Published by the Department of Computer Science, The University of Chicago.

Abstract

Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned.
We present an optimal security bound for quantum oblivious transfer protocols, in the information theoretic setting, under a natural and {arguably} demanding definition of what it means for Alice to cheat.
Our lower bound is a smooth tradeoff between the probability $P^*_{Bob}$ with which Bob can guess Alice's bit choice and the probability $P^*_{Alice}$ with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty.
We prove that $2 P^*_{Bob} + P^*_{Alice} \geq 2$ in any quantum protocol for oblivious transfer, from which it follows that one of the two parties must be able to cheat with probability at least $2/3$.
We prove that this bound is optimal by exhibiting a family of protocols whose cheating probabilities can be made arbitrarily close to any point on the tradeoff curve.

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Submitted September 29, 2014, revised August 30, 2016, published September 16, 2016.

DOI: 10.4086/cjtcs.2016.013
© Andreé Chailloux, Gus Gutoski and Jamie Sikora
Licensed under a Creative Commons Attribution License




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