PhD Proposal: Separating Quantum Black-Box Security Reductions for SNARGs from Falsifiable Assumptions

https://umd.zoom.us/j/4408046564
A reduction establishes the security of a cryptographic primitive by ruling out the existence of an adversary. A meta-reduction, on the other hand, rules out the existence of a class of reductions, thus posing an inherent limitation when proving security. In their seminal work, Gentry and Wichs (STOC'11) gave a meta-reduction for succinct non-interactive arguments from all falsifiable assumptions. Their work assumes the reduction to be classical, thus not ruling out a quantum reduction. We show that their impossibility result also extends to quantum reductions, which can invoke the adversary on a superposition of inputs.