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Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption

by Joshua Holden Princeton University Press
Pub Date:
09/2018
ISBN:
9780691183312
Format:
Pbk 392 pages
Price:
AU$44.99 NZ$47.82
Product Status: In Stock Now
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The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography'the science of sending secret messages. Most books about cryptography are organized historically, or around how codes and ciphers have been used, such as in government and military intelligence or bank transactions. Joshua Holden instead shows how mathematical principles underpin the ways that different codes and ciphers operate. Holden focuses on both code making and code breaking and he discusses the majority of ancient and modern ciphers currently known.


 


Holden begins by looking at substitution ciphers, built by substituting one letter or block of letters for another. Explaining one of the simplest and historically well-known ciphers, the Caesar cipher, Holden establishes the key mathematical idea behind the cipher and discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, including one developed by the Spartans, connections between ciphers and computer encryption, stream ciphers, and ciphers involving exponentiation. He also examines public-key ciphers, where the methods used to encrypt messages are public knowledge, and yet, intended recipients are still the only ones who are able to read the message. He concludes with a look at the future of ciphers and where cryptography might be headed. Only basic mathematics up to high school algebra is needed to understand and enjoy the book.


 


With a plethora of historical anecdotes and real-world examples, The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.


 


 


 
In The Mathematics of Secrets, Joshua Holden takes the reader on a chronological journey from Julius Caesar’s substitution cipher to modern day public-key algorithms and beyond. . . . Written for anyone with an interest in cryptography.—Noel-Ann Bradshaw, Times Higher Education


Complete in surveying cryptography. . . . This is a marvelous way of illustrating the use of simple mathematics in an important application that has triggered the wit of the designers and the ingenuity of the attackers since antiquity.—Adhemar Bultheel, European Mathematical Society


The best book I have seen on this subject.—Phil Dyke, Leonardo Reviews


This is a fascinating tour of the mathematics behind cryptography, showing how its principles underpin the ways that different codes and ciphers operate. . . . While it’s all about maths, the book is accessible—basic high school algebra is all that’s needed to understand and enjoy it.—Cosmos Magazine
Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology.