dorsal/arxiv
View SchemaNew binding-concealing trade-offs for quantum string commitment
| Authors | Rahul Jain |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506001 |
| URL | https://arxiv.org/abs/quant-ph/0506001 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
String commitment schemes are similar to the well studied bit commitment schemes in cryptography with the difference that the committing party, say Alice, is supposed to commit a long string instead of a single bit, to another party say Bob. Similar to bit commitment schemes, such schemes are supposed to be binding, i.e Alice cannot change her choice after committing, and concealing i.e. Bob cannot find Alice's committed string before Alice reveals it. Ideal commitment schemes are known to be impossible. Even if some degrees of cheating is allowed, Buhrman, Christandl, Hayden, Lo and Wehner (quant-ph/0504078) have recently shown that there are some binding-concealing trade-offs that any quantum string commitment scheme (QSC) must follow. They showed trade-offs both in the scenario of single execution of the protocol and in the asymptotic regime of sufficiently large number of parallel executions of the protocol. We present here new trade-offs in the scenario of single execution of a QSC protocol. Our trade-offs also immediately imply the trade-off shown by Buhrman et al. in the asymptotic regime. We show our results by making a central use of an important information theoretic tool called the substate theorem due to Jain, Radhakrishnan and Sen. Our techniques are quite different from that of Buhrman et al. and may be of independent interest.
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"abstract": "String commitment schemes are similar to the well studied bit commitment\nschemes in cryptography with the difference that the committing party, say\nAlice, is supposed to commit a long string instead of a single bit, to another\nparty say Bob. Similar to bit commitment schemes, such schemes are supposed to\nbe binding, i.e Alice cannot change her choice after committing, and concealing\ni.e. Bob cannot find Alice\u0027s committed string before Alice reveals it.\n Ideal commitment schemes are known to be impossible. Even if some degrees of\ncheating is allowed, Buhrman, Christandl, Hayden, Lo and Wehner\n(quant-ph/0504078) have recently shown that there are some binding-concealing\ntrade-offs that any quantum string commitment scheme (QSC) must follow. They\nshowed trade-offs both in the scenario of single execution of the protocol and\nin the asymptotic regime of sufficiently large number of parallel executions of\nthe protocol.\n We present here new trade-offs in the scenario of single execution of a QSC\nprotocol. Our trade-offs also immediately imply the trade-off shown by Buhrman\net al. in the asymptotic regime. We show our results by making a central use of\nan important information theoretic tool called the substate theorem due to\nJain, Radhakrishnan and Sen. Our techniques are quite different from that of\nBuhrman et al. and may be of independent interest.",
"arxiv_id": "quant-ph/0506001",
"authors": [
"Rahul Jain"
],
"categories": [
"quant-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "New binding-concealing trade-offs for quantum string commitment",
"url": "https://arxiv.org/abs/quant-ph/0506001"
},
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