Mathematical ciphers : from Caesar to RSA /Anne L Young

By: Anne L YoungContributor(s): Anne L YoungMaterial type: TextTextPublisher number: :Donated by Mathematical Dept. Publication details: Providence, R.I. : American Mathematical Society , ©2006Description: viii, 159 pages : illustrations ; 26 cmISBN: 9781470454760Subject(s): MathematicsGenre/Form: Number theoryDDC classification: 652.8 YOU
Contents:
Preface -- ch. 1. Introduction -- ch. 2. Caesar cipher -- ch. 3. Terminology and results from number theory -- ch. 4. Modular arithmetic -- ch. 5. Describing the Caesar cipher mathematically -- ch. 6. Cryptanalysis for the Caesar cipher -- ch. 7. Multiplication cipher -- ch. 8. Cryptanalysis for the multiplication cipher -- ch. 9. Multiplication-shift cipher -- ch. 10. Cryptanalysis for the multiplication-shift cipher -- ch. 11. Non-mathematical substitution ciphers -- ch. 12. Preparing to generalize -- ch. 13. Finding inverses modulo n -- ch. 14. General multiplication-shift cipher -- ch. 15. Security of the general multiplication-shift cipher -- ch. 16. Introduction to the exponential cipher -- ch. 17. Deciphering the exponential cipher -- ch. 18. Cryptanalysis for the exponential cipher -- ch. 19. Mathematical basis for the exponential cipher -- ch. 20. Public key ciphers -- ch. 21. RSA cipher -- ch. 22. Signatures -- ch. 23. Security and implementation of the RSA cipher -- ch. 24. Computer programs -- ch. 25. Further reading -- ch. 26. Answers to selected exercises -- Index.
Summary: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)

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

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.

There are no comments on this title.

to post a comment.
© Copyright Shiv Nadar University 2012. All Rights Reserved.  Disclaimer |  Sitemap
The Shiv Nadar University has been established under U.P. Act No 12 of 2011. Shiv Nadar University is UGC Approved.