Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Modular Arithmetic
- 3 The Addition Cypher, an Insecure Block Cypher
- 4 Functions
- 5 Probability Theory
- 6 Perfect Secrecy and Perfectly Secure Cryptosystems
- 7 Number Theory
- 8 Euclid's Algorithm
- 9 Some Uses of Perfect Secrecy
- 10 Computational Problems, Easy and Hard
- 11 Modular Exponentiation, Modular Logarithm, and One-Way Functions
- 12 Diffie and Hellman's Exponential-Key-Agreement Protocol
- 13 Computationally Secure Single-Key Cryptosystems
- 14 Public-Key Cryptosystems and Digital Signatures
- Further Reading
- Index
Preface
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Modular Arithmetic
- 3 The Addition Cypher, an Insecure Block Cypher
- 4 Functions
- 5 Probability Theory
- 6 Perfect Secrecy and Perfectly Secure Cryptosystems
- 7 Number Theory
- 8 Euclid's Algorithm
- 9 Some Uses of Perfect Secrecy
- 10 Computational Problems, Easy and Hard
- 11 Modular Exponentiation, Modular Logarithm, and One-Way Functions
- 12 Diffie and Hellman's Exponential-Key-Agreement Protocol
- 13 Computationally Secure Single-Key Cryptosystems
- 14 Public-Key Cryptosystems and Digital Signatures
- Further Reading
- Index
Summary
In his autobiography, A Mathematician's Apology, the number theorist and pacifist G. H. Hardy wrote
… both Gauss and lesser mathematicians may be justified in rejoicing that there is one science [number theory] at any rate … whose very remoteness from ordinary human activities should keep it gentle and clean.
Hardy's book was published in 1940, toward the end of his career. If he had postponed his judgment for another 30 years, he might have come to a different conclusion, for number theory became the basis for an important technology long associated with war: cryptography, the use of secret codes.
Cryptography has been in use for at least several thousand years. It is listed in the Kama Sutra as one of the 64 arts to be mastered by women. One well-known elementary cryptosystem is attributed to Julius Caesar. Numerous anecdotes attest to the importance of cryptography in war and diplomacy over the years – and to that of cryptanalysis, the cracking of codes. For example, Britain's interception and deciphering of the Zimmerman telegram, a message from Germany's foreign minister to the government of Mexico (via the ambassador), helped speed the United States' entry into World War I, for the message promised Texas, New Mexico, and Arizona to Mexico in return for its help against the United States.
- Type
- Chapter
- Information
- A Cryptography PrimerSecrets and Promises, pp. ix - xiiPublisher: Cambridge University PressPrint publication year: 2014