# Introduction to Cryptography: Principles and Applications

Springer Science & Business Media, 5 mars 2007 - 367 pages

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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### Table des matières

 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 Droits d'auteur