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Fundamentals of Cryptography

Introducing Mathematical and Algorithmic Foundations

Authors:

  • Balances the theorems of mathematics against the feasibility of computation
  • Covers the algorithmic foundations as well core mathematics and arithmetic
  • Demonstrates how cryptography is something one actually “does,” rather than theorizes about

Part of the book series: Undergraduate Topics in Computer Science (UTICS)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
  2. Introduction

    • Duncan Buell
    Pages 1-10
  3. Simple Ciphers

    • Duncan Buell
    Pages 11-26
  4. Groups, Rings, Fields

    • Duncan Buell
    Pages 49-61
  5. Square Roots and Quadratic Symbols

    • Duncan Buell
    Pages 63-71
  6. Finite Fields of Characteristic 2

    • Duncan Buell
    Pages 73-85
  7. Elliptic Curves

    • Duncan Buell
    Pages 87-98
  8. Mathematics, Computing, and Arithmetic

    • Duncan Buell
    Pages 99-122
  9. Modern Symmetric Ciphers—DES and AES

    • Duncan Buell
    Pages 123-147
  10. Asymmetric Ciphers—RSA and Others

    • Duncan Buell
    Pages 149-155
  11. How to Factor a Number

    • Duncan Buell
    Pages 157-171
  12. How to Factor More Effectively

    • Duncan Buell
    Pages 173-178
  13. Elliptic Curve Cryptography

    • Duncan Buell
    Pages 191-203
  14. Lattice-Based Cryptography and NTRU

    • Duncan Buell
    Pages 205-221
  15. Homomorphic Encryption

    • Duncan Buell
    Pages 223-229
  16. Back Matter

    Pages 231-279

About this book

Cryptography, as done in this century, is heavily mathematical. But it also has roots in what is computationally feasible.

This unique textbook text balances the theorems of mathematics against the feasibility of computation. Cryptography is something one actually “does”, not a mathematical game one proves theorems about. There is deep math; there are some theorems that must be proved; and there is a need to recognize the brilliant work done by those who focus on theory. But at the level of an undergraduate course, the emphasis should be first on knowing and understanding the algorithms and how to implement them, and also to be aware that the algorithms must be implemented carefully to avoid the “easy” ways to break the cryptography. This text covers the algorithmic foundations and is complemented by core mathematics and arithmetic.

Authors and Affiliations

  • Department of Computer Science and Engineering, University of South Carolina, Columbia, USA

    Duncan Buell

About the author

Duncan Buell, professor emeritus in the Dept. of Computer Science and Engineering at University of South Carolina, also has 15 years of experience at a research lab doing high-performance computing research in support of the US National Security Agency.

Bibliographic Information

  • Book Title: Fundamentals of Cryptography

  • Book Subtitle: Introducing Mathematical and Algorithmic Foundations

  • Authors: Duncan Buell

  • Series Title: Undergraduate Topics in Computer Science

  • DOI: https://doi.org/10.1007/978-3-030-73492-3

  • Publisher: Springer Cham

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-73491-6Published: 16 June 2021

  • eBook ISBN: 978-3-030-73492-3Published: 15 June 2021

  • Series ISSN: 1863-7310

  • Series E-ISSN: 2197-1781

  • Edition Number: 1

  • Number of Pages: XV, 279

  • Number of Illustrations: 49 b/w illustrations, 1 illustrations in colour

  • Topics: Systems and Data Security, Cryptology, Theory of Computation

Buy it now

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access