dorsal/arxiv
View SchemaA Tight High-Order Entropic Quantum Uncertainty Relation With Applications
| Authors | Ivan B. Damgaard, Serge Fehr, Renato Renner, Louis Salvail, Christian Schaffner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612014 |
| URL | https://arxiv.org/abs/quant-ph/0612014 |
| Journal | full version of CRYPTO 2007, LNCS 4622 |
Abstract
We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded quantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.
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"abstract": "We derive a new entropic quantum uncertainty relation involving min-entropy.\nThe relation is tight and can be applied in various quantum-cryptographic\nsettings.\n Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit\nCommitment are presented and the uncertainty relation is used to prove the\nsecurity of these protocols in the bounded quantum-storage model according to\nnew strong security definitions.\n As another application, we consider the realistic setting of Quantum Key\nDistribution (QKD) against quantum-memory-bounded eavesdroppers. The\nuncertainty relation allows to prove the security of QKD protocols in this\nsetting while tolerating considerably higher error rates compared to the\nstandard model with unbounded adversaries. For instance, for the six-state\nprotocol with one-way communication, a bit-flip error rate of up to 17% can be\ntolerated (compared to 13% in the standard model).\n Our uncertainty relation also yields a lower bound on the min-entropy key\nuncertainty against known-plaintext attacks when quantum ciphers are composed.\nPreviously, the key uncertainty of these ciphers was only known with respect to\nShannon entropy.",
"arxiv_id": "quant-ph/0612014",
"authors": [
"Ivan B. Damgaard",
"Serge Fehr",
"Renato Renner",
"Louis Salvail",
"Christian Schaffner"
],
"categories": [
"quant-ph",
"cs.CR"
],
"journal_ref": "full version of CRYPTO 2007, LNCS 4622",
"title": "A Tight High-Order Entropic Quantum Uncertainty Relation With Applications",
"url": "https://arxiv.org/abs/quant-ph/0612014"
},
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