Paper 2021/421

Candidate Obfuscation of Null Quantum Circuits and Witness Encryption for QMA

James Bartusek and Giulio Malavolta

Abstract

We present a construction of indistinguishability obfuscation for null quantum circuits (null-iO) with respect to a classical oracle, assuming the quantum hardness of the learning with errors (LWE) problem. Heuristically instantiating the classical oracle with quantum-secure indistinguishability obfuscation for classical circuits gives us the first candidate construction of null-iO for quantum circuits. This scheme establishes the feasibility of a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Specifically, we obtain (in some cases additionally assuming indistinguishability obfuscation for classical circuits): * A witness encryption (WE) scheme for QMA. * A publicly-verifiable non-interactive zero-knowledge (NIZK) argument for QMA. * A two-message publicly-verifiable witness-indistinguishable (ZAPR) argument for QMA. * An attribute-based encryption (ABE) scheme for BQP. * A secret sharing scheme for monotone QMA.