Non-Local Box Complexity and Secure Function Evaluation

ABSTRACT. A non-local box is an abstract device into which Alice and Bob input bits x and y respectively and receive outputs a and b respectively, where a, b are uniformly distributed and a ⊕ b = x ∧ y. Such boxes have been central to the study of quantum or generalized non-locality as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in order to compute a Boolean function f. We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We show that non-local box complexity has interesting applications to classical cryptography, in particular to secure function evaluation, and study the question posed by Beimel and Malkin [4] of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function f. We show that this question is related to the non-local box complexity of the function and conclu...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Marc Kaplan, Iordanis Kerenidis, Sophie Laplante, Jérémie Roland
• Keywords: FSTTCS 2009, Non-local Box, Non-local Box Complexity, Non-local Boxes, Theoretical Computer Science