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
9 - Some Uses of Perfect Secrecy
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
It should be clear from Chapter 6 that perfect secrecy is useful in encryption. However, the idea can be useful in constructing other cryptographic building blocks. In this chapter, we discuss two examples.
Secret-sharing and perfect secrecy
The idea of perfect secrecy can be used to cryptographically “split” a secret into two parts. Each part can be given to a different person. Either person on her own learns nothing about the secret by receiving her part; together the two people can reconstruct the secret.
Imagine, for example, that the bank president wants to give her two vice presidents the combination to the safe (in case the safe needs to be opened on a day the president is incommunicado), but wants them to have only joint access. She can use secret-sharing to split the combination between the two vice-presidents.
Let f (plain, key) be the encryption function for a perfectly secure cryptosystem. We will use this cryptosystem to split the secret. The choice of cryptosystem is not intended to be secret; we assume this choice is known to all. The choice of cryptosystem restricts the choice of secret to be shared; the secret must be one of the cryptosystem's possible plaintexts.
- Type
- Chapter
- Information
- A Cryptography PrimerSecrets and Promises, pp. 106 - 117Publisher: Cambridge University PressPrint publication year: 2014