Indistinguishability Obfuscation of Null Quantum Circuits and Applications
This work addresses foundational challenges in quantum cryptography by enabling advanced privacy and security protocols, representing a significant theoretical advancement rather than an incremental improvement.
The paper tackles the problem of constructing indistinguishability obfuscation for null quantum circuits, achieving this under assumptions including quantum LWE and post-quantum classical iO, and enabling new cryptographic primitives such as the first witness encryption for QMA and ABE for BQP.
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.