Paper 2020/1469

Succinct Blind Quantum Computation Using a Random Oracle

Jiayu Zhang

Abstract

In the universal blind quantum computation problem, a client wants to make use of a single quantum server to evaluate $C|0\rangle$ where $C$ is an arbitrary quantum circuit while keeping $C$ secret. The client's goal is to use as few resources as possible. This problem, first raised by Broadbent, Fitzsimons and Kashefi [FOCS09, arXiv:0807.4154], has become fundamental to the study of quantum cryptography, not only because of its own importance, but also because it provides a testbed for new techniques that can be later applied to related problems (for example, quantum computation verification). Known protocols on this problem are mainly either information-theoretically (IT) secure or based on trapdoor assumptions (public key encryptions). In this paper we study how the availability of symmetric-key primitives, modeled by a random oracle, changes the complexity of universal blind quantum computation. We give a new universal blind quantum computation protocol. Similar to previous works on IT-secure protocols (for example, BFK [FOCS09, arXiv:0807.4154]), our protocol can be divided into two phases. In the first phase the client prepares some quantum gadgets with relatively simple quantum gates and sends them to the server, and in the second phase the client is entirely classical -- it does not even need quantum storage. Crucially, the protocol's first phase is succinct, that is, its complexity is independent of the circuit size. Given the security parameter $\kappa$, its complexity is only a fixed polynomial of $\kappa$, and can be used to evaluate any circuit (or several circuits) of size up to a subexponential of $\kappa$. In contrast, known schemes either require the client to perform quantum computations that scale with the size of the circuit [FOCS09, arXiv:0807.4154], or require trapdoor assumptions [Mahadev, FOCS18, arXiv:1708.02130].

Note: Contain some further revisions compared to arXiv: 2004.12621v10. Changes include some typo fixes, font change and notation simplification compared to the arXiv v10 version; add one writing convention subsection to section 2 to explain the organization better and provide some pointer for very common notations; change n+1 to 1+n and 1+\log\kappa to \log\kappa+1 to be more consistent with the protocol and security; fix more typos. See cs-people.bu.edu/jyz16 for the most recent version (with some typo fixes that do not have in print/arXiv version).