### Volume 2016

#### Optimal bounds for semi-honest quantum oblivious transfer

André Chailloux
INRIA Paris, SECRET Project Team
Paris, France.
andre.chailloux AT inria DOT fr

Gus Gutoski
Perimeter Institute for Theoretical Physics
ggutoski AT perimeterinstitute DOT ca

and

Jamie Sikora
Centre for Quantum Technologies
National University of Singapore
Singapore.
cqtjwjs AT nus DOT edu DOT sg

September 16, 2016

#### 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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