Book contents
- Frontmatter
- Contents
- Foreword
- Preface
- Acknowledgments
- 1 Introduction
- 2 Classical cryptography
- 3 Information theory
- 4 Quantum information theory
- 5 Cryptosystems based on quantum key distribution
- 6 General results on secret-key distillation
- 7 Privacy amplification using hash functions
- 8 Reconciliation
- 9 Non-binary reconciliation
- 10 The BB84 protocol
- 11 Protocols with continuous variables
- 12 Security analysis of quantum key distribution
- Appendix symbols and abbreviations
- Bibliography
- Index
8 - Reconciliation
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Foreword
- Preface
- Acknowledgments
- 1 Introduction
- 2 Classical cryptography
- 3 Information theory
- 4 Quantum information theory
- 5 Cryptosystems based on quantum key distribution
- 6 General results on secret-key distillation
- 7 Privacy amplification using hash functions
- 8 Reconciliation
- 9 Non-binary reconciliation
- 10 The BB84 protocol
- 11 Protocols with continuous variables
- 12 Security analysis of quantum key distribution
- Appendix symbols and abbreviations
- Bibliography
- Index
Summary
Reconciliation is the technique needed to ensure that Claude's and Dominique's key elements are equal. Starting from outcomes of the random variables X and Y, they wish to agree on an equal string Ψ.
In this chapter, I will first give some general properties and then overview and introduce several classes of reconciliation techniques.
Problem description
The goal of the legitimate parties is to distill a secret key, i.e., to end up with a shared binary string that is unknown to Eve. We assume as a convention that Claude's outcomes of X will determine the shared key K. The common string Ψ before privacy amplification can thus be expressed as a function Ψ(X).
Reconciliation consists in exchanging messages over the public classical authenticated channel, collectively denoted M, so that Dominique can recover Ψ from M and the outcomes of Y. If we denote as x1…l a vector of l independent outcomes of X, the string can be compressed to obtain about lH(Ψ(X)) common uniform bits.
As explained in Chapter 6, the impact of reconciliation on privacy amplification is a decrease of |M| bits in the key length, where |M| is the number of bits exchanged during reconciliation.
Our goal is thus to maximize lH(Ψ(X))-|M|, or if Ψ is given, to minimize the number |M| of disclosed bits.
Characteristics of reconciliation protocols
Before dealing with the details of reconciliation, let us here review some of its characteristics.
First, reconciliation can be either one-way or interactive. The first case is obviously only possible with one-way secret-key distillation, as information is sent only from Claude to Dominique.
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- Quantum Cryptography and Secret-Key Distillation , pp. 113 - 140Publisher: Cambridge University PressPrint publication year: 2006