Quantum garbled circuits

Abstract

In classical computing, garbled circuits (and their generalization known as randomized encodings) are a versatile cryptographic tool with many applications such as secure multiparty computation, delegated computation, depth-reduction of cryptographic primitives, complexity lower-bounds, and more. Quantum analogues of garbled circuits were not known prior to this work. In this work, we introduce a definition of quantum randomized encodings and present a construction which allows us to efficiently garble any quantum circuit, assuming the existence of quantum-secure one-way functions. Our construction has comparable properties to the best known classical garbling schemes. We can also achieve perfect information-theoretic security albeit with blowup in the size of the garbled circuits. We believe that quantum garbled circuits and quantum randomized encodings can be an instrumental concept and building block for quantum computation and in particular quantum cryptography. We present some applications, including a conceptually-simple zero-knowledge proof system for QMA, a protocol for private simultaneous messages, functional encryption, and more.