Introduction to Cryptography: Principles and Applications

Predný obal
Springer Science & Business Media, 5. 3. 2007 - 367 strán (strany)

Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data.

In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises.

The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

 

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Obsah

Introduction
1
The Objectives of Cryptography
2
Attacks
4
Cryptographic Protocols
5
Provable Security
6
SymmetricKey Encryption
11
Stream Ciphers
12
Block Ciphers
15
A Fair Electronic Cash System
123
Underlying Problems
128
Probabilistic Algorithms
135
Monte Carlo and Las Vegas Algorithms
140
OneWay Functions and the Basic Assumptions
146
A Notation for Probabilities
148
Discrete Exponential Function
149
Uniform Sampling Algorithms
155

DES
16
AES
19
Modes of Operation
25
PublicKey Cryptography
32
Modular Arithmetic
35
The Integers Modulo n
37
RSA
41
Digital Signatures
45
Attacks Against RSA
46
Probabilistic RSA Encryption
51
Cryptographic Hash Functions
54
Construction of Hash Functions
56
Data Integrity and Message Authentication
62
Hash Functions as Random Functions
64
Signatures with Hash Functions
65
The Discrete Logarithm
70
ElGamals Signature Scheme
72
Digital Signature Algorithm
73
Modular Squaring
76
Rabins Signature Scheme
77
Cryptographic Protocols
81
Kerberos
82
DiffieHellman Key Agreement
85
Key Exchange and Mutual Authentication
86
StationtoStation Protocol
88
PublicKey Management Techniques
89
Identification Schemes
91
Simplified FiatShamir Identification Scheme
93
ZeroKnowledge
95
FiatShamir Identification Scheme
97
FiatShamir Signature Scheme
99
Commitment Schemes
100
A Commitment Scheme Based on Quadratic Residues
101
A Commitment Scheme Based on Discrete Logarithms
102
Homomorphic Commitments
103
Electronic Elections
104
Secret Sharing
105
A MultiAuthority Election Scheme
107
Proofs of Knowledge
110
NonInteractive Proofs of Knowledge
112
Eliminating the Trusted Center
113
Digital Cash
115
Blindly Issued Proofs
117
Modular Powers
158
Modular Squaring
161
Quadratic Residuosity Property
162
Formal Definition of OneWay Functions
163
HardCore Predicates
167
Bit Security of OneWay Functions
175
Bit Security of the RSA Family
182
Bit Security of the Square Family
190
OneWay Functions and Pseudorandomness
199
Yaos Theorem
207
Provably Secure Encryption
215
Classical InformationTheoretic Security
216
Perfect Secrecy and Probabilistic Attacks
220
PublicKey OneTime Pads
224
Passive Eavesdroppers
226
ChosenCiphertext Attacks
233
A Security Proof in the Random Oracle Model
236
Security Under Standard Assumptions
245
Unconditional Security of Cryptosystems
250
The Bounded Storage Model
251
The Noisy Channel Model
260
Provably Secure Digital Signatures
264
ClawFree Pairs and CollisionResistant Hash Functions
268
AuthenticationTreeBased Signatures
271
A StateFree Signature Scheme
273
Algebra and Number Theory
289
Residues
295
The Chinese Remainder Theorem
299
Primitive Roots and the Discrete Logarithm
301
Polynomials and Finite Fields
304
The Ring of Polynomials
305
Residue Class Rings
307
Finite Fields
308
Quadratic Residues
310
Modular Square Roots
315
Primes and Primality Tests
319
Probabilities and Information Theory
324
The Weak Law of Large Numbers
333
Distance Measures
336
Basic Concepts of Information Theory
340
References
349
Index
360
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