Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits
Abstract
Virtual black-box obfuscation is a strong cryptographic primitive: it encrypts a circuit while maintaining its full input/output functionality. A remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator that obfuscates classical circuits into classical circuits cannot exist. A promising direction that circumvents this impossibility result is to obfuscate classical circuits into quantum states, which would potentially be better capable of hiding information about the obfuscated circuit. We show that, under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant of virtual black-box obfuscation of classical circuits is generally impossible. On the way, we show that under the presence of dependent classical auxiliary input, even the small class of classical point functions cannot be quantum virtual black-box obfuscated.
Keywords
Cite
@article{arxiv.2005.06432,
title = {Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits},
author = {Gorjan Alagic and Zvika Brakerski and Yfke Dulek and Christian Schaffner},
journal= {arXiv preprint arXiv:2005.06432},
year = {2020}
}
Comments
v2: Add the notion of decomposable public keys, which allows our impossibility to hold without assuming circular security for QFHE. We also fix an auxiliary lemma (2.9 in v2) where a square root was missing (this does not influence the main result)