Algebraic Cryptanalysis

By Gregory V. Bard

Algebraic Cryptanalysis Cover Image

This book is one of the first to cover SAT-solvers and how they can be used in cryptanalysis. It includes chapters on finite field linear algebra and the equicomplexity of matrix operations.

Full Description

  • ISBN13: 978-0-3878-8756-2
  • 392 Pages
  • User Level: Science
  • Publication Date: August 14, 2009
  • Available eBook Formats: PDF
  • eBook Price: $148.00
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Full Description
Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.
Table of Contents

Table of Contents

  1. Preface.
  2. Introduction: How to Use this Book.
  3. The Block
  4. Cipher Keeloq and Algebraic Attacks.
  5. The Fixed
  6. Point Attack.
  7. Iterated Permutations.
  8. Stream Ciphers.
  9. Some Basic Facts about Linear Algebra over GF(2).
  10. The Complexity of GF(2)
  11. Matrix Operations.
  12. On the Exponent of Certain Matrix Operations.
  13. The Method of Four Russians.
  14. The Quadratic Sieve.
  15. Strategies for Polynomial Systems.
  16. Algorithms for Solving Polynomial Systems.
  17. Converting MQ to CNF
  18. SAT.
  19. How Do SAT
  20. Solvers Operate?.
  21. Applying SAT
  22. Solvers to Extension Fields of Low Degree.
  23. Appendix.
  24. Index.
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