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book: The Mathematics of Secrets
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The Mathematics of Secrets

Cryptography from Caesar Ciphers to Digital Encryption
  • and
Language: English
Published/Copyright: 2018

About this book

Explaining the mathematics of cryptography

The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.

A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.

Author / Editor information

Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology.

Reviews

"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

Topics

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    Frontmatter

    i
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    CONTENTS

    vii
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    PREFACE

    xi
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    ACKNOWLEDGMENTS

    xiii
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    1. Introduction to Ciphers and Substitution

    1
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    2. Polyalphabetic Substitution Ciphers

    29
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    3. Transposition Ciphers

    75
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    4. Ciphers and Computers

    109
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    5. Stream Ciphers

    145
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    6. Ciphers Involving Exponentiation

    182
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    7. Public-Key Ciphers

    201
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    8. Other Public-Key Systems

    241
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    9. The Future of Cryptography

    276
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    LIST OF SYMBOLS

    303
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    NOTES

    305
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    SUGGESTIONS FOR FURTHER READING

    345
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    BIBLIOGRAPHY

    349
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    INDEX

    367
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
January 14, 2019
eBook ISBN:
9780691184555
Pages and Images/Illustrations in book
View content
https://doi.org/10.1515/9780691184555
eBook ISBN: 9780691184555
Keywords for this book
Cipher; Ciphertext; Plaintext; Cryptography; Public-key cryptography; Encryption; Key (cryptography); Cryptanalysis; Block cipher; Differential cryptanalysis; Transposition cipher; Block size (cryptography); Elliptic curve cryptography; Substitution cipher; Quantum cryptography; Diffie–Hellman key exchange; Merkle's Puzzles; Linear cryptanalysis; Mathematics; Cryptographic hash function; Cryptosystem; Affine cipher; Post-quantum cryptography; Cryptogram; Cryptographic engineering; Keystream; Mathematical problem; Probabilistic encryption; Sign (mathematics); Cryptography Research; RSA (cryptosystem); Autokey cipher; Related-key attack; Stream cipher; Hill cipher; S-box; Hyperelliptic curve cryptography; Block cipher mode of operation; Vigenère cipher; Mathematician; Homomorphic encryption; Enigma machine; Computational problem; Polyalphabetic cipher; Confusion and diffusion; ElGamal encryption; Communication Theory of Secrecy Systems; Fast Software Encryption; Disquisitiones Arithmeticae; Mental poker; International Association for Cryptologic Research; Alice and Bob; Key size; Security level; Variable (computer science); Feistel cipher; Vulnerability (computing); Quantum key distribution; RSA problem; Correlation attack; Chosen-ciphertext attack; NSA Suite B Cryptography; Known-plaintext attack; Permutation; Monte Carlo algorithm; Craig Gentry (computer scientist); Spyware; Chosen-plaintext attack; Fermat's little theorem; Data Encryption Standard
Audience(s) for this book
For a non-specialist adult audience
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