The Discrete Logarithm Problem
111(3)
8.1.2 The Diffie-Hellman Key Exchange System
114(2)
8.2 Other Discrete Logarithm Based Systems
116(4)
8.2.1 ElGamal's Public-Key Cryptosystems
116(1)
Setting It Up
116(1)
ElGamal's Secrecy System
116(1)
ElGamal's Signature Scheme
117(2)
8.2.2 Further Variations
119(1)
Digital Signature Standard
119(1)
Schnorr's Signature Scheme
120(1)
The Nyberg-Rueppel Signature Scheme
120(1)
8.3 How to Take Discrete Logarithms
120(25)
8.3.1 The Pohlig-Hellman Algorithm
121(1)
Special Case: q -1 = 2n
121(2)
General Case: q - 1 has only small prime factors
123(1)
An Example of the Pohlig-Hellman Algorithm
124(3)
8.3.2 The Baby-Step Giant-Step Method
127(3)
8.3.3 The Pollard-ρ Method
130(5)
8.3.4 The Index-Calculus Method
135(1)
General Discussion
135(1)
Z*p, i.e. the Multiplicative Group of GF(p)
136(5)
GF(2n)
141(4)
8.4 Problems
145(2)
9 RSA Based Systems
147(66)
9.1 The RSA System
147(9)
9.1.1 Some Mathematics
147(1)
9.1.2 Setting Up the System
148(1)
Step 1 Computing the Modulus nU
148(1)
Step 2 Computing the Exponents eU and dU
149(1)
Step 3 Making Public: eU and nU
150(1)
9.1.3 RSA for Privacy
150(3)
9.1.4 RSA for Signatures
153(1)
9.1.5 RSA for Privacy and Signing
154(2)
9.2 The Security of RSA: Some Factorization Algorithms
156(13)
9.2.1 What the Cryptanalist Can Do
156(2)
9.2.2 A Factorization Algorithm for a Special Class of Integers
158(1)
Pollard's p - 1 Method
158(3)
9.2.3 General Factorization Algorithms
161(1)
The Pollard-Q Method
161(1)
Random Square Factoring Methods
162(5)
Quadratic Sieve
167(2)
9.3 Some Unsafe Modes for RSA
169(13)
9.3.1 A Small Public Exponent
169(1)
Sending the Same Message to More Receivers ...
169(2)
Sending Related Messages to a Receiver with Small Public Exponent
171(5)
9.3.2 A Small Secret Exponent; Wiener's Attack
176(4)
9.3.3 Some Physical Attacks
180(1)
Timing Attack
180(1)
The "Microwave" Attack
180(2)
9.4 How to Generate Large Prime Numbers; Some Primality Tests
182(15)
9.4.1 Trying Random Numbers
182(2)
9.4.2 Probabilistic Primality Tests
184(1)
The Solovay and Strassen Primality Test
184(3)
Miller-Rabin Test
187(3)
9.4.3 A Deterministic Primality Test
190(7)
9.5 The Rabin Variant
197(12)
9.5.1 The Encryption Function
197(2)
9.5.2 Decryption
199(1)
Precomputation
199(1)
Finding a Square Root Modulo a Prime Number
200(4)
The Four Solutions
204(2)
9.5.3 How to Distinguish Between the Solutions
206(2)
9.5.4 The Equivalence of Breaking Rabin's Scheme and Factoring n
208(1)
9.6 Problems
209(4)
10 Elliptic Curves Based Systems
213(23)
10.1 Some Basic Facts of Elliptic Curves
213(3)
10.2 The Geometry of Elliptic Curves
216(7)
A Line Through Two Distinct Points
219(2)
A Tangent Line
221(2)
10.3 Addition of Points on Elliptic Curves
223(6)
10.4 Cryptosystems Defined over Elliptic Curves
229(6)
10.4.1 The Discrete Logarithm Problem over Elliptic Curves
229(1)
10.4.2 The Discrete Logarithm System over Elliptic Curves
230(3)
10.4.3 The Security of Discrete Logarithm Based EC Systems
233(2)
10.5 Problems
235(1)
11 Coding Theory Based Systems
236(26)
11.1 Introduction to Goppa codes
236(4)
11.2 The McEliece Cryptosystem
240(14)
11.2.1 The System
241(1)
Setting Up the System
241(1)
Encryption
241(1)
Decryption
241(1)
11.2.2 Discussion
242(1)
Summary and Proposed Parameters
242(1)
Heuristics of the Scheme
242(1)
Not a Signature Scheme
243(1)
11.2.3 Security Aspects
243(1)
Guessing SB and PB
243(1)
Exhaustive Codewords Comparison
