The Theory of Hash Functions and Random Oracles : An Approach to Modern Cryptography

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ABOUT THE BOOK

Hash functions are the cryptographer’s Swiss Army knife. Even though they play an integral part in today’s cryptography, existing textbooks discuss hash functions only in passing and instead often put an emphasis on other primitives like encryption schemes. In this book the authors take a different approach and place hash functions at the center. The result is not only an introduction to the theory of hash functions and the random oracle model but a comprehensive introduction to modern cryptography.

After motivating their unique approach, in the first chapter the authors introduce the concepts from computability theory, probability theory, information theory, complexity theory, and information-theoretic security that are required to understand the book content. In Part I they introduce the foundations of hash functions and modern cryptography. They cover a number of schemes, concepts, and proof techniques, including computational security, one-way functions, pseudo randomness and pseudorandom functions, game-based proofs, message authentication codes, encryption schemes, signature schemes, and collision-resistant (hash) functions. In Part II the authors explain the random oracle model, proof techniques used with random oracles, random oracle constructions, and examples of real-world random oracle schemes. They also address the limitations of random oracles and the random oracle controversy, the fact that instantiable schemes exist which are provably secure in the random oracle model but which become insecure with any real-world hash function. Finally in Part III the authors focus on constructions of hash functions. This includes a treatment of iterative hash functions and generic attacks against hash functions, constructions of hash functions based on block ciphers and number-theoretic assumptions, a discussion of privately keyed hash functions including a full security proof for HMAC, and a presentation of real-world hash functions.

The text is supported with exercises, notes, references, and pointers to further reading, and it is a suitable textbook for undergraduate and graduate students, and researchers of cryptology and information security.


TABLE OF CONTENTS

  1. Foundations

    • Arno Mittelbach, Marc Fischlin
    Pages 1-68
  2. Foundations of Modern Cryptography

    1. Front Matter

      Pages 69-69

    2. Computational Security

      • Arno Mittelbach, Marc Fischlin
      Pages 71-93
    3. Pseudorandomness and Computational Indistinguishability

      • Arno Mittelbach, Marc Fischlin
      Pages 95-159
    4. Collision Resistance

      • Arno Mittelbach, Marc Fischlin
      Pages 161-208
    5. Encryption Schemes

      • Arno Mittelbach, Marc Fischlin
      Pages 209-260
    6. Signature Schemes

      • Arno Mittelbach, Marc Fischlin
      Pages 261-301
    7. Non-cryptographic Hashing

      • Arno Mittelbach, Marc Fischlin
      Pages 303-334
  3. The Random Oracle Methodology

    1. Front Matter

      Pages 335-335

    2. The Random Oracle Model

      • Arno Mittelbach, Marc Fischlin
      Pages 337-367
    3. The Full Power of Random Oracles

      • Arno Mittelbach, Marc Fischlin
      Pages 369-406
    4. Random Oracle Schemes in Practice

      • Arno Mittelbach, Marc Fischlin
      Pages 407-439
    5. Limitations of Random Oracles

      • Arno Mittelbach, Marc Fischlin
      Pages 441-459
    6. The Random Oracle Controversy

      • Arno Mittelbach, Marc Fischlin
      Pages 461-475
  4. Hash Function Constructions

    1. Front Matter

      Pages 477-477

    2. Iterated Hash Functions

      • Arno Mittelbach, Marc Fischlin
      Pages 479-538
    3. Constructing Compression Functions

      • Arno Mittelbach, Marc Fischlin
      Pages 539-583
    4. Iterated Hash Functions in Practice

      • Arno Mittelbach, Marc Fischlin
      Pages 585-618
    5. Constructions of Keyed Hash Functions

      • Arno Mittelbach, Marc Fischlin
      Pages 619-683

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