# Mathematical Ciphers: From Caesar to RSA

### About this Title

**Anne L. Young**, *Loyola College in Maryland, Baltimore, MD*

Publication: Mathematical World

Publication Year
2006: Volume 25

ISBNs: 978-0-8218-3730-6 (print); 978-1-4704-1195-4 (online)

DOI: http://dx.doi.org/10.1090/mawrld/025

MathSciNet review: MR2249094

MSC: Primary 94A60; Secondary 68P25, 94-01

### Table of Contents

**Front/Back Matter**

**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