Security of quantum bit-string generation

Journal Article · Mon Nov 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.052310· OSTI ID:20646186

Barrett, Jonathan; Massar, Serge ^[1]

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1. Physique Theorique, C.P. 225, Universite Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels (Belgium)

We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.

• OSTI ID: 20646186
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CORRELATIONS
ENERGY LEVELS
ENTROPY
INFORMATION THEORY
NOISE
QUANTUM MECHANICS
RANDOMNESS
SECRECY PROTECTION