dorsal/arxiv
View SchemaSecurity of Quantum Bit-String Generation
| Authors | Jonathan Barrett, Serge Massar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408120 |
| URL | https://arxiv.org/abs/quant-ph/0408120 |
| DOI | 10.1103/PhysRevA.70.052310 |
| Journal | Phys. Rev. A 70, 052310 (2004) |
Abstract
We consider the cryptographic task of bit-string generation. This is a generalisation 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 {\bf 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 analysed in this paper has been performed and is reported elsewhere.
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"abstract": "We consider the cryptographic task of bit-string generation. This is a\ngeneralisation of coin tossing in which two mistrustful parties wish to\ngenerate a string of random bits such that an honest party can be sure that the\nother cannot have biased the string too much. We consider a quantum protocol\nfor this task, originally introduced in Phys. Rev. A {\\bf 69}, 022322 (2004),\nthat is feasible with present day technology. We introduce security conditions\nbased on the average bias of the bits and the Shannon entropy of the string.\nFor each, we prove rigorous security bounds for this protocol in both noiseless\nand noisy conditions under the most general attacks allowed by quantum\nmechanics. Roughly speaking, in the absence of noise, a cheater can only bias\nsignificantly a vanishing fraction of the bits, whereas in the presence of\nnoise, a cheater can bias a constant fraction, with this fraction depending\nquantitatively on the level of noise. We also discuss classical protocols for\nthe same task, deriving upper bounds on how well a classical protocol can\nperform. This enables the determination of how much noise the quantum protocol\ncan tolerate while still outperforming classical protocols. We raise several\nconjectures concerning both quantum and classical possibilities for large n\ncryptography. An experiment corresponding to the scheme analysed in this paper\nhas been performed and is reported elsewhere.",
"arxiv_id": "quant-ph/0408120",
"authors": [
"Jonathan Barrett",
"Serge Massar"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.052310",
"journal_ref": "Phys. Rev. A 70, 052310 (2004)",
"title": "Security of Quantum Bit-String Generation",
"url": "https://arxiv.org/abs/quant-ph/0408120"
},
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