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
14 - Public-Key Cryptosystems and Digital Signatures
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
Public-key cryptosystems
The key agreement protocol provides a way for previously unacquainted parties to agree on a secret key. However, there are times when one party wants to unilaterally send a private message to another party without first interacting with the other party. Public-key encryption, first proposed by Diffie and Hellman in the early 1970s, provides a way to accomplish this.
In traditional (one-key) cryptography, the same key is used to encrypt a message as to decrypt it. Public-key cryptography discards this convention, and allows one (public) key to be used for encryption and another (the secret key) for decryption.
The set-up for public key cryptography is as follows. Every person intending to receive encrypted messages privately chooses a secret key and calculates a corresponding public key. All the public keys are made publically available. If I want to send an encrypted message to someone, I look up her public key and use it to encrypt a message to her; only she is able to decrypt it.
The idea of having different keys for encryption and decryption seems simple, but it represented a startling break with the past. It is worth considering why the discovery was so late in coming; after all, traditional cryptography has been used for a few thousand years. Why did the idea of two different keys not arise earlier?
- Type
- Chapter
- Information
- A Cryptography PrimerSecrets and Promises, pp. 157 - 170Publisher: Cambridge University PressPrint publication year: 2014