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Mathematics of Public Key Cryptography

$76.99 (C)

  • Date Published: April 2012
  • availability: Available
  • format: Hardback
  • isbn: 9781107013926

$ 76.99 (C)

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About the Authors
  • Public key cryptography is a major interdisciplinary subject with many real-world applications, such as digital signatures. A strong background in the mathematics underlying public key cryptography is essential for a deep understanding of the subject, and this book provides exactly that for students and researchers in mathematics, computer science and electrical engineering. Carefully written to communicate the major ideas and techniques of public key cryptography to a wide readership, this text is enlivened throughout with historical remarks and insightful perspectives on the development of the subject. Numerous examples, proofs and exercises make it suitable as a textbook for an advanced course, as well as for self-study. For more experienced researchers it serves as a convenient reference for many important topics: the Pollard algorithms, Maurer reduction, isogenies, algebraic tori, hyperelliptic curves and many more.

    • Mathematical background and cryptographic applications are covered in one book
    • Based on student feedback from author's classroom experience
    • Open problems point the reader towards potential areas of future research
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    Reviews & endorsements

    ".. the reader is assumed to have a minimum background in group theory, algorithms and complexity, together with a basic knowledge of abstract algebra that includes ring and field theory. The book is suitable in principle for PhD. students in mathematics and related areas."
    -Mathematical Reviews

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    Product details

    • Date Published: April 2012
    • format: Hardback
    • isbn: 9781107013926
    • length: 630 pages
    • dimensions: 254 x 178 x 35 mm
    • weight: 1.28kg
    • contains: 11 b/w illus. 750 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    Part I. Background:
    2. Basic algorithmic number theory
    3. Hash functions and MACs
    Part II. Algebraic Groups:
    4. Preliminary remarks on algebraic groups
    5. Varieties
    6. Tori, LUC and XTR
    7. Curves and divisor class groups
    8. Rational maps on curves and divisors
    9. Elliptic curves
    10. Hyperelliptic curves
    Part III. Exponentiation, Factoring and Discrete Logarithms:
    11. Basic algorithms for algebraic groups
    12. Primality testing and integer factorisation using algebraic groups
    13. Basic discrete logarithm algorithms
    14. Factoring and discrete logarithms using pseudorandom walks
    15. Factoring and discrete logarithms in subexponential time
    Part IV. Lattices:
    16. Lattices
    17. Lattice basis reduction
    18. Algorithms for the closest and shortest vector problems
    19. Coppersmith's method and related applications
    Part V. Cryptography Related to Discrete Logarithms:
    20. The Diffie–Hellman problem and cryptographic applications
    21. The Diffie–Hellman problem
    22. Digital signatures based on discrete logarithms
    23. Public key encryption based on discrete logarithms
    Part VI. Cryptography Related to Integer Factorisation:
    24. The RSA and Rabin cryptosystems
    Part VII. Advanced Topics in Elliptic and Hyperelliptic Curves:
    25. Isogenies of elliptic curves
    26. Pairings on elliptic curves
    Appendix A. Background mathematics
    Author index
    Subject index.

  • Resources for

    Mathematics of Public Key Cryptography

    Steven D. Galbraith

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  • Instructors have used or reviewed this title for the following courses

    • Cryptology
    • Mathematics of Cryptography
  • Author

    Steven D. Galbraith, University of Auckland
    Steven D. Galbraith is a leading international authority on the mathematics of public key cryptography. He is an Associate Professor in the Department of Mathematics at the University of Auckland.

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