# Elementary Cryptanalysis: A Mathematical Approach

### By Abraham Sinkov, Revised and Updated by Todd Feil

2nd Edition
Catalog Code: NML-22E2
Print ISBN: 978-0-88385-647-5
Electronic ISBN: 978-0-88385-937-7
232 pp., Hardbound, 2009
List Price: $58.95 MAA Member:$47.50
Series: MAA Textbooks

The revised and updated version of Elementary Cryptanalysis, originally published in the New Mathematical Library almost half a century ago, explains how to solve cryptograms based on elementary mathematical principles, starting with Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.

Exercises are given throughout the text that will help the reader understand the concepts and practice the techniques presented. The book assumes minimal mathematical prerequisites and therefore explains from scratch such concepts as summation notation, matrix multiplication, and modular arithmetic.

### Table of Contents

Preface to the First Edition
Preface to the Second Edition
1. Monoalphabetic Ciphers Using Additive Alphabets
2. General Monoalphabetic Substitution
3. Polyalphabetic Substitution
4. Polygraphic Systems
5. Transposition
6. RSA Encryption
7. Perfect Security—One-time Pads
Appendix A: Tables
Appendix B: ASCII Codes
Appendix C: Binary Codes
Solutions to Exercises
Further Reading
Index
About the Authors

### About the Authors

Abraham Sinkov was born in 1907 in Philadelphia but moved to New York City when young. He graduated from City College of New York and received his master’s in mathematics from Columbia University. Later he received his doctorate in mathematics from George Washington University. After briefly teaching in the New York City schools, he took a civil service examination in 1930 that resulted in his being offered a job as a cryptanalyst by William Friedman, one of the first three hired to form the Army’s new Signal Intelligence Service (SIS). Sinkov was instrumental in breaking the Japanese diplomatic codes in the mid 1930’s.

After World War II Sinkov continued to work for SIS. This organization eventually became the Armed Forces Security Agency and then the National Security Agency (NSA). Sinkov held high positions in the NSA until his retirement in 1963. After his retirement he taught mathematics at Arizona State University. In 1966, he wrote the original edition of this book for the MAA, one of the first books on cryptology for the general public.

Todd Feil was born in Findlay, Ohio, in 1951. He graduated from Millikin University and received his doctorate from Bowling Green State University. He has taught mathematics at Denison University since 1982. Feil has published Lattice-Ordered Groups (Reidel) and A First Course in Abstract Algebra (2nd edition by Chapman & Hall/CRC), both coauthored with Marlow Anderson, and Essential Discrete Mathematics for Computer Science (Prentice Hall), coauthored with Joan Krone. He is an avid cyclist and lives in Granville, Ohio, with his wife Robin. They have two daughters, Halley and Emma.

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