Distributional VBB security with quantum auxiliary input for conjunction obfuscation

Establish that the conjunction obfuscator of Bartusek, Lepoint, Ma, and Zhandry (2019) satisfies distributional virtual black-box security when the auxiliary input provided to the adversary is a polynomial-size quantum state and both the adversary and the simulator are quantum polynomial-time algorithms.

Background

The scheme’s classical-query security proof relies on distributional VBB security for conjunction obfuscation. The available result for Bartusek et al.’s obfuscator guarantees distributional VBB with classical auxiliary input under the LPN assumption. However, the simulation argument in this work motivates a setting where the adversary may hold quantum side information derived from the Wiesner-state component, necessitating a version of the security definition that allows quantum auxiliary input.

Given that the conjunction obfuscator is built from post-quantum assumptions (LPN) and is used in a setting where the accepting input has high entropy conditioned on auxiliary information, the paper formulates a conjecture that the distributional VBB guarantee should extend to quantum auxiliary input with QPT adversary and simulator.