文章基本信息

标题：Lower bounds for Quantum Oblivious Transfer
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作者：Andr{\'e} Chailloux ; Iordanis Kerenidis ; Jamie Sikora 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2010
卷号：8
页码：157-168
DOI：10.4230/LIPIcs.FSTTCS.2010.157
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：quantum oblivious transfer; coin flipping protocol; semidefinite programming