This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.
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Book Description
An elementary introduction to the mathematics involved in cryptology, the science of reading and writing secret messages. The book has an engaging style, and all concepts used are carefully explained. It will be suitable for all students interested in cryptology and those looking for practical applications of seemingly abstract mathematics.
About the Author
Robert Edward Lewand received his PhD in mathematics from the University of Virginia. He is the co-author of two books: Expert System Development, and Intelligent Systems Design. He has delivered numerous talks and published extensively in professional journals largely in the areas of expert systems and artificial intelligence. He has been the recipient of several awards: Outstanding Teacher in the Faculty of Science (from Goucher College, 1980), Fulbright Faculty Exchange Award (Great Britain, 1987), Outstanding Scholarship Award (Groucher College, 1989), and the Caroline Doebler Bruckerl Award for the Outstanding Faculty Member (Groucher College, 1999).
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Most Helpful Customer Reviews
16 of 16 people found the following review helpful:
5.0 out of 5 stars
Some math is just plain fun and this is one such area,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Cryptological Mathematics (Mathematical Association of America Textbooks) (Paperback)
I cannot speak for the female side of the human race, but when I was young all the boys wanted to be a spy. We formed clubs and pretended to be secret agents. It was such great fun to create and use the codes to encrypt, pass and decode our important messages. Reading this book took me back to those days, not only reminding me of the good times we had but also how serious encryption is. This book was a good deal of fun to read, but underlying the fun there is an air of extreme seriousness. It is not an exaggeration to say that secure encryption is the key to the efficient functioning of the global economy. Billions of dollars are electronically moved every day and without the security of unbreakable encryption, it would all be too unreliable to use. If the current codes were proven to be breakable, it would be a catastrophe, probably the only threat to the world economy that does not involve a major natural disaster. The mathematics of encryption are surprisingly easy to understand. Starting with the simple substitution ciphers and moving through the more complex polyalphabetic and polygraphic substitutions, the techniques to create and break them are described. For most of the codes, the most complex mathematics needed to understand them is a basic understanding of matrices and how they are added and multiplied. It is only in the last chapter of public key cryptography where some advanced mathematics of number theory are used. Each chapter ends with a set of problems and solutions to the even ones are given in an appendix. This would be an excellent textbook for a course in applied mathematics. There is an inherent fascinating quality to the subject matter and the tales of encryption are very well done. I strongly recommend that you read it. Published in Journal of Recreational Mathematics, reprinted with permission.
5.0 out of 5 stars
Wonderful book,
By Book Lover (Berkeley, CA) - See all my reviews
This review is from: Cryptological Mathematics (Mathematical Association of America Textbooks) (Paperback)
I *loved* this book. It covers the essential number theory required to understand various encryption schemes, and while it is a thin book, it doesn't omit any steps between various mathematical steps (" ... and then magic happens ..."). You end up with the satisfying feeling of being able to derive the proof for RSA, starting from high-school math.
12 of 23 people found the following review helpful:
5.0 out of 5 stars
well done,
By
This review is from: Cryptological Mathematics (Mathematical Association of America Textbooks) (Paperback)
As I do not work for M.I.6, the N.S.A. or some other `Secret Service' a computer program as Wolfram's ` Mathematical Explorer' [at Amazon for $75, or so] which can encrypt a message by R.S.A [heavy duty crypto] is `really' all I need. I have a number of books on all kinds of cryptography ... `classical' crypto, `Codes' [different from cyphers], number theory and so on. While there are `better' books on specific parts of cryptology this book is by far the best overall introduction. The title of this book scared me a bit. I have never been that `comfortable' with some sorts of maths and this book `sounded' brutal, and while it is a `math' book it is really not impossible to `figure out' [although some spots I must have read twenty times but thats the topic]. `REQUIRED BACKGROUND' You can `do' with less but it helps to know basic algebra and understand variables. The vocabulary and nomenclature of areas as Set Theory and Probability [which I had to `study up' on] would be `nice' but you can `slide' without them, Reading level: age 14 through senility :-) [ but a challenge for those `dead and encrypted'. Also covered in detail is "public key' cryptography which as I wrote I do by `pre - written' computer program.
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Inside This Book
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First Sentence:
Oops! I'm getting ahead of myself. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multiplicative cipher, multiplicative key, additive cipher, many bridge hands, enciphering scheme, affine cipher, monoalphabetic substitution cipher, keyword cipher, ciphertext characters, ciphertext letters, additive key, integer expressible, plaintext character, polyalphabetic substitution cipher, alphabetic position, ciphertext message, been enciphered, plaintext message, numeric message, plaintext letter, enciphered message, multiplication principle, substitution ciphers, message enciphered, encipher the message Key Phrases - Capitalized Phrases (CAPs): (learn more)
Index of Coincidence, Hill's System, Kasiski Test, Euler's Theorem, Friedman Test, Well-Ordering Axiom, Fundamental Theorem of Arithmetic, World War, Black Chamber, Cipher Bureau, Letter Count Letter Count, New York, Van Meter, Frank Rowlett, Step Purpose Maple Syntax Maple Output, Step Purpose Mathematica Syntax Mathematica Output, Department of State, Miss Meyer, Signal Intelligence Service New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Oops! I'm getting ahead of myself. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multiplicative cipher, multiplicative key, additive cipher, many bridge hands, enciphering scheme, affine cipher, monoalphabetic substitution cipher, keyword cipher, ciphertext characters, ciphertext letters, additive key, integer expressible, plaintext character, polyalphabetic substitution cipher, alphabetic position, ciphertext message, been enciphered, plaintext message, numeric message, plaintext letter, enciphered message, multiplication principle, substitution ciphers, message enciphered, encipher the message Key Phrases - Capitalized Phrases (CAPs): (learn more)
Index of Coincidence, Hill's System, Kasiski Test, Euler's Theorem, Friedman Test, Well-Ordering Axiom, Fundamental Theorem of Arithmetic, World War, Black Chamber, Cipher Bureau, Letter Count Letter Count, New York, Van Meter, Frank Rowlett, Step Purpose Maple Syntax Maple Output, Step Purpose Mathematica Syntax Mathematica Output, Department of State, Miss Meyer, Signal Intelligence Service New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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23
books
cite this book:
See all 23 books citing this book
- Elements of Cryptanalysis (Cryptographic Series) by William Friedman on page 101
- The Broken Seal: The Story of Operation Magic and the Pearl Harbor Disaster. by Ladislas. Farago on page 44
- Identification Numbers and Check Digit Schemes (Classroom Resource Materials) by Joseph Kirtland in Front Matter
- Calculus Mysteries and Thrillers (Classroom Resource Materials) by R. Grant Woods in Front Matter
- The Education of a Poker Player by Herbert O. Yardley on page 44
See all 19 books this book cites
- Proofs Without Words II: More Exercises in Visual Thinking (Classroom Resource Materials) (v. 2) by Roger B. Nelsen in Front Matter
- Environmental Mathematics in the Classroom (Classroom Resource Materials) by B. A. Fusaro in Front Matter
- Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them (Classroom Resource Materials) by John O. Kiltinen in Front Matter
- Conjecture and Proof (Classroom Resource Materials) by Miklós Laczkovich in Front Matter
- Ordinary Differential Equations: A Brief Eclectic Tour (Classroom Resource Materials) by David A. Sánchez in Front Matter
See all 23 books citing this book
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