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Mathematical Ciphers: From Caesar to RSA
 
Anne L. Young Loyola College in Maryland, Baltimore, MD
Front Cover for Mathematical Ciphers
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Softcover ISBN: 978-0-8218-3730-6
Product Code: MAWRLD/25
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
Electronic ISBN: 978-1-4704-1195-4
Product Code: MAWRLD/25.E
List Price: $32.00
MAA Member Price: $28.80
AMS Member Price: $25.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $51.00
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Front Cover for Mathematical Ciphers
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  • Front Cover for Mathematical Ciphers
  • Back Cover for Mathematical Ciphers
Mathematical Ciphers: From Caesar to RSA
Anne L. Young Loyola College in Maryland, Baltimore, MD
Available Formats:
Softcover ISBN:  978-0-8218-3730-6
Product Code:  MAWRLD/25
List Price: $34.00
MAA Member Price: $30.60
AMS Member Price: $27.20
Electronic ISBN:  978-1-4704-1195-4
Product Code:  MAWRLD/25.E
List Price: $32.00
MAA Member Price: $28.80
AMS Member Price: $25.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $51.00
MAA Member Price: $45.90
AMS Member Price: $40.80
  • Book Details
     
     
    Mathematical World
    Volume: 252006; 159 pp
    MSC: Primary 11; 94;

    A cipher is a scheme for creating coded messages for the secure exchange of information. Throughout history, many different coding schemes have been devised. One of the oldest and simplest mathematical systems was used by Julius Caesar. This is where Mathematical Ciphers begins. Building on that simple system, Young moves on to more complicated schemes, ultimately ending with the RSA cipher, which is used to provide security for the Internet.

    This book is structured differently from most mathematics texts. It does not begin with a mathematical topic, but rather with a cipher. The mathematics is developed as it is needed; the applications motivate the mathematics. As is typical in mathematics textbooks, most chapters end with exercises. Many of these problems are similar to solved examples and are designed to assist the reader in mastering the basic material. A few of the exercises are one-of-a-kind, intended to challenge the interested reader.

    Implementing encryption schemes is considerably easier with the use of the computer. For all the ciphers introduced in this book, JavaScript programs are available from the Web.

    In addition to developing various encryption schemes, this book also introduces the reader to number theory. Here, the study of integers and their properties is placed in the exciting and modern context of cryptology. Mathematical Ciphers can be used as a textbook for an introductory course in mathematics for all majors. The only prerequisite is high school mathematics.

    Readership

    Undergraduate students interested in number theory, cryptology, and discrete mathematics.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. Caesar cipher
    • Chapter 3. Terminology and results from number theory
    • Chapter 4. Modular arithmetic
    • Chapter 5. Describing the Caesar cipher mathematically
    • Chapter 6. Cryptanalysis for the Caesar cipher
    • Chapter 7. Multiplication cipher
    • Chapter 8. Cryptanalysis for the multiplication cipher
    • Chapter 9. Multiplication-shift cipher
    • Chapter 10. Cryptanalysis for the multiplication-shift cipher
    • Chapter 11. Non-mathematical substitution ciphers
    • Chapter 12. Preparing to generalize
    • Chapter 13. Finding inverses modulo $n$
    • Chapter 14. General multiplication-shift cipher
    • Chapter 15. Security of the general multiplication-shift cipher
    • Chapter 16. Introduction to the exponential cipher
    • Chapter 17. Deciphering the exponential cipher
    • Chapter 18. Cryptanalysis for the exponential cipher
    • Chapter 19. Mathematical basis for the exponential cipher
    • Chapter 20. Public key ciphers
    • Chapter 21. RSA cipher
    • Chapter 22. Signatures
    • Chapter 23. Security and implementation of the RSA cipher
    • Chapter 24. Computer programs
    • Chapter 25. Further reading
    • Chapter 26. Answers to selected exercises
    • 27. Index
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Volume: 252006; 159 pp
MSC: Primary 11; 94;

A cipher is a scheme for creating coded messages for the secure exchange of information. Throughout history, many different coding schemes have been devised. One of the oldest and simplest mathematical systems was used by Julius Caesar. This is where Mathematical Ciphers begins. Building on that simple system, Young moves on to more complicated schemes, ultimately ending with the RSA cipher, which is used to provide security for the Internet.

This book is structured differently from most mathematics texts. It does not begin with a mathematical topic, but rather with a cipher. The mathematics is developed as it is needed; the applications motivate the mathematics. As is typical in mathematics textbooks, most chapters end with exercises. Many of these problems are similar to solved examples and are designed to assist the reader in mastering the basic material. A few of the exercises are one-of-a-kind, intended to challenge the interested reader.

Implementing encryption schemes is considerably easier with the use of the computer. For all the ciphers introduced in this book, JavaScript programs are available from the Web.

In addition to developing various encryption schemes, this book also introduces the reader to number theory. Here, the study of integers and their properties is placed in the exciting and modern context of cryptology. Mathematical Ciphers can be used as a textbook for an introductory course in mathematics for all majors. The only prerequisite is high school mathematics.

Readership

Undergraduate students interested in number theory, cryptology, and discrete mathematics.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. Caesar cipher
  • Chapter 3. Terminology and results from number theory
  • Chapter 4. Modular arithmetic
  • Chapter 5. Describing the Caesar cipher mathematically
  • Chapter 6. Cryptanalysis for the Caesar cipher
  • Chapter 7. Multiplication cipher
  • Chapter 8. Cryptanalysis for the multiplication cipher
  • Chapter 9. Multiplication-shift cipher
  • Chapter 10. Cryptanalysis for the multiplication-shift cipher
  • Chapter 11. Non-mathematical substitution ciphers
  • Chapter 12. Preparing to generalize
  • Chapter 13. Finding inverses modulo $n$
  • Chapter 14. General multiplication-shift cipher
  • Chapter 15. Security of the general multiplication-shift cipher
  • Chapter 16. Introduction to the exponential cipher
  • Chapter 17. Deciphering the exponential cipher
  • Chapter 18. Cryptanalysis for the exponential cipher
  • Chapter 19. Mathematical basis for the exponential cipher
  • Chapter 20. Public key ciphers
  • Chapter 21. RSA cipher
  • Chapter 22. Signatures
  • Chapter 23. Security and implementation of the RSA cipher
  • Chapter 24. Computer programs
  • Chapter 25. Further reading
  • Chapter 26. Answers to selected exercises
  • 27. Index
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