Cryptography Reference
In-Depth Information
chapter 7
Practical Quantum
Cryptography: Secrecy
Capacity and Privacy
Amplification
G. Gilbert, M. Hamrick, and F.J. Thayer
Quantum Information Science Group, MITRE
Contents
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.2 Presentation of the Effective Secrecy Capacity . . . . . . . . . . . . . . . . . . . . . . . 147
7.2.1 Secrecy Capacity for Keys of Finite Length . . . . . . . . . . . . . . . . . . 153
7.3 Privacy Amplification: Pointwise Bounds and Average Bounds . . . . 154
7.3.1 Privacy Amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.3.2 Practical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.3.3 Application of Pointwise Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Abstract
Quantum cryptography has attracted much attention because of its potential
for providing secret communications that cannot be decrypted by any amount
of computational effort. Here we provide an analysis of the BB84 quantum
cryptographic protocol that simultaneously takes into account and presents
the full set of analytical expressions for effects due to the presence of pulses
containing multiple photons in the attenuated output of the laser, the finite
length of individual blocks of key material, losses due to error correction,
privacy amplification, and authentication, errors in polarization detection,
the efficiency of the detectors, and attenuation processes in the transmission
Research supported under MITRE Technology program Grant 51MSR 211.
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