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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2010.157
URN: urn:nbn:de:0030-drops-28613
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2861/
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Chailloux, André ; Kerenidis, Iordanis ; Sikora, Jamie

Lower bounds for Quantum Oblivious Transfer

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Abstract

Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players' cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than $1/2$. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a coin flipping protocol and conclude by using Kitaev's coin flipping lower bound. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most $3/4$. Last, we extend Kitaev's semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.

BibTeX - Entry

@InProceedings{chailloux_et_al:LIPIcs:2010:2861,
  author =	{Andr{\'e} Chailloux and Iordanis Kerenidis and Jamie Sikora},
  title =	{{Lower bounds for Quantum Oblivious Transfer}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{157--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Kamal Lodaya and Meena Mahajan},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2861},
  URN =		{urn:nbn:de:0030-drops-28613},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2010.157},
  annote =	{Keywords: quantum oblivious transfer, coin flipping protocol, semidefinite programming}
}

Keywords: quantum oblivious transfer, coin flipping protocol, semidefinite programming
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)
Issue Date: 2010
Date of publication: 14.12.2010


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