© 2019

Cryptology and Error Correction

An Algebraic Introduction and Real-World Applications


Table of contents

  1. Front Matter
    Pages i-xiv
  2. Lindsay N. Childs
    Pages 1-11
  3. Lindsay N. Childs
    Pages 13-26
  4. Lindsay N. Childs
    Pages 27-49
  5. Lindsay N. Childs
    Pages 51-64
  6. Lindsay N. Childs
    Pages 65-82
  7. Lindsay N. Childs
    Pages 83-91
  8. Lindsay N. Childs
    Pages 93-115
  9. Lindsay N. Childs
    Pages 117-133
  10. Lindsay N. Childs
    Pages 135-151
  11. Lindsay N. Childs
    Pages 153-169
  12. Lindsay N. Childs
    Pages 171-193
  13. Lindsay N. Childs
    Pages 195-213
  14. Lindsay N. Childs
    Pages 215-239
  15. Lindsay N. Childs
    Pages 241-257
  16. Lindsay N. Childs
    Pages 259-272
  17. Lindsay N. Childs
    Pages 273-292
  18. Lindsay N. Childs
    Pages 293-312
  19. Lindsay N. Childs
    Pages 313-330
  20. Lindsay N. Childs
    Pages 331-342

About this book


This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for  understanding these methods.  The objective is to provide a thorough understanding of RSA, Diffie–Hellman, and Blum–Goldwasser cryptosystems and Hamming and Reed–Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked.   To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra—rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets.  Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory.

This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will also take a concurrent course in linear algebra or elementary matrix theory. A solutions manual for the 400 exercises in the book is available to instructors who adopt the text for their course.


Caeser ciphers Chinese Remainder Theorem El Gamal cryptography Lagrange's Theorem Luhn's formula Vernam cipher

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsUniversity at Albany, State University of New YorkAlbanyUSA

About the authors

Lindsay N. Childs is Professor Emeritus at the University of Albany where he earned recognition as a much-loved mentor of students, and as an expert in Galois field theory. Capping his tenure at Albany, he was named a Collins Fellow for his extraordinary devotion to the University at Albany and the people in it over a sustained period of time. Post University of Albany, Professor Childs has taught a sequence of online courses whose content evolved into this book. Lindsay Childs is author of A Concrete Introduction to Higher Algebra, published in Springer's Undergraduate Texts in Mathematics series, as well as a monograph, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (American Mathematical Society), and more than 60 research publications in abstract algebra.

Bibliographic information

  • Book Title Cryptology and Error Correction
  • Book Subtitle An Algebraic Introduction and Real-World Applications
  • Authors Lindsay N. Childs
  • Series Title Springer Undergraduate Texts in Mathematics and Technology
  • Series Abbreviated Title Spr.Undergrad.Text.Math.,Technology
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-15451-6
  • eBook ISBN 978-3-030-15453-0
  • Series ISSN 1867-5506
  • Series E-ISSN 1867-5514
  • Edition Number 1
  • Number of Pages XIV, 351
  • Number of Illustrations 6 b/w illustrations, 1 illustrations in colour
  • Topics Algebra
    Number Theory
  • Buy this book on publisher's site