244(1)
Syndrome Decoding
245(2)
Guessing k Correct and Independent Coordinates
247(3)
Multiple Encryptions of the Same Message
250(1)
11.2.4 A Small Example of the McEliece System
251(3)
11.3 Another Technique to Decode Linear Codes
254(5)
11.4 The Niederreiter Scheme
259(1)
11.5 Problems
260(2)
12 Knapsack Based Systems
262(24)
12.1 The Knapsack System
262(7)
12.1.1 The Knapsack Problem
262(2)
12.1.2 The Knapsack System
264(1)
Setting Up the Knapsack System
264(1)
Encryption
265(1)
Decryption
266(1)
A Further Discussion
267(2)
12.2 The L3-Attack
269(1)
122.1 Introduction
269(1)
122.2 Lattices
270(7)
12.2.3 A Reduced Basis
272(1)
12.2.4 The L3-Attack
273(3)
12.2.5 The L3-Lartice Basis Reduction Algorithm
276(1)
12.3 The Chor-Rivest Variant
277(8)
Setting Up the System
278(3)
Encryption
281(1)
Decryption
282(3)
12.4 Problems
285(1)
13 Hash Codes & Authentication Techniques
286(28)
13.1 Introduction
286(1)
13.2 Hash Functions and Mac's
287(2)
13.3 Unconditionally Secure Authentication Codes
289(19)
13.3.1 Notions and Bounds
289(5)
13.3.2 The Projective Plane Construction
294(1)
A Finite Projective Plane
294(4)
A General Construction of a Projective Plane
298(4)
The Projective Plane Authentication Code
302(2)
13.3.3 A-Codes From Orthogonal Arrays
304(4)
133.4 A-Codes From Error-Correcting Codes
308(5)
13.4 Problems
313(1)
14 Zero Knowledge Protocols
314(6)
14.1 The Fiat-Shamir Protocol
314(2)
14.2 Schnorr's Identification Protocol
316(3)
14.3 Problems
319(1)
15 Secret Sharing Systems
320(23)
15.1 Introduction
320(2)
15.2 Threshold Schemes
322(3)
15.3 Threshold Schemes with Liars
325(2)
15.4 Secret Sharing Schemes
327(5)
15.5 Visual Secret Sharing Schemes
332(8)
15.6 Problems
340(3)
A Elementary Number Theory
343(40)
A.1 Introduction
343(5)
A.2 Euclid's Algorithm
348(4)
A.3 Congruences, Fermat, Euler, Chinese Remainder Theorem
352(12)
A.3.1 Congruences
352(2)
A.3.2 Euler and Fermat
354(4)
A.3.3 Solving Linear Congruence Relations
358(3)
A.3.4 The Chinese Remainder Theorem
361(3)
A.4 Quadratic Residues
364(5)
A.5 Continued Fractions
369(9)
A.6 Mobius Inversion Formula, the Principle of Inclusion and Exclusion
378(4)
A.6.1 Mobius Inversion Formula
378(2)
A.6.2 The Principle of Inclusion and Exclusion
380(2)
A.7 Problems
382(1)
B Finite Fields
383(42)
B.1 Algebra
383(12)
B.1.1 Abstract Algebra
383(1)
Set operations
383(1)
Group
384(2)
Ring
386(1)
Ideal
386(1)
Field
387(1)
Equivalence Relations
387(2)
Cyclic Groups
389(2)
B.1.2 Linear Algebra
391(1)
Vector Spaces and Subspaces
391(1)
Linear Independence, Basis and Dimension
392(1)
Inner Product, Orthogonality
393(2)
B.2 Constructions
395(6)
B.3 The Number of Irreducible Polynomials over GF(q)
401(4)
B.4 The Structure of Finite Fields
405(18)
B.4.1 The Cyclic Structure of a Finite Field
405(4)
B.4.2 The Cardinality of a Finite Field
409(2)
B.4.3 Some Calculus Rules over Finite Fields; Conjugates
411(2)
B.4.4 Minimal Polynomials, Primitive Polynomials
413(5)
B.4.5 Further Properties
418(2)
B.4.6 Cyclotomic Polynomials
420(3)
B.5 Problems
423(2)
C Relevant Famous Mathematicians
425(28)
Euclid of Alexandria
425(1)
Leonhard Euler
426(2)
Pierre de Fermat
428(6)
Evariste Galois
434(5)
Johann Carl Friedrich Gauss
439(6)
Karl Gustav Jacob Jacobi
445(1)
Adrien-Marie Legendre
446(1)
August Ferdinand Mobius
447(4)
Joseph Henry Maclagen Wedderburn
451(2)
D New Functions
453(8)
References 461(8)
Symbols and Notations 469(2)
Index 471