Exponential separations for one-way quantum communication complexity, with applications to cryptography

We give an exponential separation between one-way quantum and classical communication protocols for two partial Boolean functions, both of which are variants of the Boolean Hidden Matching Problem of Bar-Yossef et al. Earlier such an exponential separation was known only for a relational version of the Hidden Matching Problem. Our proofs use the Fourier coefficients inequality of Kahn, Kalai, and Linial. We also give a number of applications of this separation. In particular, we provide the first example in the bounded storage model of cryptography where the key is secure if the adversary has a certain amount of classical storage, but is completely insecure if he has a similar (or even much smaller) amount of quantum storage. Moreover, in the setting of privacy amplification, we show that there exist extractors which yield a classically secure key, but are insecure against a quantum adversary. Supported in part by Canada's NSERC. Supported in part by ACI S?ecurit?e Informatique...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, Ronald de Wolf
• Keywords: Algorithms, Hidden Matching Problem, Integrated Project Qubit, Project Qubit Applications, STOC 2007