Indistinguishability Obfuscation of Null Quantum Circuits and Applications

TL;DR

This paper introduces a new form of quantum obfuscation for null quantum circuits, leveraging assumptions like LWE, and demonstrates its applications in creating novel cryptographic primitives such as witness encryption and attribute-based encryption for quantum complexity classes.

Contribution

It presents the first construction of indistinguishability obfuscation for null quantum circuits and applies it to develop new cryptographic primitives for quantum computing.

Findings

First witness encryption scheme for QMA

First publicly verifiable NIZK for QMA

First attribute-based encryption scheme for BQP

Abstract

We study the notion of indistinguishability obfuscation for null quantum circuits (quantum null-iO). We present a construction assuming: - The quantum hardness of learning with errors (LWE). - Post-quantum indistinguishability obfuscation for classical circuits. - A notion of ''dual-mode'' classical verification of quantum computation (CVQC). We give evidence that our notion of dual-mode CVQC exists by proposing a scheme that is secure assuming LWE in the quantum random oracle model (QROM). Then we show how quantum null-iO enables a series of new cryptographic primitives that, prior to our work, were unknown to exist even making heuristic assumptions. Among others, we obtain the first witness encryption scheme for QMA, the first publicly verifiable non-interactive zero-knowledge (NIZK) scheme for QMA, and the first attribute-based encryption (ABE) scheme for BQP.