Group Theoretic Cryptography

Group Theoretic Cryptography

by Maria Isabel González Vasco, Rainer Steinwandt
Released April 2015
Publisher(s): CRC Press
ISBN: 9781584888376

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Book description

Group theoretic problems have propelled scientific achievements across a wide range of fields, including mathematics, physics, chemistry, and the life sciences. Many cryptographic constructions exploit the computational hardness of group theoretical problems, and the area is viewed as a potential source of quantum-resilient cryptographic primitives for the future.

Group Theoretic Cryptography supplies an ideal introduction to cryptography for those who are interested in group theory and want to learn about the possible interplays between the two fields. Assuming an undergraduate-level understanding of linear algebra and discrete mathematics, it details the specifics of using non-Abelian groups in the field of cryptography.

Moreover, the book evidences how group theoretic techniques help us gain new insight into well known, seemingly unrelated, cryptographic constructions, such as DES.

The book starts with brief overviews of the fundamentals of group theory, complexity theory, and cryptography. Part two is devoted to public-key encryption, including provable security guarantees, public-key encryption in the standard model, and public-key encryption using infinite groups.

The third part of the book covers secret-key encryption. It examines block ciphers, like the Advanced Encryption Standard, and cryptographic hash functions and message authentication codes. The last part delves into a number of cryptographic applications which are nowadays as relevant as encryption—identification protocols, key establishment, and signature schemes are covered.

The book supplies formal security analyses and highlights potential vulnerabilities for cryptographic constructions involving group theory. Summaries and references for further reading, as well as exercises, are included at the end of each chapter. Selected solutions for exercises are provided in the back of the book.

Table of contents

  1. Cover
  2. Dedication
  3. Contents
  4. List of Figures
  5. Symbol Description
  6. Preface
  7. Part I: Preliminaries
    1. Chapter 1: Mathematical background (1/3)
    2. Chapter 1: Mathematical background (2/3)
    3. Chapter 1: Mathematical background (3/3)
    4. Chapter 2: Basics on complexity (1/2)
    5. Chapter 2: Basics on complexity (2/2)
    6. Chapter 3: Cryptology: An introduction (1/3)
    7. Chapter 3: Cryptology: An introduction (2/3)
    8. Chapter 3: Cryptology: An introduction (3/3)
  8. Part II: Public-Key Encryption
    1. Chapter 4: Provable security guarantees (1/7)
    2. Chapter 4: Provable security guarantees (2/7)
    3. Chapter 4: Provable security guarantees (3/7)
    4. Chapter 4: Provable security guarantees (4/7)
    5. Chapter 4: Provable security guarantees (5/7)
    6. Chapter 4: Provable security guarantees (6/7)
    7. Chapter 4: Provable security guarantees (7/7)
    8. Chapter 5: Public-key encryption in the standard model (1/5)
    9. Chapter 5: Public-key encryption in the standard model (2/5)
    10. Chapter 5: Public-key encryption in the standard model (3/5)
    11. Chapter 5: Public-key encryption in the standard model (4/5)
    12. Chapter 5: Public-key encryption in the standard model (5/5)
    13. Chapter 6: Public-key encryption using infinite groups (1/5)
    14. Chapter 6: Public-key encryption using infinite groups (2/5)
    15. Chapter 6: Public-key encryption using infinite groups (3/5)
    16. Chapter 6: Public-key encryption using infinite groups (4/5)
    17. Chapter 6: Public-key encryption using infinite groups (5/5)
  9. Part III: Secret-Key Encryption
    1. Chapter 7: Block ciphers (1/5)
    2. Chapter 7: Block ciphers (2/5)
    3. Chapter 7: Block ciphers (3/5)
    4. Chapter 7: Block ciphers (4/5)
    5. Chapter 7: Block ciphers (5/5)
    6. Chapter 8: Cryptographic hash functions and message authentication codes (1/3)
    7. Chapter 8: Cryptographic hash functions and message authentication codes (2/3)
    8. Chapter 8: Cryptographic hash functions and message authentication codes (3/3)
  10. Part IV: Other Cryptographic Constructions
    1. Chapter 9: Key establishment protocols (1/5)
    2. Chapter 9: Key establishment protocols (2/5)
    3. Chapter 9: Key establishment protocols (3/5)
    4. Chapter 9: Key establishment protocols (4/5)
    5. Chapter 9: Key establishment protocols (5/5)
    6. Chapter 10: Signature and identification schemes (1/3)
    7. Chapter 10: Signature and identification schemes (2/3)
    8. Chapter 10: Signature and identification schemes (3/3)
  11. Part V: Appendix
    1. Appendix A: Solutions to selected exercises (1/2)
    2. Appendix A: Solutions to selected exercises (2/2)
  12. References (1/4)
  13. References (2/4)
  14. References (3/4)
  15. References (4/4)

Product information

  • Title: Group Theoretic Cryptography
  • Author(s): Maria Isabel González Vasco, Rainer Steinwandt
  • Release date: April 2015
  • Publisher(s): CRC Press
  • ISBN: 9781584888376